Question

Suppose​ Intel's stock has an expected return of 20.0% and a volatility of 3.0%, while​ Coca-Cola's has an expected return of 7.0% and volatility of 3.0%. If these two stocks were perfectly negatively correlated​ (i.e., their correlation coefficient is negative −1​),a. Calculate the portfolio weights that remove all risk.b. If there are no arbitrage​ opportunities, what is the​ risk-free rate of interest in this​ economy?

Answer 1

Answer:

a. The portfolio weights that remove all risk is 50% .

b. The risk-free rate of interest in this​ economy is 13.5%

Explanation:

The formula for standard deviation of a portfolio, of which i cannot type:

a. If we let  sigma p = std. deviation of portfolio

rho 1,2 = correlation

if sigma = 0 and rho = -1, then the first equation can be re-written as :

0 = w1^2 * s1^2 + w2^2 * s2^2 + 2 * w1 * w2 * s1 * s2 * -1

0 = (w1s1 - w2s2)^2

w1s1 = w2s2

w1 * 0.03 = w2 * 0.03

w1 = w2 = 50%

Therefore, The portfolio weights that remove all risk is 50% .

b.  Expected return of the portfolio = 0.5*20% + 0.5*7%

                                                         = 13.5%

This portfolio has zero risk, risk free rate = 13.5%

Therefore, The risk-free rate of interest in this​ economy is 13.5%