Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 12% and a standard deviation of return of 17%. B has an expected rate of return of 9% and a standard deviation of return of 14%. Required:
a. What are the weights of A and B in the global minimum variance portfolio respectively?
b. What is the rate of return on the risk-free portfolio that can be formed with the two securities ?

A) Weight of Security A = 0.45

Weight of Security B = 0.55

B)Risk free rate = 10.35%

Explanation:

We are given;

A) Expected rate of return for Security A; ERR = 12%

Standard deviation of return for Security A; SD = 17%

Expected rate of return for Security B; ERR = 9%

Standard deviation of return for Security B; SD = 14%

Now, formula for weight of Security A is;

Weight of security A = SD of security B ÷ (SD of security B + SD of security A)

Weight of Security A = 14%/(14% + 17%)

Weight of Security A ≈ 0.45

Weight of Security B = 1 - weight of Security A

Weight of Security B = 1 - 0.45

Weight of Security B = 0.55

B) Formula for the risk free rate is;

Risk free rate = (weight of Security A × ERR of security A) + (weight of Security B × ERR of security B)

Risk free rate = (0.45 × 12%) + (0.55 × 9%)

Risk free rate = 10.35%

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