$1$ Price Momentum $(50$ points$)$

The file Project $1.$xls in the Projects folder contains monthly data on risk$-$free rate $($RF$),$

the excess return to the market $($MKT$-$RF$),$ and the returns to the momentum strategy

$($MOM$)$ between January $1970$ and June $2009.$ The momentum strategy buys the stocks

with the most positive returns in the past year and shorts the stocks with the most negative

returns in the past year. For this problem, assume that the risk$-$free rate RF is not constant.

i$.$ Compute the monthly average and the monthly standard deviation for MOM and

RF$.(5$ points$)$

ii$.$ Based on these sample estimates, build the $95\%$ confidence interval for the return

to the MOM portfolio in the next year. Provide a concise explanation of what this

interval means in economic terms. $(10$ points$)$

iii. Assuming that the returns to the MOM strategy are uncorrelated across time, repeat

$($ii$)$ for the expected annual return to the index. Explain the difference. $(10$ points$)$

iv$.$ Assume that MOM and RF are uncorrelated. Compute the mean and standard

deviation of the daily return to strategy S$,$ which is $70\%$ MOM and $30\%$ RF$.$ Assume

$22$ trading days in a month. $(5$ points$)$

v$.$ Can you reject the hypothesis that the true expected monthly return to MOM is

zero? Use all three ways to test the hypothesis we discussed in class. $(10$ points$)$

vi$.$ Bonus question: Test the equality of the average returns to the MOM strategy and

the average excess return to the market, MKT$-$RF$.(10$ points$)$

vii. Compute VaR for strategy S if $$1,000,000$ is invested for one quarter. Assume $63$

trading days per quarter. $(10$ points$)$

$1$