Question

You form a portfolio using stock KPMG and a treasury bill with a sure rate of 5%. KPMG has an expected return of 12% and a standard deviation of 10%. Your portfolio’s standard deviation will be 18% if you ___. A. Borrow 80% at the risk-free rate and invest 180% in KPMG B. Invest 80% in KPMG and 20% in the risk-free asset C. Borrow 20% at the risk-free rate and invest 120% in KPMG D. Invest 80% in the risk-free asset and 20% in KPMG

Answer #1

Standard deviation of KPMG = 0.1

Standard deviation of T Bill = 0

Let Weight of KPMG in portfolio be w and weight of T bill be (1- w)

Std dev of portfolio = sqrt( Weight of KPMG* std dev of KPMG + weight of Tbill* std dev of T bill + 2* weight of KPMG *weight of T bill * Correlation * Std dev of KPMG * Std dev of T bill)

Std dev of portfolio = sqrt ( w^2 * 0.1^2 + (1-w) * 0 + 2*w*(1-w)*Correlation * 0.1 * 0)

or, 0.18 = w * 0.1

or w= 0.18/0.1 = 1.8 or 180%

So the investor is invested 180 % in KPMG by borrowing 80% at the risk free rate

**So the correct option is A)**

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