Question

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2. Based on your examination of the historical record, you calculate that the expected return on the S&P500 over the next year is 6% over T-bills with a standard deviation of 15% Currently a T-bill with one year to maturity and face value of $10,000 is selling for $9,615. You have $1 million to invest and you will put all of your money in some combination of the S&P500 and one-year T-bills. Calculate the expected return and standard deviation of that return for 3 different portfolios. (a) Portfolio #1 is invested 100% in the S&P500 (b) Portfolio #2 is invested 50% in the S&P500 (c) Portfolio #3 is invested in 10% in the S&500.

Answer 1

Expected return of TBills=10000/9615-1=4.004%

1.
Expected return=4.004%+6%=10.004%
Standard Deviation=15%*100%=15%

2.
Expected return=50%*(4.004%+6%)+50%*4.004%=7.004%
Standard Deviation=15%*50%=7.5%

3.
Expected return=10%*(4.004%+6%)+90%*4.004%=4.604%
Standard Deviation=15%*10%=1.5%