In the last session we distinguished between alternative types of risk and highlighted that there was only systematic risk that could not be diversified away, but investors could expect compensation for being exposed to. In this session, we're going to discuss a model that describes the exact compensation that many investors can expect on the basis of the systemic risk of the investment. So firstly, let's reset the table. So far in this course we've defined the different attitudes investors might have to the risk return trade off, settling upon risk aversion as the default position of most investors. We then showed how we could measure total risk using standard deviation, sigma, but then went on to develop a measure of risk that captured systematic or undiversifiable risk directly. That measure of risk was what we called in asset’s beta. But how is that useful to anybody? Well you might recall from course three of this finance specialization, <i>Corporate Financial Decision-Making for Value Creation</i>, that the dominant methods for project evaluation nowadays are discounted cashflow techniques, such as net present value, NPV analysis, or the internal rate of return IRR method. All of these techniques rely upon the discounting of future expected cash flows by a discount rate that reflects the time value of money. The time value of money specifically captures opportunity cost, expected inflation, and, you guessed it, risk. The risk that the discount rate captures is systematic risk. So we need a model that links systematic risk, as measured by beta, to discount rates. That's our objective of this session. So here is our model. A very intuitively appealing model, if I must say so myself. Let me show you. We begin on the left-hand side with the expected return for any asset, i. This is simply the discount rate that you would use to discount the expected cash flows from asset i, to come up with the asset's value. Looking at the right-hand side now, the expected return for any asset is equal, firstly to the risk-free rate of return. Rf. Now let's pause there. That implies that, in the absence of any risk at all, the investor can still expect at least the risk-free rate of return. So you know that old saying, no risk, no return? Well, it's rubbish. No risk, and you get the risk-free rate of return. The second half of the right hand side of the equation is an adjustment for risk, as indicated by beta. It says that for each unit of beta, an investor can expect to increase their expected return from an asset, by the difference between the expected return on the market portfolio and the risk free rate. This difference is what's referred to as the market risk premium. So to demonstrate how this works. Let's assume that your asset has a beta equal to one. So your asset has the same level of systematic risk as a market portfolio. The expected return from your asset in this case will be equal to the risk-free rate of return plus one times the market risk premium. Which is the expected return on the market portfolio less the risk-free rate of return. So the expected return from your asset will be equal to the expected return on the market portfolio. If your beta is less than one, you will end up with a lower expected return than what we expected from the market and if it's greater than one, your expected return will be higher than the expected return on the market. Pretty simple, huh? So just to reiterate, each component of the Capital Asset Pricing Model, the CAPM. E(Ri) is the Expected or Required rate of return from an asset, which can be utilized in discounted cash flow calculations such as NPV analysis. It is typically measured on a per annum basis. Rf is the risk-free rate of return that can be earned in the absence of any risk at all. Common proxies for this measure include the rate of return promised by government bonds and bills. The expected return on the market portfolio is what we expect a diversified, value-weighted portfolio to deliver in returns on a per annum basis. Now rather than working with this number directly, we tend instead to use the market risk premium, which is the amount by which we expect the market portfolio of risky assets to outperform the risk-free asset on a per annum basis. Now there's a lot of conjecture about exactly what this number should be. With estimates ranging from 2% to above 8% per annum. Indeed the wide range of market risk premium estimates is neatly demonstrated by survey evidence collected by Fernandez Linares and Acin in their 2014 paper. The researchers in this project asked over 29,000 people including academics, managers, and equity analysts for their estimate of the market risk premium. The results are astounding in their variety. We see average responses from China on the order of 8.1%. While in the UK the figure was closer to 5% per annum. Obviously this makes it a little more challenging to employ the model when there's so much uncertainty about this key input. But let's assume that you've settled on a particular measure of the market risk premium, say, 7% per annum. Assume also that the long term rate on government bonds is about 2%. So what do you do now? Well, now you can easily calculate the expected return for any asset for which you have a beta estimate. So this is the graphical representation of the Capital Asset Pricing Model, the CAPM, which by the way, we call the Security Market Line. Here we've assumed a risk-free rate of 2% and a market-risk premium of 7%. Now see how all of our estimates of expected return plot simply on the security market line. Starting at Kellogg's where we have a beta estimate of .773 and moving all the way up to Facebook with a beta estimate of 1.75. So, let's work out how we estimated those expected returns while working with Facebook. Now, the expected return for Facebook shares is simply equal to the risk-free rate of 2%, plus 1.75 times the market risk premium of 7%, which gives us an expected return on Facebook shares of 14.25% per annum. Now we can then use this estimate, the expected return on Facebook shares to discount the dividend stream that we expect to generate from Facebook over its like to arrive at an estimate of the current value of a Facebook share. But what about portfolios? Well, let's assume that we form a portfolio consisting half of our money in Facebook shares and the other half in Kellogg's shares. There are two ways for us to calculate the expected return on the portfolio. Firstly, we know that the beta for a portfolio is simply the weighted average beta of the individual assets. So we can estimate the portfolio beta to be 1.262. When we substitute that into the CAPM formula, we end up with an expected return for the portfolio of 10.83% per annum. Alternatively, we can use the CAPM to work out the expected return for Kellogg shares and that turns out to be 7.41% per annum. We can then simply work out the weighted average of the expected returns of the shares in the portfolio. So, that is 0.5 times 14.25% for Facebook, plus 0.5 times 7.41% for Kellogg’s, that gives you a portfolio expected return of 10.83% per annum, which is of course the same answer as before. Just arrived in two different yet consistent ways. In summary, in this session we have described the Capital Asset Pricing Model, the CAPM, and demonstrated how it links together the concepts of systematic risk and expected return. The Capital Asset Pricing Model suggests that the only factor that should be important in describing why some companies have different expected returns to other companies is the asset's beta. In our next session together, we will look at the evidence on this and see just how well the CAPM does in explaining realized returns from different assets.
