Question

True or False

12. If you have the historical data of S&P500 index level in the last 5 years, you can compute the returns of investment in 500 stocks in the S&P500. Assume you know the 500 constituents.

13. If you just watched bad news on the market on CNBC and if you believe the market risk premium is 0.5% for the next month and, you should short sell the market to maximize your Sharpe ratio.

14. A portfolio’s net return is a weighted arithmetic average of the net returns of its constituents while the portfolio’s long-term holding period return is the sum of the net returns of the portfolio in each period.

15. When you mix multiple risky assets to maximize Sharpe ratio, you should invest at least $1 in all assets for diversification if short sale is not allowed. It means that your optimal weights are all positive and there are no zeros.

Answer 1

12. True. the S&P index value tells the weighted average value of market capitalization of all 500 stocks. By taking index value of last 5 years, we can calculate the returns on its 500 stocks, which will be the weighted average return.

S&P index = Sum of market capitalization of all 500 stocks / Index divisor, where index divisor is the number of stocks.

13. False. As, this bad news would have impacted the volatility of market also and it will be increased after hearing the bad news. The risk premium will be +0.5%, but volatility also will increase. so, we can't say that overall the sharpe ratio will be maximize or not.

Sharpe Ratio = ( Average Returns - Risk Free Returns ) / Volatility

14. False. A portfolio's net return is a weighted arithmetic average of the net returns of its constituents. This is true as

Rp = w1 . R1 + w2 . R2
Rp = return of portfolio,
R1 & R2 = Return on security 1 & 2.

while the portfolio’s long-term holding period return is not the sum of the net returns of the portfolio in each period. we need to divide the sum of net returns in each period by the number of periods to arrive at the holding period return.

15. True. To maximize the sharpe ratio, we need to keep the total risk same and increase the risk premium rate by taking higher risk. Here, we are increasing the risk premium by investing in risky assets and also maintaining same levels of total risk by investing same amount in all assets for diversification.

Sharpe Ratio = ( Average Returns - Risk Free Returns ) / Volatility,

Risk premium = Average Returns - Risk Free Returns.