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?

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%