FIN 59 CAPM and Expected Returns

Let's examine problem 10-4a, and to do it, I'm going to have to discuss the capital asset pricing model. A fundamental concept in a corporate finance class is this CAPM model. So let's explain the model, and then we'll solve the problem, we'll use it, and hopefully that'll help. The model's about pricing or determining the value of investments, and one way of doing this is calculating the expected return of the investment, how much the investment would be expected to return. We do that. Here are the components. We take the risk-free rate, we add, and now this is all a chunk, right, beta times the expected market return minus the risk-free rate, that's the market risk premium. So let's start with the risk-free rate. Of course, it's risk-free rate plus something because if it wasn't going to return more than the risk-free rate, I would just buy T-bills, right, save myself a lot of time and hassle. I don't have to think about an investment, I can just buy T-bills and get the risk-free rate. So any investment you're contemplating, the risk-free rate is like the starting point. It's got to be at least returning the risk-free rate. So what's in the brackets, the plus beta, well, beta is, again, a measure of risk within the investment, and it's sort of saying if the stock market moves by 5%, we would expect the investment to move by beta times that. So if the beta is 2, you know, stock market moves 5%, our stock, we would expect would move 10%. It's way swingier than the market, which means riskier than the market, but also expected returns are higher with a higher risk tolerance. What's in the brackets? Well, it is the market risk premium. It's that amount we expect the market to return above the risk-free rate. Okay, let's apply that to our problem and just sort of crunch some numbers. So I'm going to erase this heading. We're going to solve. So stock number one, so let me just do number one here. So our expected return on stock one equals, what's the risk-free rate, 3.5% plus, what's the beta of that stock, 1.3 times the expected market return minus the risk-free rate. Well, I'll just do the number here, 12 minus 3.5 is 8.5%. So times 8.5%, okay. So now we can solve for the expected return of stock one, I go 1.3 times 8.5% plus 3.5. The expected return of stock number one is 14.55%. Now as our betas drop, our expected returns are going to drop as well because we're taking on less risk, there is less return needed here. Let's do stock number two, I guess I'm working upwards here. Our expected return of stock two is same risk-free rate, 3.5% plus, our beta is the only thing that changes here, 1.1 times 8.5%, 1.1 times 8.5% is 9.35. We add that to our 3.5, we get 12.85%. Our last one, make a red pen, number three, our expected return on stock three, again, our risk-free rate's the same, like you can buy T-bills the same amount, no matter what investment you buy, the only thing different here is the beta is 0.8. We multiply that by, again, the market risk, which is 12 minus the risk-free rate, which is 3.5, so it's still 8.5%. So let's run the numbers, 0.8 times 8.5%, 6.8 plus 3.5, and it's 10.3, and this is our first one, by the way, where the expected return is lower than average for the market, right? You can see the market average return is 12, we're only getting 10.3. Why is it? Because we're less risky than the market, so there's less of a premium for us. Okay, there we have it. Our first look at CAPM, that's how I say it anyway, thanks for watching. See you in our next video. Bye-bye.