Question

Assume the risk free rate is 2.0%. The SP500 is considered the market. Today (T-0), you invest $400 in Stock A and $600 in Stock B to create Portfolio A,B. Assume there are not taxes or dividends. The one year performance of the stocks and the market is summarized in the table below. Use this information to help answer questions 16-20 Investment Market Stock A Stock B Total Return 12.0% 18.0% 10.0% Total Risk 14.0% 15.0% 12.0% Beta 1.00 1.40 0.60 400 600 16. Portfolio A,B's beta is closest to: a. 0.80 b. 0.92 c. 1.00 d. 1.08 e. 1.20 17. If you doubled the size of your investment today (T 0), your total dollar return would be closest to: a. $66 b. $92 c. $184 d. $264 e. $280 18. Assuming the correlation of stock A & B is zero (which your book assumes for all securities), Portfolio A,B's total risk is closest to: a. 9.4% b. 10.2% d. 12.8% 13.2% e. 19. Compare the SP500, Stock A, Stock B, and Portfolio A,B. Which of the following statements is most likely TRUE a. Stock's B Share Ratio of 0.67 is better than the Sharpe Ratio of the Stock A, SP500, and Portfolio A,B b. Stock's A Share Ratio of 1.07 is better than the Sharpe Ratio of the Stock B, SP500, and Portfolio A,B c. Stock's A Share Ratio of 1.20 is better than the Sharpe Ratio of the Stock B, SP500, and Portfolio A,B d. Stock's A's Share Ratio of 1.40 is better than the Sharpe Ratio of the Stock B, SP500, and Portfolio A,B e. Portfolio A,B's Sharpe Ratio of 1.20 is better than the Sharpe Ratio of the Stock A, Stock B, and the SP500 20. In lecture we discussed how assuming the correlation between any two is zero is dangerous when assessing the total risk of a portfolio between two assets to be 0.40 instead of 0.00. Portfolio A,B's total risk is now closest to: assume you calculate the correlation a. 9.4% b. 10.2% d. 12.8% 13.2% e.

Answer 1

Question 16

The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio

Stock	Weight	Beta	Weight*Beta
A	0.4	1.4	0.56
B	0.6	0.6	0.36

Portfolio Beta = $\sum$Weight*Beta

= .56+.36

= 0.92

Question 17

Total dollar return = Return on stock A + Return on stock B

= 400*2*18% + 600*2*10%

= 144+120

= $264

​​​​​​​Question 18

Portfolio Standard Deviation = $\sqrt{}$ [(WA*SDA)^2 + (WB*SDB)^2 + (2*WA*WB*SDA*SDB*CorAB)]

where

WA - Weight of stock A =.4

WB - Weight of stock B =.6

SDA - Standard Deviation of stock A = .15

SDB - Standard Deviation of stock B = .12

CorAB - Correlation coefficient = 0

Portfolio Standard Deviation = $\sqrt{}$ [(.4*.15)^2 + (.6*.12)^2 + (2*.4*.6*.15*.12*0)]

= $\sqrt{}$ (0.0036+0.005184+0)

= $\sqrt{}$ 0.008784

= 0.09372299611

= 9.4%

​​​​​​​Question 19

Sharpe Ratio = (Return-Risk free rate) / Standard Deviation

Sharpe Ratio of Stock A = (18-2)/15 = 1.07

Sharpe Ratio of Stock B = (10-2)/12 = 0.67

The return of a portfolio is the weighted average return of the securities which constitute the porfolio

Portfolio Return = .4*18+.6*10 = 13.20%

Sharpe Ratio of Portfolio A,B = (13.20-2)/9.4 = 1.20

Sharpe Ratio of SP 500 = (12-2)/14 = 0.71

True Statement: Higher sharpe ratio is considered to be better. Portfolio A,B's sharpe ratio of 1.20 is better than than the sharpe ratio of Stock A, Stock B and the SP 500.

​​​​​​​Question 20

Portfolio Standard Deviation = $\sqrt{}$ [(WA*SDA)^2 + (WB*SDB)^2 + (2*WA*WB*SDA*SDB*CorAB)]

where

WA - Weight of stock A =.4

WB - Weight of stock B =.6

SDA - Standard Deviation of stock A = .15

SDB - Standard Deviation of stock B = .12

CorAB - Correlation coefficient = .4

Portfolio Standard Deviation = $\sqrt{}$ [(.4*.15)^2 + (.6*.12)^2 + (2*.4*.6*.15*.12*.4)]

= $\sqrt{}$ (0.0036+0.005184+0.003456)

= $\sqrt{}$ 0.01224

= 0.11063453348

= 11.1%