 Hi everyone, it's MJ the fellow actuary and in this video we're gonna be looking at capital asset pricing models and this is gonna be a long video and Posting it on both you to me as well as YouTube But now if you're watching it on YouTube and we start talking about things that you have no idea What's going on then you might want to come to you to me because you need to understand mean variance portfolio theory You can see there's a whole bunch of videos that we have there And I guess to even understand mean variance portfolio theory you have to understand risk measures You have to understand a little bit about economics utility theory Financial markets and all that kind of stuff which you can find on you to me So I guess this is like a little a little bit of an ad for it And you can kind of see these are what all of the various slides would have looked like for that But we are gonna be focusing on capital asset pricing models So let's start the slideshow so like I said if you need more background information check out the Udemy course Otherwise, there should be some of you who just want to have a quick refresher on capital asset pricing models Because capital asset pricing models or otherwise known as CAPM. We see that they're going to be an extension Because for individual investors we spoke about this thing called the mean variance portfolio theory Which says where should I invest my money? You know if I want to minimize risk, how do I maximize return? You know, it's like how do I go about placing my investments now? There's also multi-factor models But essentially this mean variance portfolio theory is what links to capital asset pricing models because if MVP T is for individuals We're gonna see that CAPM can be extended for all the investors in the market Now you can also do arbitrage pricing theory, which we will discuss at another time So the big idea here is that CAPM is an extension of the mean variance portfolio theory And like we see it I mean mean variance portfolio theory It's how to basically design your portfolio looking just at mean and variant remember mean you want to maximize Variants you want to minimize. It's it's not that simple, but I guess that's the idea in a nutshell Whereas capital asset pricing models We're gonna see that this is more of an equilibrium model and it tells us how the whole market invests And again, this is maybe a bit of we're thinking about it It's the rationale of why the market capitalization is the way it is, you know so why does the market allocate x percent to company a and we can use this model to determine the required rate of return of an asset in a well-diversified portfolio now it is very very academic and we're gonna be looking at some of the criticisms a lot later but reason why I say it's very academic is because it has a whole bunch of Assumptions which really limits its practical use, but we'll see that with these assumptions we can build a little bit of academic theory around it and This is also I guess the reasoning behind passive investing So if you are a passive investor, you'll find this stuff very very interesting if you're an active investor You're gonna be thinking this is so dumb So just bear that in mind depending on what type of investor you are Because what we're gonna see is that it inherits all the assumptions from the mean variants portfolio theory You know assumptions like we're not gonna be looking at taxes or transaction fees and already those of you who are working in finance You know how important those things are and how they sway a lot of behavior Then we're also gonna be assuming that investors behave rationally and have access to information Which yeah again like I said you can criticize all of these ones But let's just maybe go through them that investment decisions are based purely on risk and return It's maybe nice to think about what else to investors base their decisions on And I mean one of them is you know heard mentality What are your friends investing in that's gonna also influence what you invest in but with this academic theory We're gonna try to take away as much of the psychology out of finance, which I think is wrong, but Like I say we'll we'll hold the criticisms to cap him maybe towards the end of the video So we're also gonna be assuming that your assets are perfectly divisible and can be held in any amount And we're also gonna be inheriting a bunch of assumptions from utility theory And that is that investors are non-satiated which is just a fancy way of saying not satisfied We always want more and we're also gonna be assuming that investors are risk averse You know we'll would have scaredy cats. We don't like to take on too much risk. It makes us feel uncomfortable Then we're also going to Inherent all the assumptions from the efficient market hypothesis and the big one here is that all information is known and Accessible we're talking about returns variances covariance appears I mean that's a lot of information that we need to be aware of that. We're just assuming everyone has has access to We're assuming everyone understands it. We're assuming none of it got corrupted and yeah, I mean Mandelbrot talks a lot about the inefficiencies or the problems with this assumption But like I say it's important to be aware of all of the assumptions I mean that's a very I guess it's a very actuarial thing is Because we build models and the first thing you do when you build a model is you lay down the assumptions and a good Actuary will look not only at the explicit assumptions, but also the implicit ones I think that's why yeah, we I get excited about assumptions because it's kind of the things that you can you can pull apart If anything I get more excited about the assumptions than the actual Mathematics which we will also be looking at a little bit later on in this video but we're also gonna have some extra assumptions with CAPM and While we need some extra assumptions is because we're dealing with all investors. It's the whole market So we're gonna be assuming some things about all these investors and one thing We're gonna just assume is that they all have the same one period horizon So whether they're you know a young person who's just getting into the workforce who has maybe a 40 year time horizon to a Pension person who's you know gonna be retiring soon. That's maybe got six months You know, we're gonna just ignore ignore what the world is and and demographics and all those things and we're just gonna assume everyone has The same one period horizon We're also gonna assume that anyone can borrow and lend Unlimited amounts at the same risk-free rate. So we're just assuming that there's infinite money to be borrowed But you go to a bank and try and borrow an unlimited amount and you'll see how unrealistic that one is But we're gonna see that they also all have the same estimates of expected returns variances co variances for all Securities and I think that's an important one to also maybe just pause and reflect on because each asset house each investment firm is gonna, you know Have slightly different models put more emphasis on some information than others And it's very very unlikely that we all have the same estimates of these statistics But let's just assume that that they are the same and that we're also gonna assume that we're all using the same currency In the same real term. So we're ignoring Exchanges inflations and geopolitics and all that kind of stuff just to try and make things a little bit simpler So let's now look at the consequences of these additional assumptions And the first one is that now all investors will have the same efficient frontier of risky securities Why because of the same information on risk and return? What we're also going to see now is that this efficient frontier will collapse to a straight line Because all are subject to the same risk-free rate of interest and the risk-free rate has a zero covariance with the market Thus all the investors will hold a combination of the risk-free asset and M and we refer to M as a portfolio of risky assets and you can think of M as the market portfolio So it's consisting of all the risky assets in proportion to their market capitalization Now because of separation theorem the combination of risky assets can be determined without any knowledge of investors Preferences towards risk and return now risk averse investors will therefore hold more risk-free asset than the M and Reseeking investors will hold more M than the risk-free asset, but they will all hold M So you can think of M as the market portfolio Determined by market capitalization. It's the basket of shares that everybody's holding in the same proportion Okay, let's now understand our market approach So if the market is efficient then all prices are correct And if all prices are correct Then the current investors are currently holding the optimal market portfolio of risky assets And if the optimal portfolio risky assets is currently being held Then the proportion of each security in this portfolio is equal to its relative market capitalization So for example, if stock A has a market cap of 75 million and stock B has a market cap of 25 million Then what we can say is that the optimal market portfolio has to be 75 percent in A and 25 percent in B if these are the only two stocks in our investment universe but let's say the optimal market portfolio was actually 80 percent in A and 20 percent in B then what this means is that A is underpriced and B is overpriced Investors would now buy A until its market cap is 80 million and they would sell B until its market cap is 20 million Thus, we'll see that the market cap proportions will equal the optimal market portfolio in the long run Why because of the efficient market hypothesis? So if we had to visualize this We've got our two dimensions. We've got mean and we've got variants. Remember, we want to be Have a lot of mean and we want to have a little bit of variance So the bright green is desirable. The red is undesirable And this is I guess is also an extension of what we looked at in the previous videos Where we have our safe investment, which has got a low variance and a low mean We have a risky investment which has got a higher mean and a higher variance And what we saw with you know, the whole mean variance portfolio theory is that a combination of them isn't a linear line As one would expect but because of covariance and because of the diversification benefit, you know, you do get this bend Of course, I've exaggerated the bend quite a bit for illustrative purposes But you do get this bend which means that it's always better to hold a combination of these assets now what CAPM does is Is it says well, we've also got this risk-free rate over here You can see the risk-free rate has a very very small mean, but it has a variance of zero And what we can now do is we can combine these together So what we have here with with the purple or sorry, let's call it the pink cross you know this you can think of as the the market portfolio and Then what we will see is we've got this green cross and this yellow cross So this green cross is what someone will actually hold and you can see that if they're more risk adverse They'll be lower on the blue line and if they were seeking they'll be higher on the blue line So what we have here at the green cost is somebody who's holding Some of their portfolio in the risk-free rate or the risk-free asset and they're holding some of their portfolio in the market Now if they were to hold all of their money in the market, what we would see is oh Like I guess there's this other position here of the yellow, which is you're holding it all in the market we can see that For the exact same mean There will be a higher variance and therefore it's not an efficient portfolio Because the green one is better because for the same amount of mean you're getting less variance and based on our Assumptions and what we say investors prefer the fact that they are risk adverse They're gonna prefer the green cross rather than the yellow cross and that's why we will see that all the investors Will shift to the straight line away from this combination that excludes the risk-free asset So this is it illustrated visually. Let's maybe look at it mathematically So mathematically we have the following we have this e p is equal to r plus e m minus r Sigma p divided by sigma m So we can look at it like this We have our efficient portfolio where e p is equal to the expected return of any portfolio on the efficient frontier Sigma p is the standard deviation of the return on portfolio p The market portfolio which is e m well e m is going to be equal to our expected return on this market portfolio And sigma m is going to be the standard deviation of the return on the market portfolio And then we have our risk-free asset where r is going to be equal to the rate of this risk-free asset So what does this capital market line mean? Means that the expected return on any efficient portfolio is a linear function of its standard deviation The expected return is equal to the risk-free rate plus the risk premium times the amount of risk Now in order to get more return you need to take on more risk And the risk premium is what we can think of as the gradient of the line And you can also maybe refer to it as the market price of risk and it's given by the following formula where it is The expected return on the market portfolio less the risk-free rate Divided by the standard deviation of the return on the market portfolio So let's think about it a little bit more We have our our capital market line and we see that in order to increase EP which is the expected return of any portfolio on this frontier What we need to do is we need to increase sigma p and this is what we expect of the efficient market The only way to get more return is to take on more risk So if we invest a hundred percent in the market portfolio and zero in the risk-free rate Then what we can see is that our sigma p is going to be equal to sigma m because our portfolio is now the market portfolio And we will see that the EP will equal em as our r and our sigma will cancel each other out Now if we invest a hundred percent in the risk-free and zero in the market portfolio Then we'll see that sigma p is equal to zero because our portfolio is now risk-free Which means that the return that we're going to be getting or expected return that we can get from our portfolio Is going to equal the risk-free rate Now if the risk premium is large should we invest more aggressively? Well, yes, because we're getting a bigger reward for taking on more risk now What makes this risk premium large well a high market return a low risk-free rate, and I guess a low market risk So like I said in the beginning of the video CAPM does have a lot of criticism And I think it's mainly because the assumptions are unrealistic and we see that empirical studies Do not provide strong support for the model and it is hard to test because we need to consider the entire Investment universe and CAPM kind of wants to just focus on capital markets But what if someone invested in themselves, you know human capital for for future earnings or what about houses? I mean back when I was studying finance It was very very unheard of for large investment firms to start purchasing residential property But they're doing that now. What about art watches education NFTs defy crypto? I mean this asset universe is expanding at an accelerated rate Whereas CAPM only tends to look at you know the stock market and maybe a few of the other things in the capital markets so What has been shown though in studies is that we do have the sort of linear relationship between return and Systematic risk over the long run now systematic risk is that which comes from the market and Specific risk is the risk that has been diversified away And we see that return is not related to the specific risk because the idea is like Why should you be rewarded for a risk that you can remove through the whole action of diversification and again? That's something that mean variance portfolio theory kind of justifies But I want to look at a scenario. So, you know, what what could happen? So let's say we have these huge funds and I'm thinking about Vanguard Which gets like a billion dollars coming into it every single day, you know Once they decided to invest passively in order to keep their investment fees low Well, if they decided to take on the strategy Then they would buy the market portfolio. Why because of the efficient market hypothesis But what this starts to do is it starts to put demand pressure on the biggest companies And that's going to cause their prices to rise and because market Capitalization is the number of shares times the share price if the share price starts to rise the market capitalization is also going to rise which means next month this huge fund needs to allocate an even Greater proportion to the biggest companies Causing the prices to rise more and again price times number of shares and because number of shares is staying the same in The short term and the price is increasing the market capitalization is going even more so this passive investment is causing the market capitalization to grow and We send well, yeah I guess it's tends to spiral and spiral and spiral and keeps getting bigger and bigger and bigger It's this this feedback loop Until we have the situation where the biggest companies are so overpriced that it's really hard to justify a Passive strategy and then we see the market corrects itself That's the terminology basically it means it crashes and we see that this occurs roughly once every 10 years But you know the past is not an indicator of the future and we are seeing you know the world Evolve or develop at such an alarming rate that we could even see these things happen a lot more frequently You know so much is changing so don't think oh, you know We've just had one now because of covert we only have to worry about 20 30 when the next crash comes It could come a lot sooner and I mean if we had to look at the the S&P 500 of the past 90 years We see it hasn't just been a nice linear smooth sailing up to the top There have been these these drops right in the beginning, you know, there was the great depression in the 30s Then you know even more recently We've had the great recession There's also the dot-com bubble that burst so we see that crashes do happen Like I say almost once every 10 years, but that could occur a lot more frequently Now what I want to do is just end of this video by talking very briefly about the security Market line now This is an equation that relates the expected return on any asset to the return on the market And it is given by this equation where we have E I minus R is equal to beta I E M minus R where E I is the expected return on security. I R is the return on the risk-free asset E M is the expected return on the market portfolio Beta I is the beta factor of security. I defined as the covariance of R. I R M divided by by the M basically, it's like, you know how How much is it in in tune with the market? So when the market goes up and the beta is high then the shares also going to go up But if the market goes one way and the shape kind of goes another way or is an effected by it It's going to have a low a low beta Now what we can do is we can rearrange these terms so that we have you know The expected return of security I is going to be equal to the return on the risk-free asset Plus the beta Multiplied by this term in brackets, which is the expected return on the market portfolio minus the return on the risk-free asset What we see is that the expected return of the security is a linear function of its covariance with the market and Note that there is no alpha. There is no specific risk Why because it's been assumed to have been diversified away and we only get rewarded for this Systematic risk that we take on sometimes I say systemic which is a different type of risk altogether Which we talk about in the enterprise risk management course, but your systemic and systematic they look quite similar, but job This is definitely Systematic risk not systemic risk. So yeah, the beta determines how much systematic risk the security exposes us to So let's have a very light example to to end off with Let's say we have a security that has a standard deviation of 4% the market standard deviation is 5% There's a correlation between the two of 0.75 the risk-free rate is 5% The expected return of the market is 10% now We can say well What is the expected return of security a and why we want to know what the expected return is is because then we can Know what price we need to offer and of course if the price is different to what we've calculated to what the market is Offering us, you know, there's a trading opportunity either to go long or short and all these kind of things But it's a nice simple question a little bit of a hint to calculate the beta of the security a first Feel free to pause this video give it a go yourself Otherwise, we're gonna move on to the the answer and then conclude And what we see is that the beta of security a it's given by this formula We're essentially it's very much statistics coming into play We plug in the formula and we get our answer of 0.6 once we have the beta of security a We cannot plug it into our other formula with regards to the expected return of security a and What we now do is just put in the numbers and we get our answer of 8% So mathematically this is quite easy I guess the trick here was you know, did you remember the statistics that you had learned in an earlier course? But I do have a whole course on you to me on mathematical statistics if covariant stuff is is freaking you out But other than that, I think we're gonna end this video here Hope you guys enjoyed it on the capital asset pricing model and I'll see you for another video soon. Cheers