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In: Finance

Suppose you have a portfolio that is 40% invested in Barry Co (with expected return of...

  1. Suppose you have a portfolio that is 40% invested in Barry Co (with expected return of 14%, and standard deviation of 42%) and 60% invested in Bison Co (with expected return of 10% and standard deviation of 31%). The correlation between these two stocks is 0.20. Calculate the expected return and standard deviation of your portfolio. What is your portfolio’s reward to volatility ratio (Sharpe Ratio) if the risk free rate is 3%?

Solutions

Expert Solution

Given

Weight in portfolio (W)

Expected return (E)

Standard deviation (s)

Barry Co (B1)

40%

14%

42%

Bison Co (B2)

60%

10%

31%

Expected return of portfolio = sum of (weight of each stock * expected return of each stock)

= 0.4 * 14% + 0.6 * 10% = 11.6%

Given correlation between stocks = 0.2

Covariance (B1, B2)= Cov (B1, B2) = correlation coefficient * sB1 * sB2 = 0.2 * 42 * 31 = 260.4

Standard deviation of portfolio

Square root of

[ (WB1*sB1)2 + (WB2*sB2)2 + 2 * WB1 * WB2 * Cov (B1, B2)]

= Square root of

[ (0.4*42)2 + (0.6*31)2 + 2 * 0.4 * 0.6 * 260.4)]

= Square root of [ 282.24 + 365.96 + 124.992] = Square root of (773.192) = 27.80633 = 27.81%

Sharpe ratio = (Expected return of portfolio – risk free rate )/ Standard deviation of portfolio

Sharpe ratio = (11.6% - 3%)/ 27.81% = 0.3092

Therefore

Expected return of portfolio = 11.6%

Standard deviation of portfolio = 27.81%

Sharpe ratio (reward to volatility ratio) = 0.3092 = 0.31

jeff jeffy answered 1 year ago
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