D127 Stock X has an expected return of 8%, a standard deviation of return of 12%

Question

D127 Stock X has an expected return of 8%, a standard deviation of return of 12% and a beta of 2 Stock Y has an expected return of 10%, a standard deviation of return of 15% and a beta of 15. The corelaton coefficient between the two stocks is 06. If you m est S140 milions of your funds in 851 stock X and S60 million in stock Y. Assume risk tee rate is 2% and market risk premium is 5% 86 a. what is the actual expected return of your portfolio? (0.5) 93 b what is the standard deviation of your portfoho? (1) 94 103 c. Calculate the Sharpe ratios for stock X, stock Y AND your portfošo (0.5) introductionAnswer sheet PM 11:20 | 11/27/2017 ING ^

Explanation / Answer

1. actual expected return of portfolio = Expected return of x X Weight + Expected return of Y X Weight

= 8 % X ( 140/200) + 10% (60/200) = 8.6 %

2. Standard deviation of portfolio = (w2x * 2x + w2y* 2y + 2x * y * (wx) * (wy) * Cov(x,y))1/2

=(.72 * 122 + .32 * 152 + 2 * 12 * 15 * .7 * .3 * .6 ) 1/2

= (70.56+20.25 + 45.36)1/2

= 11.67%

3. sharpe ratio = (Rp - Rf) / Standard deviation

Rp = Return of portfolio/stock

Rf = risk free rate of return

Stock X = ( 8% - 2 %)/12% = .5

Stock Y = ( !0% - 2%)/15% = .533

Portfolio = (8.6% - 2%)/ 11.67% = .5655

4.

Beta of portfolio = Beta x  X weight x  + Beta y X weighty

= 2 X .7 + 1.5 X .3 = 1.85

5.

CAPM return of portfolio = Rf + Betap (Rm - Rf)

= 2 % + 1.85 x 5 % = 11.25%

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