FIN 60 More CAPM and Expected Returns

Let's have a look at problem 10-5-8. We're just using our capital asset pricing model to, uh, CAPM to solve for a missing variable. Essentially. We're given details of a stock. We got the expected return of the stock. So we got this one. We got the risk-free rate, so we got this one. We got the beta, so we got this one. We also have the risk-free rate there. We are just missing that one. And that's what it asks us to compute. Well, if we have all the pieces, except one in a puzzle, you can solve the puzzle, right? There's an algebra puzzle. Let's plug in the information we've got and see how we solve it. So the expected return of the stock is 14%. The risk-free rate is three. The beta is 1.2. We don't know our, uh, expected market return. That's what we're solving for, but we do, again, have the risk-free rate of, what was it? Three. Okay. So again, we got an algebra puzzle in front of us. I'm going to actually move this stuff down just to give myself a bit more room to operate. Let's solve for what we can solve. I'm going to move the three over because just subtract three from both sides. So 14 minus three is 11. That equals 1.2 times our ERM, uh, minus three. So let's multiply the 1.2 in the bracket, into the brackets, 11% equals 1.2 ERMs, uh, minus three times 1.2, which is 3.6 minus 3.6. Let's take, or let's add 3.6 to both sides. So this is 14.6 equals 1.2 times ERM. Uh, now let's divide 14.6 by 1.2 and we've solved it 14.6 divided by 1.2 equals 12.17. So, uh, well that equals ERM, I guess ERM equals 12.17%. So my expected return in the market here is 12.17%. I can check if I did the math right, uh, by just like plugging the numbers back in, you know, so solving for ERI by going, okay, well, my ERM is 12.17%. My risk-free rate was three. My beta was 1.2 risk-free rate is three. And so I can work backwards and get that that is 14. Hopefully it is. Let's see. Uh, 12. And I'm going to actually leave all the decimals 12.16666, just cause I'd be off by maybe a little bit, uh, minus three times 1.2 is 11 plus three is 14. So yeah, the, the, the math math, you solved it. There you have it. Thanks so much for watching as always. Have a great day. Bye-bye.