Daniel Macchio and Victoria Leeke each have $10,000 available to invest in the m

Question

Daniel Macchio and Victoria Leeke each have $10,000 available to invest in the market. Dan has formed a portfolio where he has invested half his funds in the riskfree security and the remaining funds in the market portfolio. Vicky has formed a portfolio by borrowing $5,000 at the riskfree rate and investing all the available funds in the market portfolio. What can you say about the relative standard deviation of returns of their portfolios? Vicky's portfolios standard deviation of returns will be:

a) One half the standard deviation of returns of Dan's portfolio.

b) One and a half times the standard deviation of returns of Dan's portfolio.

c) Three times the standard deviation of returns of Dan's portfolio.

d) None of the above.

Explanation / Answer

Observe that the standard deviation of V,s portfolio will be 3 times the standard deviation of the d’s portfolio.

This is because of the amount invested in the market.

Amount invested in the market by D is only $5000. On the other hand V has borrowed 5000 at risk free rate and invested the entire amount that is $15000 in the market.

Hence the standard deviation of V will be 3 times the standard deviation of D.

Therefore part c is correct.

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