[MUSIC] >> All right, so in this video, we're going to talk about the Capital Asset Pricing Model, or the CAPM. And this is providing a very brief recap of module two of my first investments course. So if you took that first course, this is just a quick refresher. If you didn't that the course, we want you to be able to join us in the second course. So let's give you kind of a quick recap of what we did. So first, let's just think about Simple Diversification and when you're going to simple diversification, what do I think of? I think of this old saying. It is a part of a wise man...not to venture all his eggs in one basket, from Miguel de Cervantes. I'm sure I pronounced that wrong. But hey, you want to at least bring the enthusiasm to the pronunciation, author of Don Quixote in the early 1600s. So does this kind of logic put out by the Spaniard here, does it make sense in terms of thinking of portfolio composition in terms of kind of investments? So let's go to the Variance of a Portfolio and look at just the simple formula here. And we can start with kind of two assets and the variance of our portfolio here is just going to reflect the variance of the individual components, where this w1 and w2 are the weights given to these two assets in the portfolio. w1 and w2 together add up to one, and then also this interesting term here that goes to the variance of portfolio that's representing the weights, the individual standard deviations, and then this key term here, the correlation between assets one and two. And then when you expand this to N assets, this variance of the portfolio depends upon the individual variances or the individual securities in that portfolio. But then also, all these terms here that are reflecting correlations between the various assets that we have in the portfolio. And as we'll shortly discuss, this correlation term here really becomes key in determining ultimately the volatility of any portfolio we put together. So after some algebraic pain, the punch line! If we have an equally weighted portfolio, and let's just for simplicity we have N assets, each asset gets 1 over N weight. Here's what our variance of the portfolio formula gets down to. So this is just some algebraic pain, assuming an equally weighted portfolio. Two terms, kind of 1 over N times the average variance across all the assets in the portfolio + 1- 1 over N times the average covariance across all the assets. So, what happens is N gets large. Well, the first term goes away and the 1 over 1- N basically becomes 1, so the variance of the portfolio really just reflects the average covariance across all the assets. So, not putting all your eggs in one basket is good advice. You don't want to have one stock in the portfolio. As you go from one to ten stocks, you can reduce the portfolio variance a lot, assuming these ten stocks aren't all in the same industry. But once you get to a certain point, you don't really get the benefits from the diversification in terms of lowering the volatility of the portfolio because assets, all stocks, have some sensitivity to market conditions. Okay, and we talked about that a lot in module one of module two of the first investments course. Okay, now let's take this logic and think about this Capital Asset Pricing Model or CAPM. The CAPM is really just coming up with benchmarks to determine what return, different assets, different security, should return based on their risk. And then the key part is to define, what do we mean by risk? And in the Capital Asset Pricing Model setting, we view assets as risky if their performance is sensitive to market-wide conditions. So that's a fundamental contribution of the capital asset pricing model. It provides a way to provide different benchmarks, different kind of expected or required returns for different assets and securities based on their level of risk. And the risk is quantified in the CAPM by seeing how sensitive is their performance to market wide conditions? That's a capital asset pricing model in a nutshell. And then the BETA of the stock is what matters in terms of setting up these different benchmarks for different stocks, okay? So it's useful for setting the benchmark for different assets, we've already talked about this. ALPHA, then, once we set this benchmark with the Beta, Alpha then is a measure of how an asset outperforms or underperforms its benchmark. So you can think of the Alpha as being a risk adjusted way to compare assets that have different underlying risk. So you could think an alpha's report on some website, it's a way to make an apple versus orange comparison more of an apple versus apple comparison. Different assets may have different levels of risk. Let's control for that by giving them different benchmarks, then let's assess how does the asset perform relative to its benchmark? That's this risk-adjusted return, Alpha. So a quick way to motivate the CAPM, actually, I'll give two of them. Do you hold insurance? If so, you're likely losing money on average. Why hold a security with an expected negative return? Another way of saying this is the insurance company's making profit on average, you're losing money on average. Why are you holding this insurance product? People still demand it, why? Well, the key insight, and this is the same logic really behind the CAPM, is that the payoffs from insurance differ dramatically depending upon what is happening to your wealth, okay? The insurance on your house pays off when your house burns down, so when everything around you's collapsing, here comes insurance company to pay you for a new house. So you value assets that will pay off when they're needed the most. That's why you have insurance, even though it loses money for you on average, it pays you the money when you need it the most. Another way to think about the CAPM, two firms, same expected cash flows. But firm A will do better in good times, Firm B will do better in bad times, okay. Which firm's stock should trade at a higher price today? Relatedly, which firm should offer the higher expected return in the future? So think of firm A and B, they're each expected to yield $100 million in cash flow each year. It's equally likely whether times will be good or whether they'll be bad. If times are good, A gives #200 million and B gives $0 but if times are bad, B gives $200 million and A gives $0. So their expected cash flow is each $100 million, but those cash flows occur in different states of the world across the two assets. So the simple answer is firm A and B have the same expected cash flow, they share the same value today and the same expected returns going forward. But the CAPM answer is Firm B is actually more valuable today because while it has the same expected cash flows as Firm A, Firm B gives us more cash in bad times, and likely in bad times our other assets are also falling gin value. Firm B is like insurance, it's extremely valuable, so we're willing to pay more for Firm B than for Firm A even though they have the same expected cash flows. Thus Firm B would have a lower required return because it's providing us this insurance then Firm A was. So the CAPM answer isn't about the average cash flows, it's about the state of the world, that these cash flows occur in. So insurance, state of the world, most highly valued assets pay off when they're needed the most, that's what the CAPM is really all about. Does this asset provide you insurance? Does it give you money in the states of the world where you need it the most? If so, its value should be high today. Or another way to say that, it can offer investors a lower return in the future, and the investors will be happy with that because of the insurance component this asset provides. Investors in the CAPM world are compensated for systematic or macroeconomic risk of an asset, okay? Investors are not compensated for the idiosyncratic risk, or the asset specific risk of an asset. So that's a part, don't put all your eggs in one basket. As long as you diversify, you even out all these firm specific shocks, okay? But you can't even out systematic risks. How sensitive is this firm to the macroeconomy, to interest rate changes, to oil prices, to economic growth in the US or China. Those are factors that don't go away by just adding more stocks to the portfolio. So the capital asset pricing model equation. So in the course we worked a lot, the first course in developing this. So in this course we're just going to focus on the final result. To see the magic go to my first course on investment. So now let's just get to the punchline here. The CAPM determines the expected return of a stock. The expected return on that stock is just simply what's the risk-free rate in the economy plus beta times the excess return of the market portfolio. Or rewriting this in terms of excess returns, the excess return of an asset i is simply beta times the excess return of the market, okay. Now this expected return of this asset or security i depends linearly on the systematic risk of the asset. And that systematic risk of the asset is measured by this beta, okay? And what's beta? It's a, you know, technically it's a co-variance of your asset or security i. It's performance with i to the market divided by the variance of the market. So there's the key beta. If you want to see the magic of how this was produced, go to my first course. But here we're just kind of giving what's the bottom line, CAPM equation. So the excess return of a stock is proportional to it's beta. Investors are only compensated for the market or systematic risk of an asset, not for the standard deviation of it's returns. So, what are some key kind of etas to look for? What are some key levels of beta to look for? If beta equals one, then the expected return of your asset is the same as the expected return of the market. So if you have a beta of one, you have the same benchmark for this asset security as you would for the market as a whole. If beta equals zero, this is an asset that doesn't move up or down with the state of economy. It's performance is uncorrelated with that of the overall economy. So if your asset has a beta equals zero, then your asset has a required return that's the same as the risk-free rate in the economy. The risk-free asset also has a beta of zero. If the beta is greater than one, this is an asset that amplifies market movements. Think of Tiffany, that's an example we did in my first investment course. For Tiffany it does better than the market in good times generally, it does worse than the market in bad times. because the first things people cut back on in a recession is expensive jewelry. Think of what if the beta is greater than zero but less than one, that's like a defensive stock. Think of Walmart, the highs aren't so high, the lows aren't so low. If you're buying Walmart, it's a defensive stock, it's a little hedge against the economy. When the economy's booming, Walmart is getting more profits but not going up the same rate as the market. But when the market's tanking, Walmart doesn't tank as much because there's still consistent demand, people visiting their store. So Walmart would be an example of a firm whose beta is probably between zero and one. So, Alpha measures the performance of an asset relative to its CAPM-predicted return here. So Alpha of an asset is just what's a return of it's asset, minus the benchmark set by the CAPM. So remember Alpha enables us to make an apple versus apple comparison across different securities or assets, as opposed to an apple versus orange. Because different securities have different benchmarks, right, just like different employees have different performance goals. The Alpha is just measuring how are you doing relative to your benchmark as established by the CAPM. So Alpha can be positive, you've over achieved, if you will, you've done better than your benchmark. Could be negative, you've under preformed, what you should have given your benchmark or you've just satisfied your benchmark. You earned the return that the CAPM said you should. So, you haven't under or over preformed the Alpha's zero, in that case. So, let's go through just a little example here. To highlight looking at returns, at different assets, and then deciding is this asset yield a positive, negative or zero Alpha. So let's look at three assets here, Asset 1, Asset 2, Asset 3. On the y-axis we're looking at the expected return of the asset, and then we're looking at it's beta here on the x-axis. So all of these three assets have the same expected return, straight red line through them here. But what's interesting, they have the same expected return. So you may say hey, they're each giving the same to the investor, but they have very different levels of risk. So for example, if you look at Asset 1, its beta is less than one, right, it's less than the market. It is, it's expected return from the CAPM should be right here, but instead it's having a much higher return. So this difference between the prediction from the CAPM, that's given on this security market line here, right? If the beta is zero, the expected return is the risk-free rate. If the beta equals one, the expected return of the asset is the same as the market. Asset 1 is giving a higher return than the CAPM says it needs to, to compensate for risk. So this is a great performer, positive Alpha. Asset 2 is right on this CAPM prediction line, its return is exactly what we would expect given its level of risk, its beta. Asset 3 on the other hand is underperforming, so its expected return is actually less. Then what would be predicted by the CAPM. Another way to look at this is Asset 3 and Asset 1 are giving the same return, even though Asset 3 has a beta that's much higher than Asset 1. It's like Asset 3 is Tiffany, beta greater than the market, Asset 1 is Walmart, beta less than the market. If you're telling Walmart and Tiffany are giving me the same return, I'm like I want to be invested in Walmart. Because I know Walmart's kind of more stable, lower beta, providing a little hedge against the economy. And it still giving me after all that, the same return as Tiffany. That would suggest like hey, Walmart is relatively doing better here. So two more important letters in the Greek alphabet, alpha and beta. They're still very prominent in finance language today. So let's look at beta first, this is kind of a stock screen taken from finance.yahoo accessed in May of 2015. Right on the first screen here, you see the beta. In this case, it was Apple, a 0.91, pretty close to 1.0, the beta for the market is a whole. So what would this literally mean if the market goes up 1%? Our prediction is Apple should go up 0.9%. Beta, it's a measure of systematic risk. Standard deviation is a measure of total risk. So the CAPM emphasizes assets securities with higher beta should have higher benchmarks. What matters in determining the expected returns, or benchmark for securities is their beta, not the standard deviation of their returns. Next, alpha, okay, so what does alpha mean? We talked about it, it's this risk adjusted return, a way to see how has the asset performed relative to it's benchmark, alpha is also front and center. So here, we're looking at from morningstar.com, accessed in 2015, this ticker here, FMAGX, stands for Fidelity Magellan Mutual Fund over a 10 year period here. You can see that it's had an alpha, that's actually negative. And we'll talk later, how to interpret these regression results, but Morningstar it's just showing you the CAPM regression. It's giving you this alpha, Fidelity Magellan over the 10 year period, has under performed it's benchmark by 2.4% per year. And this is after accounting for the expenses charged to investors. In this mutual fund, you see a beta here of 1.19, we just talked about the beta. So this is kind of little riskier than the market as a whole, in terms of having this beta greater than 1, and then the R-Squared of this CAPM of 90%. So both beta and alpha front and center on these financial websites, still today. So summing up, when we're looking at the CAPM, we simply can't compare the returns of assets to determine which has performed the best, right? The simple intuition would be, let's look and see which asset has done the bets historically, by just seeing which has the highest return, okay? In the CAPM world, prices and expected returns should reflect how sensitive an asset's performance is to the overall market. So that would suggest that we want to come up with different benchmarks for different assets and securities kind of using our logic. That if an asset provides us some type of insurance, we would require it to give us a lower return than assets that don't give us any insurance, and maybe even kick us when we're down. Not all risk is created equal, two key parameters from the capital asset pricing model, beta, the sensitivity of an asset to the market. Alpha, the over or under-performance of an asset.