{"version":"1.0.0","segments":[{"startTime":4.985,"endTime":6.765,"body":"My name is Rag Rao, right?"},{"startTime":6.865,"endTime":10.66,"body":"I'm the Sir Evan, the Rothchild professor of finance at University of Cambridge, most of"},{"startTime":10.66,"endTime":12.685,"body":"the Gresham professor business here at Gresham College."},{"startTime":13.065,"endTime":16.047,"body":"As a lot of people know this already because I see some familiar faces around"},{"startTime":16.047,"endTime":16.445,"body":"the room."},{"startTime":16.985,"endTime":21.17,"body":"Um, this is the second in my series of lectures this year, which is on"},{"startTime":21.17,"endTime":22.845,"body":"the big ideas of finance, right?"},{"startTime":23.145,"endTime":27.053,"body":"So what I'm gonna talk about today is the second of the big ideas, and"},{"startTime":27.053,"endTime":27.314,"body":"this is one of the first idea we're gonna talk about that actually won a"},{"startTime":27.314,"endTime":32.005,"body":"Nobel Prize in economics."},{"startTime":32.265,"endTime":35.82,"body":"So there will be some maths involved here, but I'll try to make it as"},{"startTime":35.82,"endTime":37.005,"body":"intuitive as I can, right?"},{"startTime":37.005,"endTime":38.645,"body":"Especially late evening."},{"startTime":38.945,"endTime":42.205,"body":"You don't wanna get hit with a whole blizzard of equations."},{"startTime":42.265,"endTime":43.805,"body":"So let's try to make it intuitive."},{"startTime":44.625,"endTime":50.572,"body":"So all these, um, ideas are actually in my book, which is Short Introduction to"},{"startTime":50.572,"endTime":51.365,"body":"Corporate Finance."},{"startTime":51.785,"endTime":54.685,"body":"Six chapters tells you one chapter per idea."},{"startTime":54.785,"endTime":57.925,"body":"So if you want to go back, read all about it, that's it."},{"startTime":57.925,"endTime":60.245,"body":"It's also in Chinese, if you prefer to read it in Chinese."},{"startTime":61.795,"endTime":62.085,"body":"Okay?"},{"startTime":62.145,"endTime":63.805,"body":"So what are these six basic ideas?"},{"startTime":64.425,"endTime":69.175,"body":"The first idea is the idea I talked about last time, the concept of net"},{"startTime":69.175,"endTime":70.125,"body":"present value, right?"},{"startTime":70.665,"endTime":74.525,"body":"But net present value as we see today, requires a discount rate."},{"startTime":74.645,"endTime":75.965,"body":"Requires an interest rate."},{"startTime":76.385,"endTime":81.943,"body":"So that is a topic of today's lecture, is portfolio theory and the capital Asset"},{"startTime":81.943,"endTime":82.685,"body":"pricing model."},{"startTime":83.225,"endTime":88.043,"body":"And two people, Harry Markowitz and William Sharp got a Nobel Prize for this in"},{"startTime":88.043,"endTime":88.365,"body":"1990."},{"startTime":89.385,"endTime":94.685,"body":"The other five, the other four ideas, capital Structure Theory, also won a Nobel Prize"},{"startTime":94.685,"endTime":96.805,"body":"for Ian Miller in separate years."},{"startTime":97.385,"endTime":103.325,"body":"Um, option pricing got a Nobel Prize for Shoals and Merton in 1997."},{"startTime":104.005,"endTime":109.965,"body":"Asymetic information, three people, Olof, Spence, and Sitz won a Nobel Prize in 2001."},{"startTime":110.265,"endTime":114.751,"body":"And finally the last topic, which will be in June next year, is a bit"},{"startTime":114.751,"endTime":115.05,"body":"confusing because several people won the Nobel Prize in this area, including people who said"},{"startTime":115.05,"endTime":123.125,"body":"completely the opposite things, but won the Nobel Prize in the same year."},{"startTime":123.185,"endTime":126.803,"body":"That's far and Shiller in particular, but we'll come back to that in June next"},{"startTime":126.803,"endTime":127.045,"body":"year."},{"startTime":128.425,"endTime":131.285,"body":"So what is finance all about?"},{"startTime":131.615,"endTime":131.965,"body":"Right?"},{"startTime":132.425,"endTime":134.605,"body":"At its core, finance is very simple."},{"startTime":135.355,"endTime":137.245,"body":"It's basically a set of promises."},{"startTime":137.355,"endTime":142.636,"body":"Basically, somebody is saying, you know what, gimme some money now and in return I'll"},{"startTime":142.636,"endTime":147.565,"body":"give you some fantastically large amount of money at some point in the future."},{"startTime":148.385,"endTime":153.168,"body":"The question which we have to answer as a finance person is, what are these"},{"startTime":153.168,"endTime":154.125,"body":"promises worth, right?"},{"startTime":154.265,"endTime":158.828,"body":"How much would you pay somebody who's promising to pay you a huge amount of"},{"startTime":158.828,"endTime":160.045,"body":"money in the future?"},{"startTime":160.825,"endTime":164.781,"body":"And last time you saw that, the answer to this question was about net present"},{"startTime":164.781,"endTime":165.045,"body":"value."},{"startTime":165.195,"endTime":169.677,"body":"That means we have to compute the present value of those future cash flows to"},{"startTime":169.677,"endTime":172.965,"body":"today and compared to the amount we're supposed to spend today."},{"startTime":173.465,"endTime":177.901,"body":"So if somebody says, I'll give you $500, five years from now, the question is"},{"startTime":177.901,"endTime":179.085,"body":"what's the value today?"},{"startTime":179.225,"endTime":183.165,"body":"How much are we willing to pay for that $500 worth today?"},{"startTime":184.265,"endTime":187.445,"body":"And unfortunately to get that, we need one equation."},{"startTime":187.705,"endTime":190.045,"body":"And that is the basic equation in finance."},{"startTime":190.475,"endTime":192.165,"body":"That concept of net present value."},{"startTime":192.745,"endTime":194.125,"body":"So what is that equation?"},{"startTime":194.825,"endTime":199.218,"body":"The equation is straightforward, it looks complicated, but all it's saying is the present value"},{"startTime":199.218,"endTime":199.511,"body":"of a bunch of cash flows noted by C one, C two, and C three"},{"startTime":199.511,"endTime":199.804,"body":"and so on, is just divided by one plus one plus squared, one plus of"},{"startTime":199.804,"endTime":208.885,"body":"the power three."},{"startTime":209.265,"endTime":214.326,"body":"We discussed that in the NPV, um, NPV lecture, but the I see ideas, each"},{"startTime":214.326,"endTime":214.663,"body":"of those cash flows in the future is worth c divided by one plus R"},{"startTime":214.663,"endTime":219.725,"body":"today."},{"startTime":220.075,"endTime":220.365,"body":"Okay?"},{"startTime":220.945,"endTime":225.233,"body":"The problem which we didn't answer there is that where does that interest rate come"},{"startTime":225.233,"endTime":225.805,"body":"from, right?"},{"startTime":226.385,"endTime":231.53,"body":"We have everything we need except we don't know what that discount rate, what's the"},{"startTime":231.53,"endTime":233.245,"body":"appropriate R In that equation?"},{"startTime":233.625,"endTime":235.485,"body":"We can figure out what the cash flows are."},{"startTime":235.745,"endTime":239.965,"body":"For example, if you're valuing a company, the cash flows are the earnings."},{"startTime":240.305,"endTime":242.885,"body":"If you're valuing a stock, the cash flows are the dividends."},{"startTime":243.145,"endTime":246.913,"body":"If you're valuing a valuing a bond, you're getting interest payments and the final phase"},{"startTime":246.913,"endTime":247.165,"body":"value."},{"startTime":247.265,"endTime":248.925,"body":"So those are the cash flows."},{"startTime":248.925,"endTime":252.412,"body":"You know what the cash flows are, but how do we figure out the interest"},{"startTime":252.412,"endTime":252.645,"body":"rate?"},{"startTime":252.745,"endTime":254.525,"body":"That's the subject of today's lecture."},{"startTime":256.315,"endTime":256.605,"body":"Okay?"},{"startTime":256.704,"endTime":261.565,"body":"So how do we think about this?"},{"startTime":262.195,"endTime":266.216,"body":"Well, somebody comes to you and says, I want you to invest in my company,"},{"startTime":266.216,"endTime":266.485,"body":"right?"},{"startTime":266.755,"endTime":270.907,"body":"What you are thinking about is, okay, if I don't invest in the company, what"},{"startTime":270.907,"endTime":272.845,"body":"else can I do with my money?"},{"startTime":273.695,"endTime":274.045,"body":"Right?"},{"startTime":274.355,"endTime":280.363,"body":"What you want is to find out what is the opportunity cost of investing in"},{"startTime":280.363,"endTime":281.565,"body":"this particular asset."},{"startTime":281.565,"endTime":285.085,"body":"Because the moment you invest in this guy's company, the money's locked up."},{"startTime":285.145,"endTime":287.125,"body":"You can't take it out and use it for something else."},{"startTime":287.225,"endTime":290.656,"body":"You can't spend it on a good restaurant, you can't spend it on a movie,"},{"startTime":290.656,"endTime":290.885,"body":"right?"},{"startTime":290.885,"endTime":292.525,"body":"It's locked up in this guy's investment."},{"startTime":293.025,"endTime":296.445,"body":"So the question is, what is my next best opportunity?"},{"startTime":296.865,"endTime":299.805,"body":"If I don't invest in this company, where do I put my money?"},{"startTime":300.905,"endTime":304.245,"body":"But of course, that opportunity has to be equivalent, right?"},{"startTime":304.245,"endTime":308.445,"body":"You can't say, okay, invest in my high tech company."},{"startTime":308.665,"endTime":311.285,"body":"The alternative is put my money in Barclays, right?"},{"startTime":311.505,"endTime":313.325,"body":"The interest rate at Barclays is pretty low."},{"startTime":313.665,"endTime":318.69,"body":"And so it's definitely not comparable to anything which you might get from investing, for"},{"startTime":318.69,"endTime":320.365,"body":"example, in open ai, right?"},{"startTime":321.065,"endTime":326.227,"body":"So that means the opportunity should be equivalent in terms of risk to what the"},{"startTime":326.227,"endTime":329.325,"body":"actual asset is you're being asked to invest in."},{"startTime":329.995,"endTime":330.285,"body":"Okay?"},{"startTime":330.785,"endTime":333.725,"body":"But then the question becomes what is risk, right?"},{"startTime":333.865,"endTime":335.005,"body":"How do we measure risk?"},{"startTime":336.465,"endTime":339.325,"body":"So does it depend on how risk averse you are?"},{"startTime":339.735,"endTime":340.085,"body":"Right?"},{"startTime":340.085,"endTime":341.965,"body":"Maybe someone who's risk averse says, you know what?"},{"startTime":341.965,"endTime":343.085,"body":"This is extremely risky."},{"startTime":343.285,"endTime":346.945,"body":"I don't want to invest in this, so I'm not willing to pay very much"},{"startTime":346.945,"endTime":348.165,"body":"for this very risky investment."},{"startTime":349.745,"endTime":354.005,"body":"Or does it, if you hate risk, for example, will you pay less?"},{"startTime":354.195,"endTime":359.77,"body":"That means, in other words, will your discount rate be higher than someone who doesn't"},{"startTime":359.77,"endTime":360.885,"body":"care about risk?"},{"startTime":361.145,"endTime":365.66,"body":"So basically, someone who doesn't care about risk will say, I'm willing to pay more"},{"startTime":365.66,"endTime":367.165,"body":"for this highly risky investment."},{"startTime":367.235,"endTime":370.565,"body":"Someone who hates risk says, I'm not willing to pay very much for this investment."},{"startTime":371.025,"endTime":376.47,"body":"So how do you decide what is the right level of the opportunity cost for"},{"startTime":376.47,"endTime":378.285,"body":"investing in a particular asset?"},{"startTime":379.115,"endTime":385.125,"body":"Alright, so let's ask ourselves, first question is, what does history tell us about opportunities?"},{"startTime":386.025,"endTime":389.605,"body":"So this graph here is taken from Eon and Synco fell."},{"startTime":389.635,"endTime":394.165,"body":"Basically they've been calculating every year, what happens if you invest money over time?"},{"startTime":394.505,"endTime":400.021,"body":"And so what you have here, you go back to 1926 and invest $1 in"},{"startTime":400.021,"endTime":401.125,"body":"small cap stocks."},{"startTime":401.125,"endTime":408.102,"body":"Basically small companies by the year 2022 and end of last year, you'd end up"},{"startTime":408.102,"endTime":413.685,"body":"with $49,000 today, $1 in 1926, you'd end up with $49,000 today."},{"startTime":414.195,"endTime":421.701,"body":"However, if you invest in large cap stocks, big companies, companies like gm, Tesco, large"},{"startTime":421.701,"endTime":425.205,"body":"companies, you'd end up only with $11,535."},{"startTime":426.185,"endTime":431.837,"body":"If you're invested in long-term government bonds issued by the UK, government issued by, you"},{"startTime":431.837,"endTime":435.605,"body":"know, the US government, whatever, you'd end up with $130."},{"startTime":437.025,"endTime":440.925,"body":"If you had invested in short-term bonds, bonds of less than one year."},{"startTime":441.705,"endTime":445.405,"body":"$1 in 1926 would end up with $22 today."},{"startTime":445.855,"endTime":446.205,"body":"Right?"},{"startTime":446.385,"endTime":454.391,"body":"And finally, inflation, what was worth $1 in 1926 is worth $16 and 58 cents"},{"startTime":454.391,"endTime":454.925,"body":"today."},{"startTime":455.195,"endTime":455.485,"body":"Okay?"},{"startTime":455.785,"endTime":459.005,"body":"So taking this graph, you've all seen this graph."},{"startTime":459.785,"endTime":463.005,"body":"Now imagine you've invented a time machine."},{"startTime":463.425,"endTime":468.259,"body":"You can go back to 1926 and you have the opportunity to talk to your"},{"startTime":468.259,"endTime":471.805,"body":"granddad or your great granddad depending on how old you are."},{"startTime":472.945,"endTime":477.848,"body":"And so your granddad says, you go to your granddad's, introduce yourself and say, look,"},{"startTime":477.848,"endTime":481.445,"body":"I'd like you to take $1 and put it into something."},{"startTime":482.155,"endTime":484.845,"body":"What is that something you will put it into?"},{"startTime":485.135,"endTime":487.165,"body":"Let's go and ask that question."},{"startTime":488.065,"endTime":496.365,"body":"So basically scan that code in and you can vote for any of those opportunities."},{"startTime":497.375,"endTime":498.805,"body":"Which one would you pick?"},{"startTime":498.945,"endTime":509.413,"body":"So small stocks give you 49,000, $52, $1 large cap, 11,535 long-term government bonds, $131,"},{"startTime":509.413,"endTime":512.205,"body":"US treasury bills $22."},{"startTime":513.075,"endTime":514.284,"body":"What would you invest in?"},{"startTime":515.275,"endTime":520.365,"body":"Okay, this, you know, this information, by the way, you know all this, right?"},{"startTime":520.544,"endTime":526.338,"body":"So you've gone back in time, you've gone into the past knowing what you already"},{"startTime":526.338,"endTime":526.725,"body":"know."},{"startTime":536.395,"endTime":537.005,"body":"\u003csilence\u003e"},{"startTime":537.205,"endTime":538.605,"body":"Somebody here is super risk averse."},{"startTime":539.205,"endTime":544.205,"body":"\u003claugh\u003e."},{"startTime":543.605,"endTime":547.43,"body":"I mean, given that they already know this, they're still choosing to invest in treasury"},{"startTime":547.43,"endTime":547.685,"body":"bills."},{"startTime":547.845,"endTime":551.285,"body":"I, I would really like to meet that person after this lecture."},{"startTime":555.125,"endTime":557.685,"body":"\u003claugh\u003e, two people, \u003claugh\u003e, maybe they're online."},{"startTime":557.795,"endTime":561.445,"body":"This is also open to anyone online as well, right?"},{"startTime":562.835,"endTime":568.605,"body":"Okay, so it looks like majority of people would say, yeah, makes sense, right?"},{"startTime":568.905,"endTime":571.445,"body":"So invest in small stocks."},{"startTime":571.825,"endTime":576.885,"body":"$1 in 1926 ends up with $49,052."},{"startTime":576.975,"endTime":579.325,"body":"Today it's almost a no brainer, right?"},{"startTime":579.325,"endTime":584.965,"body":"Knowing what you know, of course the problem is keep that open."},{"startTime":584.965,"endTime":586.605,"body":"By the way, I'll keep asking more questions."},{"startTime":587.385,"endTime":589.975,"body":"Um, the problem is"},{"startTime":592.275,"endTime":599.351,"body":"You've persuaded your granddad to invest in small stocks and then one year later it's"},{"startTime":599.351,"endTime":600.295,"body":"1926, right?"},{"startTime":600.755,"endTime":607.295,"body":"And great depression, his $1 has lost 92% of its value in one year."},{"startTime":608.635,"endTime":610.015,"body":"What's your granddad going to say?"},{"startTime":611.055,"endTime":611.895,"body":"I say my good for nothing."},{"startTime":612.175,"endTime":614.295,"body":"Grandkid came back from the future claims, he knows everything."},{"startTime":614.555,"endTime":615.775,"body":"And I've lost most of my money."},{"startTime":616.405,"endTime":617.935,"body":"What a kid, right?"},{"startTime":618.395,"endTime":620.415,"body":"I'm not, I wish the kid had never been born."},{"startTime":621.435,"endTime":626.403,"body":"So you have to have nerves of steel to say No, hold on, keep, keep"},{"startTime":626.403,"endTime":626.735,"body":"investing."},{"startTime":627.225,"endTime":628.255,"body":"Don't sell."},{"startTime":628.795,"endTime":633.732,"body":"At that point, and you know, eventually it'll get to 49,000, but he's like, I"},{"startTime":633.732,"endTime":636.695,"body":"have lost 92% of my money in one year."},{"startTime":637.885,"endTime":639.055,"body":"He's not gonna be very happy."},{"startTime":639.405,"endTime":639.695,"body":"Okay?"},{"startTime":640.115,"endTime":643.975,"body":"So obviously then the answer depends on how long your horizon is."},{"startTime":644.525,"endTime":644.815,"body":"Okay?"},{"startTime":645.555,"endTime":650.523,"body":"So this graph here shows you what happens if you invest in different types of"},{"startTime":650.523,"endTime":650.855,"body":"assets."},{"startTime":651.435,"endTime":656.19,"body":"If you invest for one year, what you see is there are lots of, so"},{"startTime":656.19,"endTime":656.507,"body":"the red lines there are for a portfolio of small stocks, the blue lines, the"},{"startTime":656.507,"endTime":662.215,"body":"the green line there."},{"startTime":662.215,"endTime":664.055,"body":"The blue line is the s and p 500."},{"startTime":664.685,"endTime":667.015,"body":"That is a portfolio of large stocks."},{"startTime":667.685,"endTime":672.044,"body":"Corporate bonds are the yellow line and the green line at the bottom is treasury"},{"startTime":672.044,"endTime":672.335,"body":"bills."},{"startTime":672.585,"endTime":672.935,"body":"Right?"},{"startTime":673.035,"endTime":676.095,"body":"Notice that treasury bills, you almost never lose any money, right?"},{"startTime":676.165,"endTime":676.975,"body":"It's flat."},{"startTime":677.405,"endTime":681.328,"body":"However, if you invest in small stocks for one year, there's a possibility of making"},{"startTime":681.328,"endTime":682.375,"body":"a lot of money."},{"startTime":682.525,"endTime":685.735,"body":"Look at 1927 or 1929, sorry."},{"startTime":685.875,"endTime":689.095,"body":"But there's also a possibility of losing a lot of money, right?"},{"startTime":689.315,"endTime":692.055,"body":"So you can either make a lot of money or lose a lot of money."},{"startTime":692.075,"endTime":696.135,"body":"So over a one year horizon, small stocks are not better, okay?"},{"startTime":696.425,"endTime":697.495,"body":"Large stocks aren't better."},{"startTime":697.495,"endTime":699.015,"body":"Either you can make or lose a lot of money."},{"startTime":700.005,"endTime":701.055,"body":"What about five years?"},{"startTime":701.405,"endTime":706.091,"body":"Well, there are still periods of time when you hold small stocks for a long"},{"startTime":706.091,"endTime":709.215,"body":"period of time that you see that it's better off."},{"startTime":709.605,"endTime":714.18,"body":"With treasury bills, you have to go to 10 years before the numbers start moving"},{"startTime":714.18,"endTime":714.485,"body":"up."},{"startTime":714.785,"endTime":718.507,"body":"So in over here, what you see is there are still periods of time when"},{"startTime":718.507,"endTime":720.245,"body":"you're better off with treasury bills, right?"},{"startTime":720.245,"endTime":723.565,"body":"Even over a 10 year horizon, stocks are not always better."},{"startTime":724.315,"endTime":728.236,"body":"It's only when you go to 20 years that the green line is perpetually below"},{"startTime":728.236,"endTime":729.805,"body":"the red and the blue line."},{"startTime":730.475,"endTime":734.84,"body":"However, it's still, there are points in time when you have been better off in"},{"startTime":734.84,"endTime":736.005,"body":"bonds than in stocks."},{"startTime":737.265,"endTime":742.852,"body":"So clearly the only way you can get that answer invest in small stocks is"},{"startTime":742.852,"endTime":746.205,"body":"if you know the future for 120 years, right?"},{"startTime":746.205,"endTime":750.652,"body":"If you don't, you never know going to know whether you're gonna make money or"},{"startTime":750.652,"endTime":751.245,"body":"not, okay?"},{"startTime":751.945,"endTime":755.728,"body":"In fact, we don't even know what the future is going to be in the"},{"startTime":755.728,"endTime":756.485,"body":"next five years."},{"startTime":756.505,"endTime":762.464,"body":"So if you look at, if the future is gonna be like the past, well"},{"startTime":762.464,"endTime":762.861,"body":"1987, we had a high in October, 1987 where the volatility jumped by 150% on"},{"startTime":762.861,"endTime":771.205,"body":"one day, the 19th of October, 1987."},{"startTime":771.745,"endTime":776.902,"body":"And similarly different crisis, the global financial crisis, the Greek crisis, the Euro crisis, the"},{"startTime":776.902,"endTime":780.685,"body":"C Ovid 19 oil shock, all have these spikes in risk."},{"startTime":781.065,"endTime":782.285,"body":"So how do we predict the future?"},{"startTime":782.345,"endTime":785.925,"body":"We don't even know one year ahead what's going to hit us, okay?"},{"startTime":786.265,"endTime":795.07,"body":"In fact, that particular day, October 19th, 1987, the entire Dow fell by 23% in"},{"startTime":795.07,"endTime":796.245,"body":"one day."},{"startTime":797.745,"endTime":799.125,"body":"So why did that happen?"},{"startTime":801.875,"endTime":802.445,"body":"What do you think?"},{"startTime":802.955,"endTime":803.525,"body":"What do you think?"},{"startTime":805.205,"endTime":806.005,"body":"I have no clue."},{"startTime":807.075,"endTime":809.325,"body":"That is actually a brilliant answer."},{"startTime":809.945,"endTime":812.565,"body":"The answer is nobody has a clue."},{"startTime":813.375,"endTime":813.725,"body":"Right?"},{"startTime":813.895,"endTime":816.845,"body":"45 years later, we still don't know why it happened."},{"startTime":816.845,"endTime":817.805,"body":"Could it happen again tomorrow?"},{"startTime":817.975,"endTime":819.605,"body":"Maybe we don't know."},{"startTime":819.665,"endTime":821.045,"body":"Nobody knows why it happened."},{"startTime":821.715,"endTime":822.005,"body":"Okay?"},{"startTime":822.195,"endTime":825.005,"body":"Biggest loss in history, okay?"},{"startTime":825.185,"endTime":826.725,"body":"The other ones are more explainable."},{"startTime":826.945,"endTime":832.485,"body":"2020 March Covid, uh, October, 1929, great depression."},{"startTime":832.655,"endTime":836.125,"body":"Those are sort of explainable, but the biggest drop ever."},{"startTime":836.345,"endTime":837.885,"body":"We still don't know why it happened."},{"startTime":838.775,"endTime":839.065,"body":"Okay?"},{"startTime":839.315,"endTime":840.785,"body":"Tough to figure out what risk is."},{"startTime":842.025,"endTime":845.865,"body":"I saw another documentary say that it was the dawn of agreement trading."},{"startTime":846.215,"endTime":851.625,"body":"That is absolutely, there are lots of explanations, but there's no convincing explanation."},{"startTime":851.845,"endTime":854.065,"body":"Nobody has said this is what triggered it."},{"startTime":854.065,"endTime":854.625,"body":"What happened?"},{"startTime":854.815,"endTime":857.825,"body":"What happened on that day that started it falling?"},{"startTime":857.925,"endTime":858.425,"body":"We don't know."},{"startTime":858.565,"endTime":860.185,"body":"We may think something made it worse."},{"startTime":860.185,"endTime":862.265,"body":"Portfolio insurance, other things like that."},{"startTime":862.485,"endTime":864.025,"body":"But nobody knows why it started."},{"startTime":864.895,"endTime":866.145,"body":"Okay, fine."},{"startTime":867.345,"endTime":867.915,"body":"Good answer."},{"startTime":869.585,"endTime":872.195,"body":"Okay, so what can we tell from the past?"},{"startTime":872.735,"endTime":873.675,"body":"Not very much, right?"},{"startTime":873.705,"endTime":875.835,"body":"It's not a very good guide to predicting the future."},{"startTime":876.015,"endTime":881.361,"body":"But what we can tell is if you look at the historical returns from 1926"},{"startTime":881.361,"endTime":885.995,"body":"or 2017, these are the frequency with which we see different annual returns."},{"startTime":886.055,"endTime":888.315,"body":"So the green one at the top is treasury bills."},{"startTime":888.375,"endTime":892.197,"body":"So you can notice that with treasury bills, what happens is you don't lose much,"},{"startTime":892.197,"endTime":895.765,"body":"you don't lose any money, but you make a little bit of money, right?"},{"startTime":896.515,"endTime":901.565,"body":"With AAA corporate bonds, you see there's a slightly wider dispersion over here, right?"},{"startTime":901.565,"endTime":903.885,"body":"There's some possibility you lose money, but not much money."},{"startTime":904.115,"endTime":906.085,"body":"Some possibility make money, but again, not much money."},{"startTime":906.795,"endTime":909.925,"body":"Portfolio of large stocks, well some possibility."},{"startTime":909.925,"endTime":912.125,"body":"You lose a lot of money, some possibility you make money."},{"startTime":912.185,"endTime":916.925,"body":"And of course with small stocks, there's a possibility you lose a lot of money."},{"startTime":917.025,"endTime":920.205,"body":"But it's also a possibility you make a lot of money, right?"},{"startTime":920.345,"endTime":923.997,"body":"So one way to think about risk may be you're looking at the width of"},{"startTime":923.997,"endTime":924.485,"body":"that distribution."},{"startTime":924.705,"endTime":927.005,"body":"How dispersed are those returns over time?"},{"startTime":927.745,"endTime":928.565,"body":"Are you gonna make money?"},{"startTime":928.585,"endTime":929.445,"body":"Are you gonna lose money?"},{"startTime":929.475,"endTime":932.565,"body":"There's a wide dispersion, maybe this is riskier."},{"startTime":933.315,"endTime":935.125,"body":"Okay, fine."},{"startTime":935.865,"endTime":937.085,"body":"Can we quantify this?"},{"startTime":938.035,"endTime":940.885,"body":"Well, let's take treasury bills, right?"},{"startTime":941.225,"endTime":943.005,"body":"We call treasury bills risk free."},{"startTime":943.005,"endTime":944.805,"body":"We call government bonds risk free."},{"startTime":945.545,"endTime":949.957,"body":"So taking government bonds, the question is, if I wanna buy a corporate bond, which"},{"startTime":949.957,"endTime":950.251,"body":"has some possibility of going bankrupt the company, going bankrupt and not paying back its"},{"startTime":950.251,"endTime":957.605,"body":"money, people say, okay, you want me to invest in that?"},{"startTime":957.885,"endTime":959.605,"body":"I need a little more money than"},{"startTime":961.185,"endTime":962.765,"body":"The amount I spend in treasury bills."},{"startTime":962.865,"endTime":963.565,"body":"How much more money?"},{"startTime":963.775,"endTime":965.765,"body":"About 2.9% more."},{"startTime":965.825,"endTime":968.605,"body":"That's called the risk premium, right?"},{"startTime":968.795,"endTime":973.185,"body":"It's the additional return which you ask for in order to invest in small stocks"},{"startTime":973.185,"endTime":976.405,"body":"or s and p 500 or corporate bonds and so on."},{"startTime":976.405,"endTime":979.325,"body":"So what you see over here is what we call the risk premium."},{"startTime":979.425,"endTime":983.205,"body":"How much additional return do I want for investing in something?"},{"startTime":984.155,"endTime":984.445,"body":"Okay?"},{"startTime":985.465,"endTime":990.815,"body":"Now one question at this stage is, what is that risk-free rate that's crucial to"},{"startTime":990.815,"endTime":991.885,"body":"our analysis, right?"},{"startTime":992.185,"endTime":998.216,"body":"So let me ask you at this stage to go back and ask the question,"},{"startTime":998.216,"endTime":1003.845,"body":"if I have these three government bonds, which of these is the least risky?"},{"startTime":1004.275,"endTime":1005.365,"body":"That would be number one."},{"startTime":1005.815,"endTime":1007.405,"body":"Which one is the most risky?"},{"startTime":1007.515,"endTime":1008.565,"body":"That'll be number three."},{"startTime":1008.745,"endTime":1011.925,"body":"So go ahead and use your phones to move it around."},{"startTime":1012.275,"endTime":1014.525,"body":"What do you think is the least risky?"},{"startTime":1014.705,"endTime":1016.045,"body":"And what is the most risky?"},{"startTime":1019.515,"endTime":1021.295,"body":"So you can slide it up and down."},{"startTime":1054.725,"endTime":1055.005,"body":"Excellent."},{"startTime":1055.395,"endTime":1059.645,"body":"What this basically saying, German government, born least risky, Indian, somewhere in the middle."},{"startTime":1059.865,"endTime":1063.685,"body":"And argentian government born definitely the most risky, right?"},{"startTime":1063.835,"endTime":1065.925,"body":"This is common sense, right?"},{"startTime":1065.925,"endTime":1068.605,"body":"This is what most people would say is indeed correct."},{"startTime":1069.695,"endTime":1073.265,"body":"Unfortunately, according to finance, this is wrong, right?"},{"startTime":1073.925,"endTime":1074.145,"body":"Why?"},{"startTime":1075.095,"endTime":1077.065,"body":"Well, what does risk free mean?"},{"startTime":1077.855,"endTime":1080.945,"body":"Risk free means what's the likelihood you're gonna get back the money?"},{"startTime":1081.165,"endTime":1085.854,"body":"So let's go to the bond here, which we say is the second riskiest bond,"},{"startTime":1085.854,"endTime":1087.105,"body":"the Indian government born."},{"startTime":1087.335,"endTime":1091.943,"body":"Suppose you go to the Indian government and you say you issued a bond, time"},{"startTime":1091.943,"endTime":1092.865,"body":"to pay up."},{"startTime":1093.265,"endTime":1095.545,"body":"I want my money, but the Indian government has no money."},{"startTime":1095.855,"endTime":1096.585,"body":"What can they do?"},{"startTime":1102.275,"endTime":1104.085,"body":"They can actually just print the money."},{"startTime":1104.155,"endTime":1105.565,"body":"It's just piece of paper, right?"},{"startTime":1105.695,"endTime":1108.565,"body":"Print the money, give it to you, have to print too much paper."},{"startTime":1108.955,"endTime":1109.565,"body":"It's inflation."},{"startTime":1110.425,"endTime":1115.2,"body":"And that's why no one trusts the Argentinian government because you know, they started issuing"},{"startTime":1115.2,"endTime":1115.519,"body":"pesos, but every time a peso bond was issued, they would always print more money,"},{"startTime":1115.519,"endTime":1122.205,"body":"which means hyperinflation or inflation or whatever."},{"startTime":1122.585,"endTime":1127.599,"body":"So, but as long as the government is responsible, it's completely risk free because you"},{"startTime":1127.599,"endTime":1129.605,"body":"will always get your money back."},{"startTime":1129.625,"endTime":1133.736,"body":"You will always get a piece of paper back saying this is the debt to"},{"startTime":1133.736,"endTime":1134.285,"body":"the government."},{"startTime":1134.515,"endTime":1134.805,"body":"Okay?"},{"startTime":1135.385,"endTime":1142.947,"body":"The German government, interestingly, bonds are issued in euros, however, euros are not under direct"},{"startTime":1142.947,"endTime":1147.485,"body":"control of the German government is European central bank."},{"startTime":1147.745,"endTime":1151.715,"body":"And so the chance of this is almost close to zero, but there's a tiny,"},{"startTime":1151.715,"endTime":1155.685,"body":"tiny, tiny chance of the German government says we want to issue bonds and euros."},{"startTime":1155.685,"endTime":1158.365,"body":"The ECB will say no, very, very small chance."},{"startTime":1158.585,"endTime":1163.861,"body":"But because of that very, very small chance, the safest bond is indeed your Indian"},{"startTime":1163.861,"endTime":1164.565,"body":"government bond."},{"startTime":1164.625,"endTime":1167.285,"body":"The second safest is your German government bond."},{"startTime":1167.425,"endTime":1168.885,"body":"You may say the chance of that is zero."},{"startTime":1169.065,"endTime":1169.565,"body":"It isn't."},{"startTime":1169.675,"endTime":1172.085,"body":"It's slight possibility, right?"},{"startTime":1172.085,"endTime":1174.725,"body":"And that's why we say it's not completely risk free."},{"startTime":1175.155,"endTime":1175.445,"body":"Okay?"},{"startTime":1175.705,"endTime":1178.245,"body":"So now risk free is a very simple definition."},{"startTime":1178.425,"endTime":1179.405,"body":"Do you get your money back?"},{"startTime":1179.625,"endTime":1180.885,"body":"And the answer is yes."},{"startTime":1181.105,"endTime":1185.071,"body":"If the government issues bonds in its own currency, you will get your money back"},{"startTime":1185.071,"endTime":1188.245,"body":"because the government will just print the money if it needs to."},{"startTime":1189.115,"endTime":1189.405,"body":"Okay?"},{"startTime":1189.545,"endTime":1193.73,"body":"So that's the definition of a risk-free rate, which essentially means there is only one"},{"startTime":1193.73,"endTime":1195.125,"body":"risk-free rate around the world."},{"startTime":1195.585,"endTime":1199.34,"body":"You can think of American risk-free rate, you can think of English risk-free rate, doesn't"},{"startTime":1199.34,"endTime":1199.591,"body":"matter because one of the principles of finance is if there were two different risk"},{"startTime":1199.591,"endTime":1199.841,"body":"free rates, you would borrow it a cheaper amount, you would sell it the more"},{"startTime":1199.841,"endTime":1208.605,"body":"expensive amount and you could make money."},{"startTime":1209.105,"endTime":1212.91,"body":"And as we'll see, as we saw last time, there's no such thing as a"},{"startTime":1212.91,"endTime":1213.925,"body":"free lunch in finance."},{"startTime":1214.515,"endTime":1217.005,"body":"This is the basis of something called the carry trade."},{"startTime":1217.215,"endTime":1218.845,"body":"We'll talk about that in the last lecture."},{"startTime":1219.385,"endTime":1221.725,"body":"But even the carrier trade carries risks."},{"startTime":1221.995,"endTime":1223.725,"body":"It's not risk free, it's not arbitrage."},{"startTime":1224.065,"endTime":1228.299,"body":"But at the moment, let's leave that out, we are gonna assume risk free rate"},{"startTime":1228.299,"endTime":1231.405,"body":"is a bond issued by the government in its own currency."},{"startTime":1232.235,"endTime":1232.525,"body":"Okay?"},{"startTime":1233.265,"endTime":1237.285,"body":"So if you plot these returns, this one we just saw against risk."},{"startTime":1237.345,"endTime":1241.435,"body":"So you've got the volatility here, you've got the right return here, and what we"},{"startTime":1241.435,"endTime":1245.525,"body":"see is a beautiful straight line and you say, oh wow, this is pretty cool."},{"startTime":1245.595,"endTime":1246.365,"body":"I've solved the problem."},{"startTime":1246.475,"endTime":1251.687,"body":"Because what this is telling you is high volatility, the higher the width of that"},{"startTime":1251.687,"endTime":1253.425,"body":"distribution, the higher the return."},{"startTime":1253.485,"endTime":1255.585,"body":"And I've got a line, the line explains it."},{"startTime":1255.805,"endTime":1259.116,"body":"So if you tell me what the volatility is, I can put it on the"},{"startTime":1259.116,"endTime":1261.545,"body":"line and I can tell you what the return should be."},{"startTime":1261.545,"endTime":1262.425,"body":"And that's what I'm looking for."},{"startTime":1262.745,"endTime":1267.545,"body":"Remember the return is the discount rate in that equation, which I'm trying to find"},{"startTime":1267.545,"endTime":1267.865,"body":"out."},{"startTime":1267.865,"endTime":1271.185,"body":"The NPV equation, the R is a denominator at the bottom."},{"startTime":1271.445,"endTime":1273.185,"body":"And this graph seems to tell me everything."},{"startTime":1275.135,"endTime":1281.669,"body":"Well, no, the problem is it works for portfolios, but it doesn't work for individual"},{"startTime":1281.669,"endTime":1282.105,"body":"securities."},{"startTime":1282.445,"endTime":1288.595,"body":"So if you look at IBM, Tesla, general Motors, Tesco, doesn't matter, they're scattered all"},{"startTime":1288.595,"endTime":1289.825,"body":"over the place."},{"startTime":1289.825,"endTime":1294.385,"body":"There is no relationship between risk and return for all the individual securities."},{"startTime":1294.645,"endTime":1296.585,"body":"But that's what you're being asked to invest in."},{"startTime":1296.685,"endTime":1298.425,"body":"You're not being asked to invest in a portfolio."},{"startTime":1298.645,"endTime":1303.785,"body":"You're saying if I invest in something, one of those is what you're doing, okay?"},{"startTime":1304.135,"endTime":1305.265,"body":"This is the problem we have."},{"startTime":1305.285,"endTime":1307.985,"body":"It doesn't work for individual stocks, alright?"},{"startTime":1308.285,"endTime":1312.185,"body":"So what we have established so far is history is useless, right?"},{"startTime":1312.315,"endTime":1315.585,"body":"We've also established that it doesn't for outside anything."},{"startTime":1315.585,"endTime":1318.265,"body":"Individual securities doesn't tell us very much."},{"startTime":1319.765,"endTime":1322.025,"body":"So we need to step back, right?"},{"startTime":1322.175,"endTime":1323.305,"body":"What does theory say?"},{"startTime":1323.455,"endTime":1324.185,"body":"What is risk?"},{"startTime":1324.185,"endTime":1328.865,"body":"According to theory, the answer is we don't know, right?"},{"startTime":1329.085,"endTime":1332.465,"body":"We really as finance people, we don't know very much, right?"},{"startTime":1332.685,"endTime":1336.462,"body":"But honestly the good news is we get paid a lot of money for not"},{"startTime":1336.462,"endTime":1338.225,"body":"knowing anything, which is a good thing."},{"startTime":1340.245,"endTime":1345.66,"body":"But anyway, the point of this is we can't, we finance people think about risk"},{"startTime":1345.66,"endTime":1347.105,"body":"in one particular context."},{"startTime":1347.525,"endTime":1351.345,"body":"We focus on something called the variance and the standard deviation."},{"startTime":1352.415,"endTime":1352.705,"body":"What?"},{"startTime":1352.925,"endTime":1353.945,"body":"Why do we focus on that?"},{"startTime":1354.605,"endTime":1359.065,"body":"To understand that the variance is just the width of a distribution."},{"startTime":1359.165,"endTime":1362.225,"body":"How wide that distribution is, that's the average number."},{"startTime":1362.485,"endTime":1366.049,"body":"So how much do you see numbers on the left and how much you see"},{"startTime":1366.049,"endTime":1368.425,"body":"numbers on the, like that's the width of the distribution."},{"startTime":1368.725,"endTime":1371.745,"body":"So you want a quantitative measure trying to find that width."},{"startTime":1372.095,"endTime":1373.505,"body":"Okay, fine."},{"startTime":1373.885,"endTime":1375.305,"body":"Why do we focus on variance?"},{"startTime":1376.085,"endTime":1381.888,"body":"The good news is if you, if stocks are drawn according to a normal distribution,"},{"startTime":1381.888,"endTime":1386.145,"body":"we only need two things to know everything about that distribution."},{"startTime":1386.725,"endTime":1391.713,"body":"We need to know the number in the middle, where the peak of that distribution"},{"startTime":1391.713,"endTime":1395.705,"body":"is and the dis standard deviation, how wide that deviation can be."},{"startTime":1396.485,"endTime":1402.11,"body":"Now what's interesting about this, what's interesting about this is you can appear incredibly smart"},{"startTime":1402.11,"endTime":1403.985,"body":"as a finance person, right?"},{"startTime":1404.285,"endTime":1408.065,"body":"So let's assume, and normal distributions are everywhere, right?"},{"startTime":1408.365,"endTime":1412.607,"body":"If you take all the heights, so people in this room, it'll be a normal"},{"startTime":1412.607,"endTime":1412.889,"body":"distribution, most people will be in the middle, some people will be short, some people"},{"startTime":1412.889,"endTime":1413.172,"body":"will be tall, weights of people, normal distribution, IQs of people, normal distribution, everything in"},{"startTime":1413.172,"endTime":1422.505,"body":"nature is a normal distribution."},{"startTime":1423.205,"endTime":1426.485,"body":"So we assume that stocks follow a normal distribution."},{"startTime":1426.705,"endTime":1430.68,"body":"And the advantage now is, let's say your client comes to you and says, I'd"},{"startTime":1430.68,"endTime":1432.005,"body":"like to invest in something."},{"startTime":1432.705,"endTime":1436.565,"body":"And you say, Hmm, I think I should invest in large company stocks."},{"startTime":1436.985,"endTime":1437.405,"body":"Really?"},{"startTime":1437.665,"endTime":1438.925,"body":"How much money can I make?"},{"startTime":1439.345,"endTime":1441.725,"body":"Say okay, I think you're gonna make about 13%."},{"startTime":1442.065,"endTime":1442.285,"body":"Why?"},{"startTime":1442.285,"endTime":1445.285,"body":"Because history tells you that's a normal distribution."},{"startTime":1445.705,"endTime":1449.645,"body":"So okay, that's fine, but I'm also worried about losing my money."},{"startTime":1450.105,"endTime":1452.845,"body":"What's the chance I'm gonna lose my money again?"},{"startTime":1452.845,"endTime":1457.477,"body":"Normal distribution tells you there's a 68% chance that a return drawn from a normal"},{"startTime":1457.477,"endTime":1460.565,"body":"distribution will be within one standard deviation of the mean."},{"startTime":1461.345,"endTime":1464.125,"body":"So basically you say, you know what, you're not gonna lose."},{"startTime":1464.125,"endTime":1467.605,"body":"There's a two third chance, you're not gonna lose more than 7%, but you're not"},{"startTime":1467.605,"endTime":1468.765,"body":"gonna make more than 33%."},{"startTime":1469.805,"endTime":1471.405,"body":"I said, well that still leaves one third."},{"startTime":1471.435,"endTime":1472.285,"body":"What about the other one?"},{"startTime":1472.285,"endTime":1473.245,"body":"Third, no worries."},{"startTime":1473.595,"endTime":1479.053,"body":"There's a 99% chance you won't lose more than half your money and a 99%"},{"startTime":1479.053,"endTime":1481.965,"body":"chance you won't more make more than 75%."},{"startTime":1482.555,"endTime":1485.445,"body":"That makes you sound super smart, right?"},{"startTime":1485.825,"endTime":1486.685,"body":"I'm giving you numbers."},{"startTime":1487.325,"endTime":1488.605,"body":"A 99% chunk."},{"startTime":1488.605,"endTime":1493.841,"body":"People are like, wow, this guy is an amazing financial advisor, but all you're doing,"},{"startTime":1493.841,"endTime":1494.19,"body":"pulling the numbers out of a normal distribution, so our stocks distributed normally answer is"},{"startTime":1494.19,"endTime":1500.125,"body":"not quite right."},{"startTime":1500.435,"endTime":1505.923,"body":"What happens is bad stuff and good stuff happens a little more nor a little"},{"startTime":1505.923,"endTime":1508.485,"body":"more than predicted by the normal distribution."},{"startTime":1508.905,"endTime":1509.125,"body":"Why?"},{"startTime":1509.515,"endTime":1513.365,"body":"Because portfolio theory assume that everybody is acting by themselves."},{"startTime":1513.825,"endTime":1518.765,"body":"All of us are making individual decisions, but reality we don't."},{"startTime":1519.065,"endTime":1519.925,"body":"We look at each other."},{"startTime":1520.265,"endTime":1522.725,"body":"So if everybody's panicking, what happens to us?"},{"startTime":1522.905,"endTime":1523.765,"body":"We panic too."},{"startTime":1524.185,"endTime":1527.645,"body":"So bad stuff happens a little more frequently than predicted."},{"startTime":1527.875,"endTime":1528.485,"body":"Good stuff."},{"startTime":1528.755,"endTime":1529.645,"body":"Fear missing out."},{"startTime":1529.645,"endTime":1531.565,"body":"They're like, oh my God, everybody else is making money."},{"startTime":1531.745,"endTime":1532.765,"body":"How am I not making money?"},{"startTime":1533.345,"endTime":1535.885,"body":"So we buy more shares than we can."},{"startTime":1536.705,"endTime":1541.365,"body":"So, but for most of us it sort of looks like a normal distribution."},{"startTime":1541.465,"endTime":1543.805,"body":"So I'm gonna pretend it's a normal distribution."},{"startTime":1544.395,"endTime":1544.685,"body":"Okay?"},{"startTime":1545.035,"endTime":1547.845,"body":"Alright, so let's restate this problem."},{"startTime":1548.025,"endTime":1550.925,"body":"Now, the problem we have is we want the opportunity cost."},{"startTime":1550.925,"endTime":1554.925,"body":"If you don't invest in a particular investment, okay, fine."},{"startTime":1555.555,"endTime":1558.045,"body":"That is the return, the next best opportunity."},{"startTime":1558.545,"endTime":1563.888,"body":"That's the return we need for the NPV formula we discussed in the last lecture,"},{"startTime":1563.888,"endTime":1564.245,"body":"okay?"},{"startTime":1564.825,"endTime":1569.445,"body":"But every individual security will have its own expected return and its own standard deviation."},{"startTime":1570.135,"endTime":1575.495,"body":"We'll see that in a minute, but, and in addition, every investor has his or"},{"startTime":1575.495,"endTime":1576.925,"body":"her own risk preferences."},{"startTime":1577.345,"endTime":1582.216,"body":"So how do we come up with one number that everybody agrees is the only"},{"startTime":1582.216,"endTime":1584.165,"body":"interest rate for that particular security?"},{"startTime":1584.955,"endTime":1587.685,"body":"This is the problem that Markowitz and Sharp were faced with."},{"startTime":1587.705,"endTime":1592.898,"body":"Nobody had solved this and that solution to this question got them both a Nobel"},{"startTime":1592.898,"endTime":1593.245,"body":"Prize."},{"startTime":1593.715,"endTime":1594.005,"body":"Okay?"},{"startTime":1594.265,"endTime":1595.445,"body":"So let's see how that works."},{"startTime":1596.055,"endTime":1597.165,"body":"Let's start with the intuition."},{"startTime":1598.025,"endTime":1600.085,"body":"You have three possibilities, right?"},{"startTime":1600.265,"endTime":1604.525,"body":"You can invest in an ice cream company in sunny weather, everybody eats ice cream."},{"startTime":1605.305,"endTime":1608.685,"body":"So your a thousand dollars investment becomes $1,200."},{"startTime":1608.995,"endTime":1611.565,"body":"That is a 20% return."},{"startTime":1612.735,"endTime":1614.565,"body":"Rainy weather, nobody eats ice cream."},{"startTime":1614.825,"endTime":1617.805,"body":"So the a hundred thousand dollars investment becomes 920."},{"startTime":1618.145,"endTime":1619.965,"body":"You have lost 8% of your money."},{"startTime":1621.405,"endTime":1622.805,"body":"Umbrella company the other way around."},{"startTime":1622.815,"endTime":1626.125,"body":"Sunny weather, nobody uh, buys umbrellas."},{"startTime":1626.335,"endTime":1629.165,"body":"Rainy weather, everybody buys umbrellas, the numbers are flipped."},{"startTime":1629.475,"endTime":1629.765,"body":"Okay?"},{"startTime":1629.865,"endTime":1633.085,"body":"You make 20% or you lose 8%, okay?"},{"startTime":1633.465,"endTime":1637.325,"body":"Uh, the probabilities of sunny and rain running weather are 50 50."},{"startTime":1637.955,"endTime":1641.205,"body":"This slide was not written in England, right?"},{"startTime":1641.355,"endTime":1644.325,"body":"Obviously 'cause you'd say 80 20, but no, that's fine."},{"startTime":1645.705,"endTime":1651.445,"body":"So the expected profit, sometimes you're gonna make 1200, sometimes you're gonna make nine 20."},{"startTime":1651.745,"endTime":1654.005,"body":"The average of the two is 1 0, 6 0."},{"startTime":1654.385,"endTime":1656.085,"body":"That's the $60 profit you make."},{"startTime":1656.675,"endTime":1656.965,"body":"Okay?"},{"startTime":1656.985,"endTime":1660.405,"body":"You've invested a thousand, that's 6% expected return."},{"startTime":1661.145,"endTime":1667.995,"body":"And the standard deviation is sometimes you make $140 more than 1 0, 6 0,"},{"startTime":1667.995,"endTime":1669.365,"body":"that's a 1200."},{"startTime":1669.635,"endTime":1674.965,"body":"Sometimes you make a hundred and uh, $40 less than 1 0 6 0."},{"startTime":1674.985,"endTime":1679.485,"body":"That's nine 20, that's 14% here and there, right?"},{"startTime":1679.875,"endTime":1680.165,"body":"Fine."},{"startTime":1681.005,"endTime":1681.965,"body":"Umbrella company, same thing."},{"startTime":1682.245,"endTime":1682.845,"body":"Opposite directions."},{"startTime":1683.285,"endTime":1684.445,"body":"T-bills don't depend on the weather."},{"startTime":1684.625,"endTime":1688.837,"body":"So regardless of whether it's sunny or rainy weather, you get back 1 0, 3"},{"startTime":1688.837,"endTime":1691.365,"body":"0, that's a 3% return and no standard deviation."},{"startTime":1691.365,"endTime":1693.125,"body":"You're getting the same amount every period."},{"startTime":1693.715,"endTime":1694.005,"body":"Okay?"},{"startTime":1694.225,"endTime":1700.975,"body":"So if you have a choice between these three things, right?"},{"startTime":1701.205,"endTime":1705.766,"body":"What would you choose to invest in the ice cream company, the umbrella company or"},{"startTime":1705.766,"endTime":1706.375,"body":"treasury bottles?"},{"startTime":1706.475,"endTime":1711.181,"body":"To put that into perspective, let me show you again what I'm actually looking for,"},{"startTime":1711.181,"endTime":1711.495,"body":"right?"},{"startTime":1711.835,"endTime":1715.695,"body":"So you have a treasury bill, zero risk, and 3% return."},{"startTime":1716.035,"endTime":1720.375,"body":"Ice cream umbrella, 14% standard deviation and 6% return."},{"startTime":1720.485,"endTime":1722.615,"body":"Well that's what you, what you are looking at"},{"startTime":1758.395,"endTime":1759.085,"body":"."},{"startTime":1759.325,"endTime":1760.165,"body":"Excellent, right?"},{"startTime":1760.705,"endTime":1763.245,"body":"Key part that you can see here is there's no pattern."},{"startTime":1763.465,"endTime":1764.085,"body":"You can see it."},{"startTime":1764.085,"endTime":1767.658,"body":"People are a little, they like ice creams a little more than umbrellas, but you"},{"startTime":1767.658,"endTime":1769.565,"body":"know, there's nothing wrong with these answers, right?"},{"startTime":1769.765,"endTime":1773.565,"body":"I mean all of the answers are totally fine, right?"},{"startTime":1773.585,"endTime":1776.845,"body":"So you can't say that anybody's wrong on this basis."},{"startTime":1776.905,"endTime":1780.725,"body":"You like umbrellas fine, that's you over there, you like ice cream fine."},{"startTime":1780.725,"endTime":1783.685,"body":"That's you over here, you like to be safe, that's you over here."},{"startTime":1783.745,"endTime":1785.125,"body":"No big deal, okay?"},{"startTime":1785.125,"endTime":1785.685,"body":"Nothing wrong."},{"startTime":1786.635,"endTime":1786.925,"body":"Okay?"},{"startTime":1787.105,"endTime":1788.805,"body":"Now let's change the question a little bit."},{"startTime":1791.745,"endTime":1792.885,"body":"I'm gonna add a portfolio."},{"startTime":1793.595,"endTime":1796.716,"body":"Half my money in the ice cream company and half the money in the umbrella"},{"startTime":1796.716,"endTime":1796.925,"body":"company."},{"startTime":1797.345,"endTime":1801.045,"body":"So in rainy weather, in sunny weather, the ice cream company makes money."},{"startTime":1801.425,"endTime":1804.085,"body":"So my $500 investment becomes $600."},{"startTime":1805.065,"endTime":1806.765,"body":"But the umbrella company loses money."},{"startTime":1807.825,"endTime":1812.325,"body":"The 900, uh, the thousand, the $500 investment becomes four 60."},{"startTime":1812.985,"endTime":1813.805,"body":"Add the two together."},{"startTime":1814.025,"endTime":1814.925,"body":"1 0 6 0."},{"startTime":1815.745,"endTime":1816.035,"body":"Okay?"},{"startTime":1816.345,"endTime":1817.275,"body":"Same thing over here."},{"startTime":1818.075,"endTime":1818.715,"body":"Opposite, right?"},{"startTime":1818.895,"endTime":1820.435,"body":"The umbrella scheme company is making money."},{"startTime":1820.435,"endTime":1821.835,"body":"The umbrella company's losing money."},{"startTime":1822.135,"endTime":1826.603,"body":"And so you make $60 on average, which is a 6% return, but with no"},{"startTime":1826.603,"endTime":1826.901,"body":"standard deviation, again, you're basically saying I'm going to get 1 0 6 0 because"},{"startTime":1826.901,"endTime":1827.199,"body":"what you make in one company, you lose the other, they cancel each other out,"},{"startTime":1827.199,"endTime":1836.435,"body":"put it together."},{"startTime":1836.585,"endTime":1841.866,"body":"What you have is a portfolio investment, which has the same returns as the tbi,"},{"startTime":1841.866,"endTime":1843.275,"body":"but higher returns, right?"},{"startTime":1843.305,"endTime":1845.235,"body":"Same risk as the tbi, but higher return."},{"startTime":1845.375,"endTime":1848.795,"body":"It has a lower risk than the ICM umbrella company and the same returns."},{"startTime":1849.375,"endTime":1854.843,"body":"So the question now is, if you have a choice between these four investments, which"},{"startTime":1854.843,"endTime":1857.395,"body":"one do you choose to invest in?"},{"startTime":1865.835,"endTime":1868.075,"body":"Somebody who's still obsessed with ice cream \u003claugh\u003e,"},{"startTime":1874.835,"endTime":1875.185,"body":"Right?"},{"startTime":1875.605,"endTime":1880.825,"body":"And that's what I mean by the intuition behind portfolio theory."},{"startTime":1881.055,"endTime":1885.297,"body":"What you have over here is individually, when you're given all these things, it's very"},{"startTime":1885.297,"endTime":1885.58,"body":"difficult to choose, but once you start combining things into a portfolio, some of that"},{"startTime":1885.58,"endTime":1890.105,"body":"risk disappears."},{"startTime":1890.285,"endTime":1896.665,"body":"And so there is an overwhelming consensus that you should invest in the portfolio company."},{"startTime":1896.885,"endTime":1901.265,"body":"It is giving you the highest return per unit of risk, right?"},{"startTime":1901.285,"endTime":1902.025,"body":"That's the idea."},{"startTime":1902.045,"endTime":1903.305,"body":"That's what we're going for."},{"startTime":1903.615,"endTime":1903.905,"body":"Okay?"},{"startTime":1904.245,"endTime":1907.905,"body":"But to get there, we need a couple of additional steps."},{"startTime":1908.795,"endTime":1910.865,"body":"Let's start with a pair of securities."},{"startTime":1910.925,"endTime":1914.121,"body":"And I'm trying to find, this is the way the math comes in, so I'm"},{"startTime":1914.121,"endTime":1916.465,"body":"gonna spend a little bit of time talking about that, right?"},{"startTime":1916.465,"endTime":1920.255,"body":"So we are gonna compute the expected return, the variance and the standard deviation of"},{"startTime":1920.255,"endTime":1922.025,"body":"a stock fund and a bond fund."},{"startTime":1922.245,"endTime":1926.232,"body":"And what I'm gonna point out is there are three states of the world, a"},{"startTime":1926.232,"endTime":1928.625,"body":"recession, normal times, and a boom in a recession."},{"startTime":1928.895,"endTime":1930.385,"body":"Probability is 20%."},{"startTime":1930.925,"endTime":1931.945,"body":"Stocks do really badly."},{"startTime":1932.125,"endTime":1935.705,"body":"You earn, you lose 7%, but bonds do well."},{"startTime":1935.885,"endTime":1941.301,"body":"So you earn 17%, normal times, most of the time stocks earn about 12 bonds,"},{"startTime":1941.301,"endTime":1942.385,"body":"own about seven."},{"startTime":1943.095,"endTime":1943.385,"body":"Boom."},{"startTime":1943.605,"endTime":1946.065,"body":"30% of the time stocks own 28%."},{"startTime":1946.395,"endTime":1949.025,"body":"Bonds own lose 3% of the value."},{"startTime":1949.455,"endTime":1949.745,"body":"Okay?"},{"startTime":1949.765,"endTime":1952.345,"body":"So this is what you have and you have to compute the same thing."},{"startTime":1952.865,"endTime":1955.065,"body":"Expected return, standard deviation or variance."},{"startTime":1955.165,"endTime":1956.745,"body":"Why normal distribution?"},{"startTime":1956.745,"endTime":1959.205,"body":"Those are the only things you need for a normal distribution."},{"startTime":1959.715,"endTime":1961.125,"body":"Okay, let's do that."},{"startTime":1961.705,"endTime":1963.405,"body":"So how do you do the expected return?"},{"startTime":1963.585,"endTime":1964.365,"body":"The answer is simple."},{"startTime":1964.665,"endTime":1966.965,"body":"You just say what are the different states of the world?"},{"startTime":1968.105,"endTime":1969.685,"body":"And multiply it by the probability."},{"startTime":1970.105,"endTime":1975.335,"body":"So for example, the expected return to a stock fund is 20% of the time"},{"startTime":1975.335,"endTime":1978.125,"body":"you get minus seven, 20% times minus seven."},{"startTime":1978.375,"endTime":1981.485,"body":"50% of the time you get 12, 50% times 12."},{"startTime":1981.705,"endTime":1985.125,"body":"30% of the time you get 28, 30% times 28."},{"startTime":1985.225,"endTime":1987.045,"body":"The expected return is 13%."},{"startTime":1987.755,"endTime":1988.045,"body":"Okay?"},{"startTime":1988.195,"endTime":1990.645,"body":"It's just a weighted probability of those numbers."},{"startTime":1991.635,"endTime":1993.205,"body":"What about the bond fund?"},{"startTime":1993.275,"endTime":1993.765,"body":"Same thing."},{"startTime":1993.785,"endTime":1999.803,"body":"20% chance of getting 17, 50% chance of getting seven 30% chance of getting minus"},{"startTime":1999.803,"endTime":2000.205,"body":"three."},{"startTime":2000.425,"endTime":2001.805,"body":"That's this equation over here."},{"startTime":2002.705,"endTime":2003.685,"body":"6%, right?"},{"startTime":2003.685,"endTime":2004.965,"body":"So that's the expected return."},{"startTime":2006.355,"endTime":2007.845,"body":"Okay, what about the variance?"},{"startTime":2008.795,"endTime":2014.855,"body":"Well, for the variance, what you notice, you never actually get 13%, right?"},{"startTime":2014.855,"endTime":2017.495,"body":"Sometimes you get more, sometimes you get less."},{"startTime":2018.155,"endTime":2022.071,"body":"So what you want is a measure that tells you how far away are you"},{"startTime":2022.071,"endTime":2022.855,"body":"from that 13%."},{"startTime":2023.955,"endTime":2031.097,"body":"So in a in a recession, how far away are you from 13%, you're 20%"},{"startTime":2031.097,"endTime":2036.335,"body":"less than 13 minus seven minus 13, 20% below 13, right?"},{"startTime":2037.915,"endTime":2044.335,"body":"Normal times your 1% below 13, and then boom, you're 15% above 13."},{"startTime":2045.035,"endTime":2046.935,"body":"But if you just add 'em up, what do you get?"},{"startTime":2047.305,"endTime":2051.054,"body":"First case you get minus 22nd case, you get minus one."},{"startTime":2051.225,"endTime":2052.735,"body":"Third case you get plus 15."},{"startTime":2052.835,"endTime":2057.286,"body":"If you just add 'em up, the negative number will cancel the positive number and"},{"startTime":2057.286,"endTime":2060.255,"body":"it'll look like, oh, this is very safe security, right?"},{"startTime":2060.875,"endTime":2064.215,"body":"So how do you convert a negative number to a positive number?"},{"startTime":2064.995,"endTime":2067.094,"body":"Simple square it, right?"},{"startTime":2067.315,"endTime":2068.655,"body":"So that's what we are gonna do here."},{"startTime":2069.195,"endTime":2074.012,"body":"So what we're gonna say is minus seven, minus 13, how far away are you"},{"startTime":2074.012,"endTime":2074.655,"body":"from 13%."},{"startTime":2075.034,"endTime":2079.175,"body":"That's 20% below square it 0.04, same thing."},{"startTime":2079.715,"endTime":2084.655,"body":"How do you get your 1% below 13% square it, you get 0.01, same thing."},{"startTime":2084.755,"endTime":2089.255,"body":"28% minus 13%, 15% 0.0 2, 2 5, right?"},{"startTime":2089.635,"endTime":2096.522,"body":"And once you have those deviations, square deviations multiply by the probabilities, 20% time 0.04,"},{"startTime":2096.522,"endTime":2100.655,"body":"50% time 0.01, same thing, which you just did."},{"startTime":2100.835,"endTime":2104.444,"body":"You get the variance and of course take the square root to the variance, you"},{"startTime":2104.444,"endTime":2104.685,"body":"get the standard deviation, you're going back, you're taking out the square, which you just"},{"startTime":2104.685,"endTime":2108.535,"body":"did, right?"},{"startTime":2108.675,"endTime":2114.735,"body":"So this is pretty much high school statistics, okay, next."},{"startTime":2114.955,"endTime":2116.895,"body":"So this is okay, we can do this, right?"},{"startTime":2118.715,"endTime":2122.655,"body":"But what about now putting these things into a portfolio, what's the same thing?"},{"startTime":2122.795,"endTime":2126.095,"body":"The expected return and the standard deviation of a portfolio."},{"startTime":2126.445,"endTime":2129.415,"body":"Half my money in the stock fund and half in the bond fund."},{"startTime":2130.355,"endTime":2131.055,"body":"How do I do that?"},{"startTime":2131.485,"endTime":2135.055,"body":"Well, one way you can do that is to treat it just like another security."},{"startTime":2135.475,"endTime":2140.944,"body":"You say, you know, 50% of my money is in the stock fund, so 50%"},{"startTime":2140.944,"endTime":2145.685,"body":"times seven plus 50% times 17, add them together, I get 5%, right?"},{"startTime":2146.185,"endTime":2147.205,"body":"So that's it."},{"startTime":2147.545,"endTime":2150.765,"body":"And they do the same thing 50% times 12, 50% times seven."},{"startTime":2150.785,"endTime":2155.845,"body":"That's 9.5 50% times 48 plus 50% times minus three, 12.5."},{"startTime":2156.265,"endTime":2158.245,"body":"And that's a new security run."},{"startTime":2158.245,"endTime":2161.005,"body":"The whole process all over again, okay?"},{"startTime":2161.195,"endTime":2164.085,"body":"However, in real life we don't have those probabilities."},{"startTime":2165.035,"endTime":2168.208,"body":"So I can't do this because I don't know what the probabilities are for a"},{"startTime":2168.208,"endTime":2170.535,"body":"recession are what a boom is, what a normal time is."},{"startTime":2170.935,"endTime":2171.695,"body":"I have do something else."},{"startTime":2172.375,"endTime":2175.895,"body":"I want to go directly from here and here to here."},{"startTime":2176.795,"endTime":2177.415,"body":"And that's easy."},{"startTime":2178.065,"endTime":2182.466,"body":"Turns out if I do it this way, the PO expected return of portfolio is"},{"startTime":2182.466,"endTime":2186.575,"body":"a weighted average with the amount of money I've invested in each of these."},{"startTime":2187.115,"endTime":2189.935,"body":"So in this case, 50% of my money is in the stock fund."},{"startTime":2189.935,"endTime":2195.546,"body":"That's earning me 13% on average, 50% in the bond fund, that's earning me 6%"},{"startTime":2195.546,"endTime":2196.295,"body":"on average."},{"startTime":2196.395,"endTime":2198.655,"body":"Put the two together, I get my 9.5 straight."},{"startTime":2198.895,"endTime":2201.975,"body":"I don't have to go through the probabilities, right?"},{"startTime":2202.485,"endTime":2206.956,"body":"Okay, so expected return is easy, I just wait all the numbers and put it"},{"startTime":2206.956,"endTime":2207.255,"body":"together."},{"startTime":2207.965,"endTime":2208.455,"body":"Alright?"},{"startTime":2208.595,"endTime":2210.215,"body":"But now I want to go to the variance."},{"startTime":2210.525,"endTime":2211.895,"body":"I've got these two variances."},{"startTime":2212.135,"endTime":2215.655,"body":"I wanna figure out what's the variance of my portfolio directly."},{"startTime":2215.735,"endTime":2219.546,"body":"I don't want to go through all those intermediate steps so I understand what the"},{"startTime":2219.546,"endTime":2220.055,"body":"variance is."},{"startTime":2220.335,"endTime":2223.855,"body":"I need a new term called how these assets move together."},{"startTime":2223.855,"endTime":2228.58,"body":"Because remember the ice cream company and the umbrella company, they were moving in opposite"},{"startTime":2228.58,"endTime":2228.895,"body":"directions."},{"startTime":2228.955,"endTime":2230.615,"body":"That's why I could reduce my risk."},{"startTime":2230.995,"endTime":2234.472,"body":"So I wanna figure out, get a measure that tells me whether they go in"},{"startTime":2234.472,"endTime":2236.095,"body":"the same direction or in opposite directions."},{"startTime":2236.645,"endTime":2237.655,"body":"What do you think over here?"},{"startTime":2237.755,"endTime":2241.975,"body":"Do they go in the same direction or opposite directions in a recession?"},{"startTime":2242.515,"endTime":2248.046,"body":"One is losing money, the other's making money, normal times making money, sort of making"},{"startTime":2248.046,"endTime":2248.415,"body":"money."},{"startTime":2249.045,"endTime":2250.855,"body":"This is making money that's losing money."},{"startTime":2250.955,"endTime":2254.615,"body":"So essentially they're going in opposite directions, right?"},{"startTime":2254.835,"endTime":2259.306,"body":"So you wanna measure that's high when they're going in the same direction and low"},{"startTime":2259.306,"endTime":2261.095,"body":"when they're going in opposite directions."},{"startTime":2261.795,"endTime":2264.935,"body":"And that's all the core variance of two securities."},{"startTime":2266.035,"endTime":2269.015,"body":"So this is like core variances over time."},{"startTime":2269.035,"endTime":2270.495,"body":"And usually this is the case."},{"startTime":2270.675,"endTime":2274.095,"body":"Stocks and bonds go in opposite directions except this year, right?"},{"startTime":2274.115,"endTime":2278.175,"body":"So where everything crashed at the same time, but you know, that's bad luck."},{"startTime":2279.005,"endTime":2279.295,"body":"Okay?"},{"startTime":2279.715,"endTime":2281.615,"body":"So how do we figure out what the core variance is?"},{"startTime":2282.245,"endTime":2284.655,"body":"What it turns out it's actually surprisingly easy."},{"startTime":2285.475,"endTime":2291.592,"body":"So what we have is when security one, the stock fund is doing really badly,"},{"startTime":2291.592,"endTime":2294.855,"body":"it's making 20% less than what we expected."},{"startTime":2295.635,"endTime":2296.975,"body":"The bond fund is doing really well."},{"startTime":2297.845,"endTime":2300.495,"body":"It's earning 5% more than what you expected."},{"startTime":2300.915,"endTime":2305.975,"body":"So what you're doing is multiplying minus 20 with 11 to get minus 0.02."},{"startTime":2305.975,"endTime":2310.535,"body":"So you're multiplying the two deviations together, one's doing well, the other's doing badly."},{"startTime":2311.095,"endTime":2315.548,"body":"Positive number multiply by negative number, negative number, both are doing badly at the same"},{"startTime":2315.548,"endTime":2315.845,"body":"time."},{"startTime":2316.325,"endTime":2319.285,"body":"Negative number multiply by negative number, positive number, right?"},{"startTime":2319.345,"endTime":2324.365,"body":"So basically if you're just multiplying the deviation, you should get all these answers right?"},{"startTime":2324.425,"endTime":2330.16,"body":"So 0.05 in this case is a core variance here and we call it we"},{"startTime":2330.16,"endTime":2330.925,"body":"sigma times."},{"startTime":2331.385,"endTime":2334.525,"body":"sp by the way, finance involves a lot of Greek."},{"startTime":2334.705,"endTime":2338.023,"body":"So if you sit through all these lectures, you'll end up with working knowledge of"},{"startTime":2338.023,"endTime":2338.245,"body":"Greek."},{"startTime":2338.255,"endTime":2341.365,"body":"We'll talk about alphas, we'll talk about gammas, we'll talk about deltas."},{"startTime":2341.665,"endTime":2344.838,"body":"So when you go to Greece on a holiday, you'll be able to read the"},{"startTime":2344.838,"endTime":2345.685,"body":"street science for sure."},{"startTime":2346.835,"endTime":2347.125,"body":"Okay?"},{"startTime":2347.435,"endTime":2347.925,"body":"Alright."},{"startTime":2348.105,"endTime":2350.365,"body":"What's the relation between the variance in the cos?"},{"startTime":2350.495,"endTime":2351.805,"body":"We've already done it."},{"startTime":2352.865,"endTime":2357.443,"body":"If he replaced the bond fund with a stock fund, the you product of the"},{"startTime":2357.443,"endTime":2359.885,"body":"two deviations is a square of the product."},{"startTime":2360.505,"endTime":2364.685,"body":"So the variance is a special form of the co variance."},{"startTime":2365.065,"endTime":2367.685,"body":"The co variance of something with itself is its variance."},{"startTime":2368.675,"endTime":2368.965,"body":"Okay?"},{"startTime":2369.225,"endTime":2370.085,"body":"So let's leave that."},{"startTime":2370.745,"endTime":2373.005,"body":"Now we get to a really complicated looking formula."},{"startTime":2373.995,"endTime":2379.493,"body":"This one says that the variance of portfolio is a weighted average of the variances,"},{"startTime":2379.493,"endTime":2383.525,"body":"the individual parts plus a product of the two core variances."},{"startTime":2384.025,"endTime":2385.445,"body":"How do we understand this formula?"},{"startTime":2386.375,"endTime":2387.405,"body":"Let's take an example."},{"startTime":2388.595,"endTime":2393.205,"body":"Imagine that you have a giant sack with two animals on it, right?"},{"startTime":2393.425,"endTime":2394.805,"body":"An elephant and a mouse."},{"startTime":2396.105,"endTime":2399.005,"body":"So what's the, how much is the sack moving?"},{"startTime":2399.025,"endTime":2401.365,"body":"That's a question you want to answer, right?"},{"startTime":2401.785,"endTime":2403.125,"body":"So how much is the sack moves?"},{"startTime":2403.125,"endTime":2403.925,"body":"Depends on two things."},{"startTime":2404.225,"endTime":2405.725,"body":"One is how much the elephant moves."},{"startTime":2405.905,"endTime":2408.685,"body":"That's the standard deviation of the elephant, right?"},{"startTime":2408.705,"endTime":2411.885,"body":"You square it, the elephant is big, so it'll really dominated."},{"startTime":2412.345,"endTime":2413.725,"body":"The mouse is relatively small."},{"startTime":2414.065,"endTime":2418.317,"body":"So regardless of how much the mouse moves, the bag is not gonna move very"},{"startTime":2418.317,"endTime":2418.885,"body":"much, okay?"},{"startTime":2418.955,"endTime":2422.885,"body":"However, it also depends on how they react to each other, right?"},{"startTime":2422.915,"endTime":2425.805,"body":"Obviously with the elephant and the mouse, the elephant dominates completely."},{"startTime":2426.305,"endTime":2428.525,"body":"So you're really not gonna see much of a difference."},{"startTime":2428.625,"endTime":2429.325,"body":"So no problem."},{"startTime":2429.415,"endTime":2431.205,"body":"Let's say put in two elephants into the back."},{"startTime":2432.355,"endTime":2432.645,"body":"Okay?"},{"startTime":2432.905,"endTime":2436.405,"body":"So what you have here, same thing, how much does the sac move?"},{"startTime":2436.505,"endTime":2439.925,"body":"But now it depends on where the elephant's moving in the same or opposite directions."},{"startTime":2440.145,"endTime":2442.285,"body":"If they're moving in the same direction, the back will move."},{"startTime":2442.515,"endTime":2443.885,"body":"That means high core variance."},{"startTime":2444.425,"endTime":2445.485,"body":"The back will move a lot."},{"startTime":2446.185,"endTime":2447.645,"body":"You can move in opposite directions."},{"startTime":2448.405,"endTime":2450.365,"body":"Negative Covance, the bag won't move at all."},{"startTime":2451.065,"endTime":2452.205,"body":"That's the idea here."},{"startTime":2452.795,"endTime":2453.085,"body":"Okay?"},{"startTime":2453.905,"endTime":2458.978,"body":"So putting that into that formula, we're talking about a stock fund and a bond"},{"startTime":2458.978,"endTime":2461.685,"body":"fund or an elephant and a mouse, okay?"},{"startTime":2461.745,"endTime":2463.685,"body":"How many combinations can you have?"},{"startTime":2464.335,"endTime":2468.085,"body":"Turns out you might think I only have two combinations, elephant or mouse."},{"startTime":2468.925,"endTime":2469.565,"body":"Actually there are four."},{"startTime":2470.275,"endTime":2471.445,"body":"What are the four combinations?"},{"startTime":2471.835,"endTime":2475.485,"body":"Well, the elephant by itself, the mouse with itself, right?"},{"startTime":2475.625,"endTime":2477.125,"body":"The elephant first and then the mouse."},{"startTime":2477.305,"endTime":2478.685,"body":"The mouse first, and then the elephant."},{"startTime":2479.625,"endTime":2481.405,"body":"The all four different combinations."},{"startTime":2482.075,"endTime":2482.365,"body":"Okay?"},{"startTime":2482.625,"endTime":2485.685,"body":"So to put that, what you're going to do is four different boxes."},{"startTime":2485.865,"endTime":2489.965,"body":"So what you have is how much is the elephant moving the elephant by itself?"},{"startTime":2490.025,"endTime":2491.965,"body":"How much is the elephant moving relative to the mouse?"},{"startTime":2492.105,"endTime":2494.205,"body":"How much is the mouse moving relative to the elephant?"},{"startTime":2494.345,"endTime":2496.805,"body":"How much is the mouse moving by itself, right?"},{"startTime":2496.865,"endTime":2502.494,"body":"So that is essentially our formula here kind of looks complicated, but essentially that's all"},{"startTime":2502.494,"endTime":2503.245,"body":"it is."},{"startTime":2504.065,"endTime":2507.925,"body":"So plugging all these things in, you get a variance, right?"},{"startTime":2507.925,"endTime":2513.365,"body":"Which is looks like complicated thing, but we already got the numbers."},{"startTime":2513.385,"endTime":2514.405,"body":"That's the core variance."},{"startTime":2514.405,"endTime":2517.525,"body":"Those are the two variances, and over here are the weights."},{"startTime":2518.995,"endTime":2520.845,"body":"Okay, fine."},{"startTime":2522.055,"endTime":2523.195,"body":"So that's the ultimate."},{"startTime":2523.195,"endTime":2525.035,"body":"When you take all this, what do you conclude?"},{"startTime":2526.175,"endTime":2529.515,"body":"Not really so much about being calculating the expected portfolio."},{"startTime":2529.775,"endTime":2535.537,"body":"The key is, if you look at that portfolio, that portfolio has a lower risk,"},{"startTime":2535.537,"endTime":2540.915,"body":"lower standard deviation and a higher return than the bond funder by itself, right?"},{"startTime":2541.415,"endTime":2544.515,"body":"So in fact, you can do this for any length of combinations."},{"startTime":2545.975,"endTime":2550.275,"body":"So 0% in stocks all the way to a hundred percent in stocks."},{"startTime":2550.415,"endTime":2555.008,"body":"You just keep running that formula again, and you get a graph that looks like"},{"startTime":2555.008,"endTime":2555.315,"body":"this."},{"startTime":2555.535,"endTime":2559.39,"body":"The top line there a hundred percent in stocks, the bottom line point there is"},{"startTime":2559.39,"endTime":2560.675,"body":"a hundred percent in bonds."},{"startTime":2560.775,"endTime":2564.395,"body":"That's 95% bonds, that's 90% bonds and so on."},{"startTime":2564.415,"endTime":2568.035,"body":"So the numbers are, you know, go on this."},{"startTime":2568.455,"endTime":2571.875,"body":"But looking at that one here, this is a hundred percent bonds, right?"},{"startTime":2571.875,"endTime":2576.555,"body":"That's 7% standard deviation and a really low 6% return."},{"startTime":2577.415,"endTime":2586.167,"body":"So a question for you is, would you choose to buy a portfolio consisting of"},{"startTime":2586.167,"endTime":2587.335,"body":"100% bonds?"},{"startTime":2607.425,"endTime":2607.715,"body":"Okay?"},{"startTime":2612.085,"endTime":2612.435,"body":"Right?"},{"startTime":2612.615,"endTime":2615.155,"body":"So again, pretty much of a no brainer."},{"startTime":2615.535,"endTime":2620.766,"body":"If you look at this, almost a no brainer, if you look at this, what"},{"startTime":2620.766,"endTime":2621.115,"body":"you will see is if you invest a hundred percent in bonds, you end up"},{"startTime":2621.115,"endTime":2627.045,"body":"right there, right?"},{"startTime":2627.385,"endTime":2633.285,"body":"But if you go up straight here from, oops, sorry, if you go up,"},{"startTime":2635.585,"endTime":2639.461,"body":"If you go straight up from the a hundred percent bonds to a hundred percent"},{"startTime":2639.461,"endTime":2642.045,"body":"stock for the same risk, you get a higher return."},{"startTime":2642.465,"endTime":2645.805,"body":"Nobody should pick any of those combinations at the bottom."},{"startTime":2645.945,"endTime":2647.165,"body":"Forget a hundred percent bond."},{"startTime":2647.225,"endTime":2649.165,"body":"You should not even go for 95% bond."},{"startTime":2649.265,"endTime":2650.805,"body":"You shouldn't go for 90% bond."},{"startTime":2650.825,"endTime":2653.725,"body":"You shouldn't go for 85% bond because they're all at the bottom."},{"startTime":2654.665,"endTime":2660.445,"body":"So essentially what you have is what we call the efficient frontier."},{"startTime":2660.785,"endTime":2665.735,"body":"So this is basically saying these are some portfolio combinations which give you the highest"},{"startTime":2665.735,"endTime":2668.045,"body":"return for the minimum amount of risk."},{"startTime":2668.305,"endTime":2672.487,"body":"Nobody will pick a portfolio that gives you a low return for a high amount"},{"startTime":2672.487,"endTime":2673.045,"body":"of risk."},{"startTime":2673.585,"endTime":2676.765,"body":"That's pure and simple statistics, right?"},{"startTime":2676.765,"endTime":2679.765,"body":"There's nothing beyond statistics at this stage, okay?"},{"startTime":2680.705,"endTime":2684.59,"body":"You can generalize this to many securities, I won't go through this, but literally what"},{"startTime":2684.59,"endTime":2684.849,"body":"it's saying is the weighted average of the expected returns, the individual parts, and this"},{"startTime":2684.849,"endTime":2691.325,"body":"is every potential pair of co variances multiplied by each other."},{"startTime":2691.625,"endTime":2693.245,"body":"And I promise you more Greek symbols."},{"startTime":2693.245,"endTime":2695.045,"body":"So that is a double summation sign."},{"startTime":2695.105,"endTime":2696.125,"body":"I'm just adding 'em all up."},{"startTime":2696.995,"endTime":2697.285,"body":"Okay?"},{"startTime":2697.915,"endTime":2701.285,"body":"Alright, so with three securities, what do you get?"},{"startTime":2701.545,"endTime":2703.085,"body":"You get nine combinations."},{"startTime":2703.465,"endTime":2707.509,"body":"So one with itself, one with two, one with three, two with one, two with"},{"startTime":2707.509,"endTime":2711.285,"body":"itself, two with three, three with one, three with two, three with itself, right?"},{"startTime":2711.665,"endTime":2713.885,"body":"So with four you get 16 combinations."},{"startTime":2714.195,"endTime":2718.045,"body":"When I was working at BGI, we had about 3000 securities in our portfolio."},{"startTime":2718.275,"endTime":2722.325,"body":"That meant we had to deal with 9 million portfolio combinations."},{"startTime":2722.665,"endTime":2725.045,"body":"It would take us two days to, no, we wouldn't do it."},{"startTime":2725.065,"endTime":2726.565,"body":"The computer would do it, right?"},{"startTime":2726.685,"endTime":2729.885,"body":"But it'll still take the computer two days to do it, right?"},{"startTime":2730.305,"endTime":2731.325,"body":"But that's it."},{"startTime":2731.395,"endTime":2732.685,"body":"This is the formula, right?"},{"startTime":2732.685,"endTime":2737.427,"body":"So it looks really complicated, but literally all you're doing is taking every possible pair"},{"startTime":2737.427,"endTime":2739.325,"body":"and just adding 'em up, fine."},{"startTime":2739.905,"endTime":2744.085,"body":"So the veins of a portfolio is basically a matrix that looks like this."},{"startTime":2744.545,"endTime":2746.845,"body":"So what you have over here is the stocks."},{"startTime":2747.175,"endTime":2752.525,"body":"Every diagonal term is a variance, and every off diagonal term is a core variance."},{"startTime":2753.155,"endTime":2753.445,"body":"Okay?"},{"startTime":2753.735,"endTime":2757.293,"body":"Let's keep this in the back of our head and now let's say in a"},{"startTime":2757.293,"endTime":2758.005,"body":"many security world."},{"startTime":2758.625,"endTime":2763.465,"body":"So we sort of get the intuition that you put these securities together, you can"},{"startTime":2763.465,"endTime":2765.725,"body":"come up with a portfolio frontier, right?"},{"startTime":2766.145,"endTime":2771.92,"body":"So we take all these securities, add 'em together, you have every possible combination of"},{"startTime":2771.92,"endTime":2773.845,"body":"every security in the world."},{"startTime":2774.625,"endTime":2777.365,"body":"You'll end up with curve connecting to curve connect."},{"startTime":2777.385,"endTime":2777.765,"body":"All this."},{"startTime":2778.025,"endTime":2784.198,"body":"And what you see is the outermost convex hull of all the securities is called"},{"startTime":2784.198,"endTime":2785.845,"body":"our efficient frontier, right?"},{"startTime":2786.225,"endTime":2793.205,"body":"So anything above the minimum variance portfolio is what we call the efficient frontier, right?"},{"startTime":2793.705,"endTime":2795.045,"body":"So that's why Markovitz stopped."},{"startTime":2795.425,"endTime":2796.925,"body":"So Markovitz said, okay, you know what?"},{"startTime":2797.705,"endTime":2801.427,"body":"We have so many combinations we worry about that people will hold, but we don't"},{"startTime":2801.427,"endTime":2803.165,"body":"need to worry about most of them."},{"startTime":2803.425,"endTime":2808.085,"body":"People will only hold efficient portfolios, only portfolios on the frontier."},{"startTime":2808.235,"endTime":2813.285,"body":"They will not hold any of the internal portfolios because the efficient portfolios dominate them."},{"startTime":2814.315,"endTime":2815.415,"body":"That's a brilliant conclusion."},{"startTime":2816.285,"endTime":2818.255,"body":"Also completely useless."},{"startTime":2819.315,"endTime":2819.535,"body":"Why?"},{"startTime":2819.925,"endTime":2823.695,"body":"Because there is an infinite number of efficient portfolios, right?"},{"startTime":2823.695,"endTime":2825.335,"body":"Because that curve goes on all the way."},{"startTime":2825.715,"endTime":2830.911,"body":"So what Markowitz essentially said was infinite number of portfolio combinations, get rid of the"},{"startTime":2830.911,"endTime":2831.258,"body":"infinite number of inefficient portfolio combination and you end up with infinite number of efficient"},{"startTime":2831.258,"endTime":2836.455,"body":"combinations."},{"startTime":2837.035,"endTime":2840.175,"body":"So that's why you only got half a Nobel price, right?"},{"startTime":2841.035,"endTime":2843.015,"body":"So what did William S. Sharp add to this?"},{"startTime":2843.165,"endTime":2847.338,"body":"William S. Sharp said, well, there's something you've left out here and the one thing"},{"startTime":2847.338,"endTime":2849.565,"body":"he had left out was a risk asset."},{"startTime":2849.565,"endTime":2853.845,"body":"Risk-free asset will be there on the Y axis, right?"},{"startTime":2854.075,"endTime":2855.125,"body":"That is not there."},{"startTime":2855.865,"endTime":2859.805,"body":"So William Sharp said, fine, what happens if you put in a risk-free asset?"},{"startTime":2860.385,"endTime":2862.325,"body":"How does it change what we are gonna do?"},{"startTime":2863.025,"endTime":2867.588,"body":"It turns out that every combination of a risk-free asset and any other asset lies"},{"startTime":2867.588,"endTime":2868.805,"body":"on a straight line."},{"startTime":2869.465,"endTime":2869.685,"body":"Why?"},{"startTime":2869.715,"endTime":2873.205,"body":"Because the core variance of anything, how much does the risk-free asset move?"},{"startTime":2873.265,"endTime":2877.401,"body":"It doesn't move, doesn't depend on the weather, doesn't depend on the economy, gives you"},{"startTime":2877.401,"endTime":2877.677,"body":"the same amount, the core variance of anything with the risk-free asset, zero variance, the"},{"startTime":2877.677,"endTime":2882.365,"body":"risk-free asset zero."},{"startTime":2882.985,"endTime":2887.725,"body":"So every combination of anything, the risk-free asset will lie on a straight line, right?"},{"startTime":2888.025,"endTime":2891.349,"body":"If you have half your money in the risk-free asset, half money in the risk"},{"startTime":2891.349,"endTime":2893.565,"body":"is halfway there and so on and so forth, fine."},{"startTime":2893.945,"endTime":2899.304,"body":"So what he then said was, alright, let's draw a tangent line between any of"},{"startTime":2899.304,"endTime":2901.805,"body":"the intermediate points to the efficient frontier."},{"startTime":2902.825,"endTime":2907.156,"body":"Now, if you don't like risk at all, you can invest all your money in"},{"startTime":2907.156,"endTime":2907.445,"body":"rf."},{"startTime":2907.985,"endTime":2911.445,"body":"If you like a moderate amount of risk, you can invest on the white line."},{"startTime":2911.945,"endTime":2916.805,"body":"The white line is always above every efficient portfolio on the curve."},{"startTime":2917.425,"endTime":2924.347,"body":"So what he's basically saying is a white line is a combination of RF and"},{"startTime":2924.347,"endTime":2929.885,"body":"a balanced fund, which is a ency portfolio to that curve, right?"},{"startTime":2929.885,"endTime":2930.725,"body":"That's all we need."},{"startTime":2930.865,"endTime":2934.165,"body":"So he says, everybody in the world should invest only in two assets."},{"startTime":2934.565,"endTime":2939.927,"body":"A risk-free asset, and a broad based market fund, which covers every security in the"},{"startTime":2939.927,"endTime":2940.285,"body":"world."},{"startTime":2940.345,"endTime":2944.395,"body":"If you can get it, if you can't get it, take as broad based an"},{"startTime":2944.395,"endTime":2945.205,"body":"index as possible."},{"startTime":2945.745,"endTime":2950.967,"body":"So the s and p 500 index or the MSC global MSCI global index take"},{"startTime":2950.967,"endTime":2953.405,"body":"as broad based an index as possible."},{"startTime":2953.705,"endTime":2956.285,"body":"That's the efficient way to proceed, okay?"},{"startTime":2956.705,"endTime":2959.645,"body":"But that means we can now derive an equation."},{"startTime":2959.785,"endTime":2963.79,"body":"Now this goes back to high school trigonometry, and the equation of a line is"},{"startTime":2963.79,"endTime":2964.325,"body":"very straightforward."},{"startTime":2964.765,"endTime":2968.647,"body":"Y the number on the Y axis is equal to the intercept plus slope times"},{"startTime":2968.647,"endTime":2969.165,"body":"X axis."},{"startTime":2969.555,"endTime":2972.045,"body":"Everybody presumably remembers that from high school."},{"startTime":2972.555,"endTime":2973.885,"body":"Okay, fine."},{"startTime":2974.195,"endTime":2975.605,"body":"What is, we'll drop that."},{"startTime":2975.605,"endTime":2976.485,"body":"That's Sigma M."},{"startTime":2976.985,"endTime":2982.826,"body":"That's the expected return on M, that's rf and that's the distance, the perpendicular and"},{"startTime":2982.826,"endTime":2983.605,"body":"the base."},{"startTime":2983.705,"endTime":2986.965,"body":"So the slope of a line perpendicular divided by the base, right?"},{"startTime":2987.425,"endTime":2992.439,"body":"So what do we have the expected return to a portfolio number in the Y"},{"startTime":2992.439,"endTime":2992.773,"body":"axis is the risk free rate, the intercept plus the perpendicular RMM minus RF divided"},{"startTime":2992.773,"endTime":3001.465,"body":"by the base sigma M times the standard deviation of the portfolio."},{"startTime":3001.695,"endTime":3004.065,"body":"That is a version of the CAPM."},{"startTime":3004.495,"endTime":3007.993,"body":"What that tells you is if you give me the expected, the standard deviation of"},{"startTime":3007.993,"endTime":3008.226,"body":"the portfolio, I can plug it in here and tell you what the expected return"},{"startTime":3008.226,"endTime":3012.425,"body":"of the portfolio is."},{"startTime":3014.245,"endTime":3015.905,"body":"How useful is this equation?"},{"startTime":3018.695,"endTime":3019.705,"body":"Totally useless."},{"startTime":3020.285,"endTime":3020.505,"body":"Why?"},{"startTime":3021.295,"endTime":3026.945,"body":"Well, it's because we already know that all these lines lie on a straight line."},{"startTime":3027.025,"endTime":3030.718,"body":"We don't need all those calculations to figure out what is the equation of that"},{"startTime":3030.718,"endTime":3030.965,"body":"line."},{"startTime":3030.965,"endTime":3032.285,"body":"We already had it from history."},{"startTime":3032.755,"endTime":3035.205,"body":"What we want is the individual assets."},{"startTime":3036.305,"endTime":3039.445,"body":"How do the individual assets, what's the formula for that?"},{"startTime":3039.745,"endTime":3041.845,"body":"And this formula doesn't work for that."},{"startTime":3043.025,"endTime":3048.125,"body":"So how do we go from a portfolio to an individual asset to understand that?"},{"startTime":3048.295,"endTime":3050.245,"body":"Let's go back to this one here, right?"},{"startTime":3051.275,"endTime":3057.959,"body":"I've now established that everybody in the whole world is holding the risk-free asset and"},{"startTime":3057.959,"endTime":3061.525,"body":"the market portfolio M the balanced portfolio, right?"},{"startTime":3061.785,"endTime":3063.165,"body":"The global portfolio."},{"startTime":3063.795,"endTime":3068.328,"body":"That means if I say invest in my company, that person is gonna say, okay,"},{"startTime":3068.328,"endTime":3068.631,"body":"how much does my risk go up if I add you to what I'm already"},{"startTime":3068.631,"endTime":3073.165,"body":"holding?"},{"startTime":3073.385,"endTime":3075.325,"body":"But what am I holding the market portfolio?"},{"startTime":3075.785,"endTime":3081.728,"body":"So the measure of risk is relative to what I'm already holding the market portfolio,"},{"startTime":3081.728,"endTime":3082.125,"body":"okay?"},{"startTime":3082.625,"endTime":3088.495,"body":"But going back to this line here, if I add one new asset to my,"},{"startTime":3088.495,"endTime":3088.886,"body":"to my portfolio over there, I'm adding only one variance term the diagonal, but I'm"},{"startTime":3088.886,"endTime":3099.845,"body":"adding two NN here and N there core variance terms, which is more important."},{"startTime":3100.065,"endTime":3108.399,"body":"The core variance or the variance, obviously two end core variances only one core variance"},{"startTime":3108.399,"endTime":3108.955,"body":"term."},{"startTime":3109.495,"endTime":3111.955,"body":"The core variance is way more important than the variance."},{"startTime":3112.295,"endTime":3117.545,"body":"Put that into another way of thinking about it is you have a bag full"},{"startTime":3117.545,"endTime":3118.595,"body":"of animals, right?"},{"startTime":3118.595,"endTime":3119.635,"body":"They're all in the bag."},{"startTime":3119.815,"endTime":3124.068,"body":"You stick a tiger into the bag, the movement of the tiger isn't as important"},{"startTime":3124.068,"endTime":3127.755,"body":"as the movement of all the other animals reacting to the tiger, right?"},{"startTime":3127.935,"endTime":3131.657,"body":"That's why we say the core variance is how the other animals in the bag"},{"startTime":3131.657,"endTime":3133.395,"body":"react to the introduction of the tiger."},{"startTime":3134.255,"endTime":3138.858,"body":"But the tiger itself moves a little bit, not going to really affect how much"},{"startTime":3138.858,"endTime":3143.155,"body":"a bag moves may affect it a little bit, but really not very much."},{"startTime":3143.985,"endTime":3144.275,"body":"Okay?"},{"startTime":3144.695,"endTime":3149.716,"body":"So the idea therefore is if everybody's holding the market portfolio, what we want is"},{"startTime":3149.716,"endTime":3151.725,"body":"the core variance with the market."},{"startTime":3152.395,"endTime":3155.005,"body":"That means how much does the market move?"},{"startTime":3155.025,"endTime":3159.045,"body":"If you add your security to that market, how close are you to that market?"},{"startTime":3159.515,"endTime":3163.975,"body":"Okay, that is called the beta, another Greek letter."},{"startTime":3164.925,"endTime":3166.575,"body":"Okay, so what is the beta?"},{"startTime":3166.805,"endTime":3171.084,"body":"Well, that's a core variance, but the core variance changes depending on how much the"},{"startTime":3171.084,"endTime":3171.655,"body":"market's moving."},{"startTime":3171.995,"endTime":3175.7,"body":"If the market's moving a lot, the core variance will be high, purely artificially, nothing"},{"startTime":3175.7,"endTime":3176.935,"body":"to do with the stock."},{"startTime":3177.355,"endTime":3178.415,"body":"The core variance is high."},{"startTime":3179.115,"endTime":3183.133,"body":"So you need to standardize it by dividing it by the variance in the market"},{"startTime":3183.133,"endTime":3183.401,"body":"to control for points in time when the variance is high and the core variance,"},{"startTime":3183.401,"endTime":3189.295,"body":"uh, or when the variance is low, right?"},{"startTime":3189.295,"endTime":3190.575,"body":"You're controlling for all of that."},{"startTime":3191.515,"endTime":3195.857,"body":"So we also know if everyone's holding the market portfolio, the beta of the risk-free"},{"startTime":3195.857,"endTime":3197.015,"body":"asset must be zero."},{"startTime":3197.675,"endTime":3197.895,"body":"Why?"},{"startTime":3197.895,"endTime":3201.655,"body":"Because the co variance of anything with a risk-free asset is zero."},{"startTime":3202.395,"endTime":3204.735,"body":"We also know the beta, the market must be one."},{"startTime":3205.025,"endTime":3205.245,"body":"Why?"},{"startTime":3205.245,"endTime":3208.405,"body":"Because the core variance of the market with itself is its variance."},{"startTime":3208.405,"endTime":3210.085,"body":"Variance divided by variance is one."},{"startTime":3211.145,"endTime":3216.038,"body":"So putting that into context, this is the final equation we are going to look"},{"startTime":3216.038,"endTime":3216.365,"body":"at."},{"startTime":3216.755,"endTime":3220.575,"body":"What this says is the risk-free asset has a beta zero, the market has a"},{"startTime":3220.575,"endTime":3221.085,"body":"beta one."},{"startTime":3222.555,"endTime":3224.655,"body":"So what is the equation of this line?"},{"startTime":3225.325,"endTime":3226.935,"body":"Well, again, the same thing."},{"startTime":3227.335,"endTime":3233.362,"body":"Y is intercept plus slope times x, the intercept, the slope is perpendicular divided by"},{"startTime":3233.362,"endTime":3236.175,"body":"base RM minus RF divided by one."},{"startTime":3237.515,"endTime":3239.095,"body":"The intercept is just rf."},{"startTime":3240.155,"endTime":3241.975,"body":"So that's a formula, right?"},{"startTime":3242.575,"endTime":3246.575,"body":"Expected return is RF plus beta times RM minus rf, right?"},{"startTime":3246.885,"endTime":3252.145,"body":"That number, that equation is called the capital asset pricing model."},{"startTime":3252.415,"endTime":3256.5,"body":"What that basically says is if you can compute the beta, which is the core"},{"startTime":3256.5,"endTime":3260.585,"body":"variance of anything with the market, that tells you how risky that asset is, okay?"},{"startTime":3260.805,"endTime":3267.225,"body":"In this particular case, expected return is RF plus beta time RM minus rf, right?"},{"startTime":3267.575,"endTime":3271.825,"body":"That formula got William Sharp, his half of the Nobel price, right?"},{"startTime":3272.085,"endTime":3277.541,"body":"So two parts, one part, getting to the fact that only people would hold efficient"},{"startTime":3277.541,"endTime":3277.905,"body":"portfolios."},{"startTime":3278.125,"endTime":3282.641,"body":"The other one going one step beyond introducing a risk-free asset, which would give you"},{"startTime":3282.641,"endTime":3283.545,"body":"this formula here."},{"startTime":3284.525,"endTime":3286.505,"body":"So everybody okay with this?"},{"startTime":3286.505,"endTime":3291.545,"body":"With risk sort of, okay, let's see if you really understood this."},{"startTime":3292.155,"endTime":3298.366,"body":"Let's say we have two companies, solar mat in Madagascar where the environment, lots of"},{"startTime":3298.366,"endTime":3301.265,"body":"degradation, deforestation over overgrazing and so on."},{"startTime":3301.535,"endTime":3307.906,"body":"Lots of major infectious diseases, high food insecurity, and it has repeated bouts of political"},{"startTime":3307.906,"endTime":3311.305,"body":"instability including coups, violent unrest, and disputed elections."},{"startTime":3311.445,"endTime":3312.425,"body":"That's Madagascar."},{"startTime":3312.735,"endTime":3313.025,"body":"Okay?"},{"startTime":3313.525,"endTime":3319.341,"body":"The other side, Tesco in the uk, while the UK has a whole bunch of"},{"startTime":3319.341,"endTime":3320.505,"body":"environmental problems, right?"},{"startTime":3320.805,"endTime":3324.105,"body":"We have health, we have obesity issues, ozempic, all these things."},{"startTime":3324.565,"endTime":3327.065,"body":"We also have high inflation, right?"},{"startTime":3327.405,"endTime":3330.305,"body":"Um, and we have high political uncertainty, right?"},{"startTime":3330.925,"endTime":3338.945,"body":"So all these things together, the question is right, which one is riskier?"},{"startTime":3339.415,"endTime":3339.705,"body":"Okay?"},{"startTime":3339.885,"endTime":3341.825,"body":"So that's what we want to establish, right?"},{"startTime":3341.835,"endTime":3343.825,"body":"Which should have a higher discount rate."},{"startTime":3344.245,"endTime":3348.225,"body":"So what we have is the Madagascar central bank rate is nine 8.9."},{"startTime":3348.245,"endTime":3352.185,"body":"The Bank of England bank rate is 5.25 GDP growth rate 4.4."},{"startTime":3352.295,"endTime":3357.105,"body":"This is about 0.2 inflation rate 9.31, inflation rate 6.5."},{"startTime":3357.205,"endTime":3361.625,"body":"And the Madagascar market is about four times as volatile as the UK market."},{"startTime":3362.045,"endTime":3370.105,"body":"So for you guys, final question, what do you think should be the risk-free rates."},{"startTime":3370.445,"endTime":3372.425,"body":"Uh, sorry, the discount rates."},{"startTime":3372.965,"endTime":3376.265,"body":"So if you think Tesco is low risk, that should be here."},{"startTime":3376.565,"endTime":3378.705,"body":"If you think solar matter is low risk, it should be there."},{"startTime":3378.845,"endTime":3381.465,"body":"If you think solar matter is high risk, it should be here and so on."},{"startTime":3381.465,"endTime":3384.045,"body":"So just drag your pointer on your phone."},{"startTime":3415.905,"endTime":3416.185,"body":"Brilliant."},{"startTime":3416.355,"endTime":3416.705,"body":"Right?"},{"startTime":3416.725,"endTime":3418.865,"body":"And this is common sense, right?"},{"startTime":3419.075,"endTime":3421.505,"body":"Solar MAD is riskier than Tesco."},{"startTime":3422.685,"endTime":3425.775,"body":"Also completely wrong, right?"},{"startTime":3426.155,"endTime":3426.375,"body":"Why?"},{"startTime":3427.005,"endTime":3429.575,"body":"Well think about what the CAPM is telling you."},{"startTime":3429.995,"endTime":3435.066,"body":"It says how much risk do you take on when you add solar MAD or"},{"startTime":3435.066,"endTime":3437.095,"body":"Tesco to what you're already holding."},{"startTime":3437.835,"endTime":3441.735,"body":"But we here in the uk, what are we holding the UK stock market."},{"startTime":3442.355,"endTime":3448.43,"body":"So if something happens in Madagascar, yes, solar mat is incredibly risky, but it's a"},{"startTime":3448.43,"endTime":3450.455,"body":"small part of a portfolio."},{"startTime":3450.745,"endTime":3454.535,"body":"Madagascar is uncorrelated with the restaurant portfolio, the risk doesn't matter."},{"startTime":3456.385,"endTime":3458.135,"body":"Tesco is a big part of the UK market."},{"startTime":3458.555,"endTime":3463.338,"body":"If something happens to Tesco, our entire portfolio is affected because we are already holding"},{"startTime":3463.338,"endTime":3464.295,"body":"the UK market."},{"startTime":3464.555,"endTime":3468.805,"body":"If you're a global investor, the UK is the bigger part of the world than"},{"startTime":3468.805,"endTime":3469.655,"body":"Madagascar is, right?"},{"startTime":3470.195,"endTime":3472.255,"body":"The key part is what are you holding?"},{"startTime":3472.595,"endTime":3477.255,"body":"If you're holding a big global diversified index, which you should be,"},{"startTime":3479.545,"endTime":3483.355,"body":"Tesco is way riskier than Solared, okay?"},{"startTime":3483.575,"endTime":3486.035,"body":"That's the takeaway which we have over here."},{"startTime":3486.035,"endTime":3487.715,"body":"That's the counterintuitive part."},{"startTime":3488.055,"endTime":3493.235,"body":"We don't care about risk, which is unique to Madagascar."},{"startTime":3493.235,"endTime":3493.835,"body":"That's risk."},{"startTime":3493.835,"endTime":3495.115,"body":"You can diversify away from."},{"startTime":3495.615,"endTime":3499.571,"body":"You can just buy as many securities as you can and you don't care about"},{"startTime":3499.571,"endTime":3499.835,"body":"Madagascar."},{"startTime":3499.835,"endTime":3501.075,"body":"It's a tiny part of your portfolio."},{"startTime":3501.895,"endTime":3504.315,"body":"But some stuff you cannot get away from."},{"startTime":3504.385,"endTime":3507.731,"body":"Even if you hold every stock in the world, the price of oil will affect"},{"startTime":3507.731,"endTime":3507.955,"body":"you."},{"startTime":3508.695,"endTime":3510.395,"body":"War geopolitical risk will affect you."},{"startTime":3510.395,"endTime":3511.635,"body":"Climate change will affect you."},{"startTime":3511.975,"endTime":3514.115,"body":"How much it affects you depends on the beta."},{"startTime":3514.535,"endTime":3516.115,"body":"And that's what the CAPM says."},{"startTime":3516.615,"endTime":3521.431,"body":"The higher the beta, the higher the level of risk and therefore the more returns"},{"startTime":3521.431,"endTime":3522.395,"body":"you ask for."},{"startTime":3523.145,"endTime":3523.435,"body":"Okay?"},{"startTime":3525.255,"endTime":3526.475,"body":"And that's it."},{"startTime":3537.445,"endTime":3539.795,"body":"Thank you very much Professor Rao."},{"startTime":3539.795,"endTime":3540.395,"body":"That was great."},{"startTime":3540.705,"endTime":3543.36,"body":"I've got a few questions on here, then I'm gonna come to the audience in"},{"startTime":3543.36,"endTime":3543.715,"body":"the room."},{"startTime":3544.455,"endTime":3548.805,"body":"So first question is, how do we account for the fact the correlations we input"},{"startTime":3548.805,"endTime":3550.835,"body":"into the model are only historically relevant?"},{"startTime":3551.215,"endTime":3553.475,"body":"We don't know how they're gonna work as forecasts."},{"startTime":3554.175,"endTime":3555.195,"body":"Um, good question."},{"startTime":3555.385,"endTime":3555.995,"body":"Good question."},{"startTime":3556.415,"endTime":3562.005,"body":"Yes, the numbers are all historical numbers and ideally we would like forward looking numbers."},{"startTime":3562.505,"endTime":3565.868,"body":"But with all due respect, if you know the forward correlations, you should not be"},{"startTime":3565.868,"endTime":3566.765,"body":"here in this lecture."},{"startTime":3566.985,"endTime":3569.685,"body":"You should have your own private island somewhere in the Caribbean."},{"startTime":3569.855,"endTime":3573.085,"body":"Maybe not island anymore because of climate change, but whatever, right?"},{"startTime":3573.185,"endTime":3574.485,"body":"You should have your own layer."},{"startTime":3574.905,"endTime":3579.067,"body":"So the best we can do indeed, is to look at historical stuff, but look"},{"startTime":3579.067,"endTime":3581.565,"body":"at it for a very long period of time."},{"startTime":3582.025,"endTime":3586.051,"body":"So for example, when we compute things like the risk premium, we go back all"},{"startTime":3586.051,"endTime":3587.125,"body":"the way to 1925."},{"startTime":3587.705,"endTime":3587.925,"body":"Why?"},{"startTime":3587.925,"endTime":3589.205,"body":"Because we have that data."},{"startTime":3589.625,"endTime":3591.445,"body":"And why do we need to go so far back?"},{"startTime":3591.515,"endTime":3592.845,"body":"Well think of 1925."},{"startTime":3593.295,"endTime":3595.245,"body":"We've had great depression."},{"startTime":3595.305,"endTime":3596.525,"body":"We have had world wars."},{"startTime":3596.575,"endTime":3602.845,"body":"We've had multiple local conflicts, we've had disease outbreaks, we've had literally everything."},{"startTime":3603.145,"endTime":3605.365,"body":"So the number is going to be there."},{"startTime":3605.365,"endTime":3607.165,"body":"Something history repeats itself."},{"startTime":3607.185,"endTime":3612.228,"body":"So the idea is long periods of history should indeed be work for future we"},{"startTime":3612.228,"endTime":3612.565,"body":"hope."},{"startTime":3612.615,"endTime":3612.965,"body":"Right?"},{"startTime":3613.465,"endTime":3614.445,"body":"Of course, we hope."},{"startTime":3614.645,"endTime":3616.165,"body":"I can't guarantee anything \u003claugh\u003e."},{"startTime":3616.785,"endTime":3617.205,"body":"We hope."},{"startTime":3617.425,"endTime":3621.193,"body":"And and also we have to bear in mind that they don't affect the individual"},{"startTime":3621.193,"endTime":3621.445,"body":"stocks."},{"startTime":3621.445,"endTime":3621.925,"body":"We have to be careful."},{"startTime":3621.985,"endTime":3628.228,"body":"We don't put a whole theory onto buying one stock, which 'cause basically people are"},{"startTime":3628.228,"endTime":3628.645,"body":"gamblers."},{"startTime":3628.645,"endTime":3629.925,"body":"They, they're, they're optimists."},{"startTime":3629.925,"endTime":3632.085,"body":"That's why more people wanted ice cream than umbrellas."},{"startTime":3634.365,"endTime":3634.605,"body":"Excellent."},{"startTime":3635.085,"endTime":3636.285,"body":"Actually that is an interesting point."},{"startTime":3636.345,"endTime":3637.485,"body":"I'm gonna build on that a little bit."},{"startTime":3637.545,"endTime":3640.901,"body":"One of the things which a lot of people say is, I'm not diversified myself,"},{"startTime":3640.901,"endTime":3641.125,"body":"right?"},{"startTime":3641.185,"endTime":3642.285,"body":"I'm only holding Tesco."},{"startTime":3642.385,"endTime":3644.725,"body":"I'm, I'm not really holding the entire market."},{"startTime":3645.185,"endTime":3649.614,"body":"Why does this risk, why am I not taking solar Mat is very risky compared"},{"startTime":3649.614,"endTime":3650.205,"body":"to Tesco."},{"startTime":3650.825,"endTime":3655.241,"body":"The answer is if you're holding, if you're not diversified, you are taking on a"},{"startTime":3655.241,"endTime":3656.125,"body":"lot of risk."},{"startTime":3656.435,"endTime":3659.125,"body":"That means you're not willing to pay so much per share."},{"startTime":3659.665,"endTime":3661.845,"body":"Who is the person who pays a lot per share?"},{"startTime":3662.065,"endTime":3663.205,"body":"The guy who's diversified."},{"startTime":3663.205,"endTime":3665.405,"body":"Because the risk doesn't matter that much to that person."},{"startTime":3666.005,"endTime":3669.325,"body":"A big mutual fund, a big pension fund, they're highly diversified."},{"startTime":3669.745,"endTime":3671.245,"body":"So they set the price."},{"startTime":3672.145,"endTime":3674.445,"body":"If you're not diversified, you're not in the market."},{"startTime":3674.445,"endTime":3677.445,"body":"You're not willing to pay high enough a price to get there."},{"startTime":3677.825,"endTime":3678.725,"body":"So it doesn't matter."},{"startTime":3679.305,"endTime":3683.485,"body":"So the people who are setting the prices are indeed the diversified investors."},{"startTime":3683.785,"endTime":3684.965,"body":"That's why all this works."},{"startTime":3686.035,"endTime":3686.325,"body":"Okay,"},{"startTime":3686.975,"endTime":3687.445,"body":"Thank you."},{"startTime":3687.785,"endTime":3690.485,"body":"Now, anyone here would like to ask a question?"},{"startTime":3692.125,"endTime":3694.365,"body":"I gentleman down here, just wait one moment for the microphone."},{"startTime":3697.495,"endTime":3702.173,"body":"Going back to the very early part of your talk, you didn't build in several"},{"startTime":3702.173,"endTime":3702.485,"body":"factors."},{"startTime":3702.665,"endTime":3707.942,"body":"One, the inflation rate going at the current time in any market, which, which actually"},{"startTime":3707.942,"endTime":3710.405,"body":"influences the way trading happens in markets."},{"startTime":3711.105,"endTime":3716.31,"body":"Um, which infl again impacts on the rates you get on various, uh, uh, on"},{"startTime":3716.31,"endTime":3717.005,"body":"various investments."},{"startTime":3717.305,"endTime":3721.069,"body":"Um, and the other thing, you didn't actually on the, on the umbrella and ice"},{"startTime":3721.069,"endTime":3721.32,"body":"cream model, you didn't allow us to have shares in ice cream for the six"},{"startTime":3721.32,"endTime":3721.571,"body":"months in the warmer period and uh, six months for umbrellas in the winter period,"},{"startTime":3721.571,"endTime":3730.605,"body":"which is where you get make the profit."},{"startTime":3731.745,"endTime":3732.685,"body":"That's a very good point."},{"startTime":3732.745,"endTime":3736.557,"body":"The second point in particular, you can switch back and forth between in the different"},{"startTime":3736.557,"endTime":3738.845,"body":"parts of the year, warmer months, cooler month, fine."},{"startTime":3739.015,"endTime":3739.365,"body":"Right?"},{"startTime":3739.545,"endTime":3741.405,"body":"But that doesn't affect the basic model."},{"startTime":3741.475,"endTime":3745.781,"body":"Even if you do that, allow that you can actually still run through exactly the"},{"startTime":3745.781,"endTime":3748.365,"body":"same calculations to get the idea that you're diversifying."},{"startTime":3748.415,"endTime":3748.765,"body":"Right."},{"startTime":3749.025,"endTime":3751.565,"body":"And again, think climate change, right?"},{"startTime":3751.665,"endTime":3754.405,"body":"Are you really gonna have warm winters or warm summers here?"},{"startTime":3754.405,"endTime":3754.885,"body":"We don't know."},{"startTime":3755.175,"endTime":3755.685,"body":"Could be."},{"startTime":3756.345,"endTime":3757.085,"body":"But you couldn't."},{"startTime":3757.145,"endTime":3759.485,"body":"But we don't, can't predict the future, right?"},{"startTime":3759.985,"endTime":3765.778,"body":"Um, your other question, um, was about things like inflation and other factors, expectations built"},{"startTime":3765.778,"endTime":3766.165,"body":"in."},{"startTime":3766.465,"endTime":3770.085,"body":"We are assuming they're built into the rates which people are asking for."},{"startTime":3770.105,"endTime":3774.288,"body":"So they take that into account when deciding, number one, how much do government bonds"},{"startTime":3774.288,"endTime":3775.125,"body":"to buy, right?"},{"startTime":3775.125,"endTime":3776.565,"body":"Because they have to worry about inflation."},{"startTime":3776.665,"endTime":3778.525,"body":"How much will the bond actually by me?"},{"startTime":3778.825,"endTime":3781.685,"body":"So those expectations are built into the numbers already."},{"startTime":3784.145,"endTime":3784.565,"body":"Lovely."},{"startTime":3785.175,"endTime":3785.605,"body":"Thank you."},{"startTime":3785.635,"endTime":3788.725,"body":"It's past, oh sorry, one more question and then that's the last one."},{"startTime":3788.885,"endTime":3790.005,"body":"'cause we are past seven o'clock."},{"startTime":3790.005,"endTime":3790.285,"body":"Sorry."},{"startTime":3790.325,"endTime":3790.805,"body":"I just realized"},{"startTime":3792.785,"endTime":3794.005,"body":"Thanks for a great talk."},{"startTime":3794.505,"endTime":3798.833,"body":"Um, it seems like the core variance between one stock to all the other stocks"},{"startTime":3798.833,"endTime":3800.565,"body":"in your portfolio is very important."},{"startTime":3801.185,"endTime":3802.725,"body":"How do you exactly calculate that?"},{"startTime":3802.985,"endTime":3808.307,"body":"It seems like you assume that you need to have the expected, like the performance"},{"startTime":3808.307,"endTime":3812.565,"body":"in three different categories, like normal time, refresh, uh, recession, and um"},{"startTime":3813.495,"endTime":3813.845,"body":"Right."},{"startTime":3814.155,"endTime":3814.645,"body":"Good time."},{"startTime":3814.955,"endTime":3815.245,"body":"Okay."},{"startTime":3815.245,"endTime":3819.94,"body":"So the background to everything we did was to assume that we knew different states"},{"startTime":3819.94,"endTime":3822.445,"body":"of the world and we assumed the probabilities."},{"startTime":3822.985,"endTime":3827.173,"body":"But later on, once we know what the returns are, right, based on historical factors"},{"startTime":3827.173,"endTime":3830.245,"body":"goes back to a little bit what Lucy was talking about."},{"startTime":3830.785,"endTime":3834.535,"body":"We kind of say, okay, over the past a hundred years, that's the expected return"},{"startTime":3834.535,"endTime":3835.285,"body":"for the stock."},{"startTime":3835.305,"endTime":3836.645,"body":"We are using historical data."},{"startTime":3837.065,"endTime":3841.208,"body":"But once you have the returns to each individual security, you don't need the probabilities"},{"startTime":3841.208,"endTime":3841.485,"body":"anymore."},{"startTime":3841.905,"endTime":3843.405,"body":"You assume that built into the numbers."},{"startTime":3844.145,"endTime":3847.805,"body":"So it doesn't apply to new stocks that you don't have that historical, uh, true."},{"startTime":3847.805,"endTime":3851.862,"body":"But then think of the fact here that these are market, make, uh, market participants"},{"startTime":3851.862,"endTime":3853.485,"body":"who are taking this into account."},{"startTime":3853.825,"endTime":3858.275,"body":"If you think a recession is now much higher probability than before, do you buy"},{"startTime":3858.275,"endTime":3859.165,"body":"stocks or bonds?"},{"startTime":3859.385,"endTime":3862.891,"body":"You buy bonds because you know that stocks are gonna do badly in a recession,"},{"startTime":3862.891,"endTime":3863.125,"body":"right?"},{"startTime":3863.225,"endTime":3868.085,"body":"So the numbers, the prices will adjust based on people's estimates of the true probability."},{"startTime":3869.955,"endTime":3870.245,"body":"Okay?"},{"startTime":3870.375,"endTime":3875.128,"body":"These are assumptions and we'll see in the last lecture on, in June next year,"},{"startTime":3875.128,"endTime":3879.565,"body":"that people sometimes go crazy and the market behave in very weird ways, right?"},{"startTime":3879.585,"endTime":3881.565,"body":"But that's a subject for next year."},{"startTime":3881.995,"endTime":3882.285,"body":"Okay."},{"startTime":3882.945,"endTime":3884.685,"body":"On that note, can you please join me in?"},{"startTime":3884.685,"endTime":3886.285,"body":"Thank you Professor ."},{"startTime":3886.735,"endTime":3887.245,"body":"Thank you."}]}