s. (Lecture note pages 13-21, pages 30-41, Recitation exercise ) Stock X has an
ID: 2791819 • Letter: S
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s. (Lecture note pages 13-21, pages 30-41, Recitation exercise ) Stock X has an expected return of8%, a standard devato ofreturn of i 2% and a beta of 2. Stock has an expected return of i0% a s dar devaten beta of 1.5. The correlation coeficient between the two stocks is 0.6. Ifyou invest $140 millions of your fiunds in stock X and $60 mlion n stock Y Assume rak free rate is 2% and market risk premam s 5% a what is the actual expected retun of your portíolio? (0.5) Answer b what is the standard deviation of your portfolio?(1) Answer e Calculate the Sharpe ratios for stock X, stock Y AND your portfolio (O.5) Stock Y Your portfol Answer d. what is the beta of your portfolio? (0.5) Answer e what is the expected return of your portfolio, according to CAPM? (0.5) AnswerExplanation / Answer
Answer a) :- Total Investment in portfolio = Investment In stock X + Investment in Stock Y
= $ ( 140 + 60 ) Million
= $ 200 Million
Weight of Portfolio of Stock X = $ 140 / 200 = 70%
Weight of Portfolio of Stock Y = $ 60 / 200 = 30%
Therfore Portfolio Expected Return = 0.7 (0.08 ) + 0.3 (0.10)
= 0.056 +0.03 = 0.086 or 8.6%
Answer b) Standard Deviation of Stock X =12%
Standard Deviation of Stock Y = 15%
Weight of Stock X = 70%
Weight of Stock Y = 30%
Correlation Coefficent between two stocks =0.6
Variance of portfolio = (0.7 ^ 2) (0.12 ^ 2) + ( 0.3 ^ 2) (0.15 ^ 2) + 2 x 0.7 x 0.12 x 0.3 x 0.15 x 0.6
= 0.49 x 0.0144 + 0.09 x 0.0225 + 0.004536 =0.007056 +0.002025 +0.004536 = 0.013617
SD OF 0.013617 = 0.11669 OR 11.67 %
Answer c) Sharpe Ratios = E(R) - Risk free rate / SD (R)
Stock X = 0.08-0.02 /0.12 =0.50
Stock Y = 0.10-0.02/ 0.15 = 0.53
Portfolio = 0.086-0.02/0.1167 = 0.066 /0.1167 = 0.5656
d) Beta of the Portfolio = ( W x ) (Beta x ) + (W y ) (Beta y)
= 0.70 x 2 + 0.30 x 1.5 = 1.4 +0.45 = 1.85
e) Expected Return of portfolio according to CAPM =
Expected Return (P) = R f + Beta of P ( R m - R f)
= 2% + 1.85 ( 8.6 % -2 %) =
= 2% +12.21 % = 14.21 %
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