In: Finance
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