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Borrowing to invest: return, volatility and beta

EXERCISE 01

You have €10,000, borrow another €10,000 at the risk-free rate of 4%, and invest €20,000 in a risky portfolio with expected return 20% and standard deviation 16%.

  1. A.Find your portfolio return and volatility relative to your equity.

A.

E[RC]=wPE[RP]+(1−wP)rf,σC=∣wP∣σPE[R_C]=w_PE[R_P]+(1-w_P)r_f,\quad\sigma_C=|w_P|\sigma_P
wP=20,000/10,000=2,wf=−1w_P=20{,}000/10{,}000=2,\quad w_f=-1
E[RC]=2(0.20)−0.04=0.36E[R_C]=2(0.20)-0.04=0.36
σC=2(0.16)\sigma_C=2(0.16)

Expected return 36%; volatility 32%.