Question

Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 12% and a standard deviation of 17%. L has an expected rate of return of 9% and a standard deviation of 11%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Answer 1

We need the compute the weight of K and L

Weight of K = Standard deviation of security L / Standard deviation of security K + Standard deviation of security L

Weight of K = 11% / 17% + 11%

Weight of K = 11% / 28%

Weight of K = 0.39286

Hence, the weight of security K is 0.39286

Weight of L = Standard deviation of security K / Standard deviation of security L + Standard deviation of security K

Weight of L = 17% / 11% + 17%

Weight of L = 17% / 28%

Weight of L = 0.607143

Hence, the weight of security L is 0.607143

Now we compute the rate of return risk-free portfolio as follow:

Return of portfolio = [Return of K * Weight of K] + [Return of L * Weight of L]

Return of portfolio = [12% * 0.39286] + [9% * 0.607143]

Return of portfolio = 0.0471432 + 0.05464287

Return of portfolio = 0.10178607

Return of portfolio = 10.18%

Hence, the rate of return of risk-free portfolio is 10.18%