Question

Answer Problems below:

Q1. Mr. Miles is a first time investor and wants to build a portfolio using only U.S. T-bills and an index fund that closely tracks the S&P 500 Index. The T-bills have a return of 5%. The S&P 500 has a standard deviation of 20% and an expected return of 15%.

1. Draw the CML and mark the points where the investment in the market is 0%, 25%, 75%, and 100%.

2. Mr. Miles is also interested in determining the exact risk and return at each point.

Q2. Mr. Miles decides to set aside a small part of his wealth for investment in a portfolio that has greater risk than his previous investments because he anticipates that the overall market will generate attractive returns in the future. He assumes that he can borrow money at 5% and achieve the same return on the S&P 500 as before: an expected return of 15% with a standard deviation of 20%. Calculate his expected risk and return if he borrows 25%, 50%, and 100% of his initial investment amount.

Answer 1

For the given.

There are major 4 points with different weights.

For 0% market investment: return = 5%, Std dev = 0. For 25%: return = 7.5% std dev = 5%. For 75%: return = 12.5% and std dev = 15%. for 100%: return = 15% and stddev = 20%.

From the diagram shown points A,B,C,M represent points with different weights and their corresponding returns and standard deviations. Also efficient frontier has been shown for effecient set of portfolios with M being most efficient one as its the market portfolio. Line drawn is CML.

(B) Now suppose he borrows at 5% rate to invest in S&P 500 i.e now he has moved above point M where there is higher risk and weight of risk free security is negative and that of market portfolio is >1.

So the amount of return on portfolio calulated initially will decrease by the amount of weighted interest paid by Miles on the borrowed rate i.e 5%. So the expected risk wont change only returns would do, i.e for 25% borrowed money, returns would decrease by 1.25%. for 50% borrowed money returns would reduce by 2.5% and for 100% borrowed money returns would reduce by 5%, and this would again depend on what are the weights of both the components of portfolio.