**Must show work - handwritten please**

Q1. Compute the covariance and the correlation for the following example: 1. Three scenarios (1,2,3) with respective probabilities (20%,30%, and 50%). 2. Two stocks: Apple and GM. 3. Apple's and GM's retums for the three scenarios are (5%,5%,0%) and (3%,4%,2%), respectively. (Solution) 1. Compute covariance. a. cov[rA,rB]=E[rAE[rA]][rBE[rB]]=i=1Spi[rA,iE[rA]][rB,iE[rB]] b. First, compute expected return on both stocks. i. E[rApple]=0.25%+0.3(5%)+0.5(0%)= ??? ii. E[rGM]=0.23%+0.3(4%)+0.5(2%)= ??? c. cov=0.2(5%(0.5%))(3%???)+0.3(5%(0.5%)) (4%0.4%)+0.5(0%(???))(2%0.4%)=??? 2. Then compute correlation a. A,B=ABcov[rA,rB] b. First, we need to compute the variance. 2=state=1I[probstate(ReturnstateExpectedreturn)2] ii. Apple2=0.2(5%(0.5%))2+0.3(5%(0.5%))2+0.5 (0%(0.5%))2=??? iii. GM2=0.2(3%0.4%)2+0.3(4%0.4%)2+0.5 (2%0.4%)2= ??? c. Then, let us calculate the standard deviation. i. Apple=Apple2= ??? ii. GM=GM2= ??? d. A,B=ABcov[rA,rB]=???+???m?=0.90479 Q3. You have $100 invested in Portfolio P in the Figure below. It has E[Rp]=10.5% and SD(Rp)=8%. Assume rf=5%, and the tangent portfolio, Portfolio T, has an expected return of 18.5% and a volatility of 13%. Note that each black dot represents a portfolio. a. To maximize your expected return without increasing your volatility, which portfolio would you invest in? Explain your answer. b. To keep your expected return the same but minimize your risk, which portfolio would you invest in? Explain your answer. c. Which portfolio is not possible to invest in? In other words, which portfolio is impossible to construct? Explain your answer. Q4. A firm has beta of 1.5. Let the estimated market premium be 8% and the risk-free rate 4%. Using CAPM, what is the expected return of this stock? Q1. Compute the covariance and the correlation for the following example: 1. Three scenarios (1,2,3) with respective probabilities (20%,30%, and 50%). 2. Two stocks: Apple and GM. 3. Apple's and GM's retums for the three scenarios are (5%,5%,0%) and (3%,4%,2%), respectively. (Solution) 1. Compute covariance. a. cov[rA,rB]=E[rAE[rA]][rBE[rB]]=i=1Spi[rA,iE[rA]][rB,iE[rB]] b. First, compute expected return on both stocks. i. E[rApple]=0.25%+0.3(5%)+0.5(0%)= ??? ii. E[rGM]=0.23%+0.3(4%)+0.5(2%)= ??? c. cov=0.2(5%(0.5%))(3%???)+0.3(5%(0.5%)) (4%0.4%)+0.5(0%(???))(2%0.4%)=??? 2. Then compute correlation a. A,B=ABcov[rA,rB] b. First, we need to compute the variance. 2=state=1I[probstate(ReturnstateExpectedreturn)2] ii. Apple2=0.2(5%(0.5%))2+0.3(5%(0.5%))2+0.5 (0%(0.5%))2=??? iii. GM2=0.2(3%0.4%)2+0.3(4%0.4%)2+0.5 (2%0.4%)2= ??? c. Then, let us calculate the standard deviation. i. Apple=Apple2= ??? ii. GM=GM2= ??? d. A,B=ABcov[rA,rB]=???+???m?=0.90479 Q3. You have $100 invested in Portfolio P in the Figure below. It has E[Rp]=10.5% and SD(Rp)=8%. Assume rf=5%, and the tangent portfolio, Portfolio T, has an expected return of 18.5% and a volatility of 13%. Note that each black dot represents a portfolio. a. To maximize your expected return without increasing your volatility, which portfolio would you invest in? Explain your answer. b. To keep your expected return the same but minimize your risk, which portfolio would you invest in? Explain your answer. c. Which portfolio is not possible to invest in? In other words, which portfolio is impossible to construct? Explain your answer. Q4. A firm has beta of 1.5. Let the estimated market premium be 8% and the risk-free rate 4%. Using CAPM, what is the expected return of this stock