Question

The expected return of Security A is 12 percent with a standard deviation of 15 percent. The expected return of Security B is 9 percent with a standard deviation of 10 percent. Securities A and B have a correlation of 0.4. The market return is 11 percent with a standard deviation of 13 percent and the risk-free rate is 4 percent. What is the Sharpe ratio of a portfolio if 35 percent of the portfolio is in Security A and the remainder in Security B?

Answer 1

Solution :-

Expected Return of Portfolio = ( W a * ER a ) + ( W b * ER b )

= ( 0.35 * 12% ) + ( 0.65 * 9% )

= 10.05%

Variance of Portfolio = ( W a * SD a )² + ( W b * SD b )² + 2 * Wa * Wb * SDa * SDb * r

= ( 0.35 * 0.15 )² + ( 0.65 * 0.10 )² + ( 2 * 0.35 * 0.65 * 0.15 * 0.10 * 0.4 )

= 0.002756 + 0.004225 + 0.00273

= 0.009711

= 0.97%

Now standard Deviation of Portfolio = ( 0.9711% )^1/2

= 9.855%

Now Sharper Ratio = ( Portfolio Return - Risk Free Rate ) / SD of Portfolio

= ( 10.05% - 4.00% ) / 9.85%

= 0.61

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