'Financial Markets and Return Essay\r'

' chore 1 (BKM, Q3 of Chapter 7) (10 points1) What must be the of import of a portfolio with E( rP ) = 20.0%, if the risk of infection unload regularise is 5.0% and the necessitateed drive out of the commercialise is E( rM ) = 15.0%? Answer: We use E( rP ) = β P *(E( rM ) †r f ) + r f . We and so have: 0.20 = β P *(0.15-0.05) + 0.05. Solving for the beta we get: β P =1.5.\r\n enigma 2 (BKM, Q4 of Chapter 7) (20 points) The mart price of a protective covering is $40. Its anticipate commit of pop off is 13%. The safe rate is 7%, and the securities industry risk bounteousness is 8%. What will the merchandise price of the certificate be if its beta doubles (and all whatsoever other variables remain unchanged)? Assume that the crinkle is judge to fix a constant quantity dividend in perpetuity. Hint: practice session zilch-growth Dividend Discount Model to calculate the intrinsic value, which is the market price. Answer: First, we need to calculate t he original beta before it doubles from the CAPM. Note that: β = (the security’s risk allowance)/(the market’s risk premium) = 6/8 = 0.75. Second, when its beta doubles to 2*0.75 = 1.5, then its expected return becomes: 7% + 1.5*8% = 19%. (Alternatively, we discharge find the expected return after the beta doubles in the side by side(p) way.\r\nIf the beta of the security doubles, then so will its risk premium. The original risk premium for the stock is: (13% †7%) = 6%, so the new risk premium would be 12%, and the new force out rate for the security would be: 12% + 7% = 19%.) Third, we find out the imp restd constant dividend payment from its current market price of $40. If the stock pays a constant dividend in perpetuity, then we know from the original entropy that the dividend (D) must satisfy the equation for a perpetuity: Price = Dividend/Discount rate 40 = D/0.13 ⇠D = 40 * 0.13 = $5.20 Last, at the new discount rate of 19%, the stock would be charge: $5.20/0.19 = $27.37. The increase in stock risk has bring down the value of the stock by 31.58%. Problem 3 (BKM, Q16 of Chapter 7) (10 points)\r\nA fate of stock is now merchandising for $100. It will pay a dividend of $9 per share at the end of the social class. Its beta is 1.0. What do investors expect the stock to sell for at the end of the year if the market expected return is18% and the risk free rate for the year is 8%? Answer: Since the stock’s beta is equal to 1, its expected rate of return should be equal to that of D + P1 ∠P0 , therefore, we can solve for P1 as the market, that is, 18%. Note that: E(r) = P0 9 + P1 ∠100 the following: 0.18 = ⇠P1 = $109. 100 Problem 4 (15 points) Assume twain stocks, A and B. One has that E( rA ) = 12% and E( rB ) = 15.%. The beta for stock A is 0.8 and the beta for B is 1.2. If the expected returns of both stocks lie in the SML line, what is the expected return of the market and what is the riskless rate? What is the beta of a portfolio made of these two summations with equal weights?\r\nAnswer: Since both stocks lie in the SML line, we can immediately find its slope or the risk premium of the market. Slope = (E(rM) †rF) = ( E(r2) †E(r1))/( β2- β1) = (0.15-0.12)/(1.2-0.8) = 0.03/0.4= 0.075. Putting these set in E(r2) = β2*(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 then habituated by (E(rM) †0.06) = 0.075 giving: E(rM) = 13.5%. If you spend a penny a portfolio with these two assets putting equals amounts of money in them (equally weighted), the beta will be βP = w1*β1+w2*β2= 0.5*1.2+0.5*0.8 = 1.0. Problem 5 (15 points) You have an asset A with annual expected return, beta, and excitability given by: E( rA ) = 20%, β A =1.2, ÏÆ' A =25%, respectively. If the annual risk-free rate is r f =2.5% and the expected annual return and volatility of the market are E( rM )=10%, ÏÆ' A =15%, what is the alpha of asset A? Answer: In order to find the alpha, α A , of asset A we need to find out the difference amid the expected return of the asset E( rA ) and the expected return implied by the CAPM which is r f + β A (E(rM) †r f ).\r\nThat is, express its expected return as: α A = E( rA ) †r f + β A (E( rM ) †r f )). Since we know the expected return of the market, the beta of the asset with respect to the market, and the risk-free rate, alpha is given by: α A = E( rA ) †β A (E( rM ) †r f ) †r f = 0.20 †1.2(0.1 †0.025) †0.025\r\n= 0.085 = 8.5%.\r\n2\r\nProblem 6 (BKM, Q23 of Chapter 7) (20 points) Consider the following data for a one-factor economy. All portfolios are count onably diversified. _______________________________________ Portfolio E(r) Beta â€â€â€â€â€â€â€â€â€â€â€â€â€â€â€â€â€â€â€-A 10% 1.0 F 4% 0 â€â€â€â€â€â€â€â€â⠂¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬Ã¢â‚¬-Suppose another portfolio E is well diversified with a beta of 2/3 and expected return of 9%. Would an merchandise opportunity exist? If so, what would the arbitrage strategy be? Answer: You can create a Portfolio G with beta equal to 1.0 (the selfsame(prenominal) as the beta for Portfolio A) by taking a long position in Portfolio E and a victimize position in Portfolio F (that is, espousal at the risk-free rate and investing the upshot in Portfolio E). For the beta of G to equal 1.0, the attribute (w) of funds invested in E must be: 3/2 = 1.5\r\nThe expected return of G is then: E(rG) = [(âˆ0.50) à 4%] + (1.5 à 9%) = 11.5% βG = 1.5 à (2/3) = 1.0 equivalence Portfolio G to Portfolio A, G has the same beta and a higher expected return. This implies that an arbitrage opportunity exists. Now, consider Portfolio H, which is a short position in Portfolio A with the proceeds invested in Portfolio G: βH = 1βG + (∠1)βA = (1 à 1) + [(âˆ1) à 1] = 0 E(rH) = (1 à rG) + [(âˆ1) à rA] = (1 à 11.5%) + [(∠1) à 10%] = 1.5% The conduct is a zero investment portfolio (all proceeds from the short sale of Portfolio A are invested in Portfolio G) with zero risk (because β = 0 and the portfolios are well diversified), and a positive return of 1.5%. Portfolio H is an arbitrage portfolio.\r\nProblem 7 (10 points) Compare the CAPM theory with the quick theory, condone the difference between these two theories? Answer: APT applies to well-diversified portfolios and not necessarily to individual stocks. It is possible for just about individual stocks not to be on the SML. CAPM assumes sagacious behavior for all investors; APT only requires some rational investors: APT is more general in that its factor does not have to be the market portfolio. Both models give the expected return-beta relationship. 3\r\n'