Question

True or False and why: If we assume you invest 50% of your portfolio in each of two stocks that are perfectly negatively correlated, you should expect to realize the risk-free rate of return.

Answer 1

let the two stocks be a and b

volatility of a = v_a

volatility of b = v_b

volatility of total portfolio ₌ v_p

as equal amount is invested in both stocks the weight of both stocks are equal

let be thw correltion between two stocks which is -1

v_p = (v_a² + v_b² + 2v_av_b*)^(1/2) = (v_a² + v_b² + 2v_av_b*(-1))^(1/2) = (v_a² + v_b² - 2v_av_b)^(1/2)= v_a - v_b

so the portfolio can only have risk free return when volatility of both are equal, otherwise there will remain some risk

False -answer