Difficulty 1 (BKM, Q3 of Chapter 7) (10 points1) What must be the beta of a portfolio with E( rP ) = twenty. 0%, in the event the risk free level is your five. 0% plus the expected returning of the market is E( rM ) sama dengan 15. 0%? Answer: All of us use E( rP ) = Î² P *(E( rM ) ” l f ) + 3rd there’s r f. We then have got: 0. 20 = Î² P *(0. 15-0. 05) + zero. 05. Solving for the beta we get: Î² P =1. 5.
Problem a couple of (BKM, Q4 of Chapter 7) (20 points) The marketplace price of any security is definitely $40. The expected rate of return is 13%. The risk-free rate is 7%, plus the market risk premium is definitely 8%.
What will the market cost of the reliability be if perhaps its beta doubles (and all other variables remain unchanged)? Assume that the stock can be expected to spend a constant dividend in perpetuity. Hint: Employ zero-growth Dividend Discount Model to estimate the inbuilt value, which can be the market selling price. Answer: Initial, we need to compute the original beta before it doubles through the CAPM. Remember that: Î² = (the security’s risk premium)/(the market’s risk premium) sama dengan 6/8 sama dengan 0.
seventy five. Second, once its beta doubles to 2*0. seventy five = 1 ) 5, then its predicted return becomes: 7% + 1 . 5*8% = 19%. (Alternatively, we can find the expected return after the beta doubles inside the following approach.
If the beta of the protection doubles, then so is going to its risk premium. The current risk superior for the stock is usually: (13% ” 7%) sama dengan 6%, so the new risk premium can be 12%, as well as the new price cut rate intended for the security will be: 12% + 7% sama dengan 19%. ) Third, we find out the intended constant dividend payment from its current market value of $40. If the share pays a constant dividend in perpetuity, then we know in the original data that the gross (D) must satisfy the formula for a perpetuity: Price sama dengan Dividend/Discount price 40 = D/0. 13 ‘ D = 45 * 0. 13 = $5. 20 Last, in the new discount rate of 19%, the stock will be worth: $5. 20/0. 19 = $27. 37. The increase in inventory risk offers lowered the cost of the stock by thirty-one. 58%. Trouble 3 (BKM, Q16 of Chapter 7) (10 points)
A reveal of share is now offering for $100. It will pay a gross of $9 per talk about at the end of the year. The beta is definitely 1 . zero. What do traders expect the stock to trade for towards the end of the year if the marketplace expected come back is18% as well as the risk free level for the year is 8%? Answer: Considering that the stock’s beta is corresponding to 1, it is expected charge of returning should be corresponding to that of Deb + P1 ‘ P0, therefore , we could solve to get P1 as the market, that is certainly, 18%. Be aware that: E(r) = P0 on the lookout for + P1 ‘ 100 the following: 0. 18 = ‘ P1 = $109. 100 Issue 4 (15 points) Presume two stocks and options, A and B. Speculate if this trade that E( rA ) = 12% and E( rB ) = 12-15. %. The beta to get stock A is 0. 8 as well as the beta for B can be 1 . installment payments on your If the anticipated returns of both stocks and options lie inside the SML collection, what is the expected come back of the industry and what is the free of risk rate? Precisely what is the beta of a portfolio made of these two assets with equal dumbbells?
Answer: As both stocks and options lie inside the SML collection, we can immediately find its slope or the risk superior of the industry. Slope sama dengan (E(rM) ” rF) sama dengan ( E(r2) ” E(r1))/( Î²2- Î²1) = (0. 15-0. 12)/(1. 2-0. 8) = zero. 03/0. 4= 0. 075. Putting these values in E(r2) = Î²2*(E(rM) ” rF) + rF one gets: 0. 15 = 1 . 2*0. 075 & rF or rF =0. 06=6. 0%. The Expected return of the market is in that case given by (E(rM) ” 0. 06) = 0. 075 giving: E(rM) = 13. 5%. In the event you create a profile with these two property putting equals amounts of money in them (equally weighted), the beta will be Î²P = w1*Î²1+w2*Î²2= zero. 5*1. 2+0. 5*0. eight = 1 ) 0. Difficulty 5 (15 points) You could have an asset A with gross annual expected come back, beta, and volatility given by: E( rA ) sama dengan 20%, Î² A =1. 2, Ïƒ A =25%, respectively. In case the annual risk-free rate is definitely r farrenheit =2. five per cent and the predicted annual go back and movements of the marketplace are E( rM )=10%, Ïƒ A =15%, what is the alpha dog of asset A? Solution: In order to find the alpha, Î± A, of asset A we need to understand the difference involving the expected go back of the property E( rA ) plus the expected come back implied by the CAPM which is r f + Î² A (E(rM) ” l f ).
That is, express its predicted return while: Î± A = E( rA ) ” l f + Î² A (E( rM ) ” r n )). Seeing that we know the expected returning of the industry, the beta of the advantage with respect to the marketplace, and the risk-free rate, alpha is given simply by: Î± A = E( rA ) ” Î² A (E( rM ) ” ur f ) ” l f = 0. 20 ” 1 ) 2(0. one particular ” 0. 025) ” 0. 025
= 0. 085 = eight. 5%.
a couple of
Difficulty 6 (BKM, Q23 of Chapter 7) (20 points) Consider this data to get a one-factor economic climate. All portfolios are well diversified. _______________________________________ Collection E(r) Beta “””””””””””””””””””-A 10% 1 . zero F 4% 0 “””””””””””””””””””-Suppose another portfolio E is definitely well varied with a beta of 2/3 and anticipated return of 9%. Might an arbitrage opportunity are present? If therefore , what could the arbitrage strategy become? Answer: You are able to create a Profile G with beta comparable to 1 . 0 (the identical to the beta for Portfolio A) if you take a long placement in Stock portfolio E and a short position in Collection F (that is, borrowing at the risk-free rate and investing the proceeds in Portfolio E). For the beta of G to equal 1 . 0, the proportion (w) of funds invested in E must be: 3/2 = 1 . 5
The expected return of G is then: E(rG) = [(‘0. 50) Ã— 4%] + (1. a few Ã— 9%) = 14. 5% Î²G = 1 . 5 Ã— (2/3) sama dengan 1 . zero Comparing Profile G to Portfolio A, G provides the same beta and a better expected returning. This implies that an arbitrage prospect exists. Today, consider Profile H, the short position in Portfolio A while using proceeds committed to Portfolio G: Î²H = 1Î²G & (‘1)Î²A sama dengan (1 Ã— 1) & [(‘1) Ã— 1] = 0 E(rH) = (1 Ã— rG) + [(‘1) Ã— rA] = (1 Ã— 11. 5%) + [(‘ 1) Ã— 10%] = 1 . 5% In this way a no investment collection (all proceeds from the deal of this specific nature of Stock portfolio A will be invested in Stock portfolio G) with zero risk (because Î² = zero and the portfolios are well diversified), and a good return of just one. 5%. Portfolio H is usually an arbitrage portfolio.
Problem 7 (10 points) Review the CAPM theory with the APT theory, explain the difference between both of these theories? Solution: APT applies to well-diversified portfolios and not actually to specific stocks. It will be easy for some person stocks to not be on the SML. CAPM assumes logical behavior for any investors; LIKELY only requires some rational investors: APT is more standard in that their factor will not have to be the industry portfolio. Both models give the expected return-beta relationship. a few