Each month for the past several years, you have collected the monthly returns to an index of large$-$cap value stocks and an index of large$-$cap growth stocks. For the last two years, for both of the indexes you have converted these monthly returns into a series of rolling average annualized returns by taking an average of the previous $12$ monthly returns and multiplying that average by $12.$ These rolling average annualized returns are shown below for each index over the past $24$ months.

Month Value Index Annualized

Return $(\%)$ Growth Index Annualized

Return $(\%)$

$19\mathrm{.}07\%9\mathrm{.}39\%$

$215\mathrm{.}6816\mathrm{.}72$

$326\mathrm{.}5529\mathrm{.}49$

$417\mathrm{.}6117\mathrm{.}87$

$517\mathrm{.}6716\mathrm{.}43$

$618\mathrm{.}1716\mathrm{.}73$

$718\mathrm{.}7911\mathrm{.}44$

$817\mathrm{.}2610\mathrm{.}44$

$918\mathrm{.}2610\mathrm{.}47$

$1020\mathrm{.}9812\mathrm{.}68$

$1128\mathrm{.}1622\mathrm{.}50$

$1222\mathrm{.}0218\mathrm{.}07$

$1326\mathrm{.}5320\mathrm{.}23$

$1421\mathrm{.}9116\mathrm{.}82$

$1523\mathrm{.}0219\mathrm{.}42$

$1625\mathrm{.}3724\mathrm{.}65$

$1728\mathrm{.}1527\mathrm{.}71$

$1829\mathrm{.}4028\mathrm{.}51$

$1915\mathrm{.}9420\mathrm{.}87$

$2024\mathrm{.}5723\mathrm{.}75$

$2123\mathrm{.}0922\mathrm{.}25$

$2217\mathrm{.}5718\mathrm{.}99$

$2317\mathrm{.}6818\mathrm{.}88$

$2424\mathrm{.}5826\mathrm{.}23$

For both the value and growth indexes, calculate the arithmetic mean of the $24$ monthly average annualized returns. Which index appears to have outperformed the other over this period? Explain. Do not round intermediate calculations. Round your answers to two decimal places.

The Value Index:

$\%$

The Growth Index:

$\%$

The

$-$Select$-$

appears to have outperformed the

$-$Select$-$

over the $24-$month period by

$\%.$

For each month in this sample period, compute the difference in annualized returns between the value index and the growth index $($Rvalue $-$ Rgrowth$).$ Calculate the average of this return differential series and compare it to your answers from part $($a$).$ Do not round intermediate calculations. Round your answers to two decimal places. Negative values, if any, should be indicated by a minus sign. If your answer is zero, enter $0.$

Month Rvalue $-$ Rgrowth

$1$

$\%$

$2$

$\%$

$3$

$\%$

$4$

$\%$

$5$

$\%$

$6$

$\%$

$7$

$\%$

$8$

$\%$

$9$

$\%$

$10$

$\%$

$11$

$\%$

$12$

$\%$

$13$

$\%$

$14$

$\%$

$15$

$\%$

$16$

$\%$

$17$

$\%$

$18$

$\%$

$19$

$\%$

$20$

$\%$

$21$

$\%$

$22$

$\%$

$23$

$\%$

$24$

$\%$

Average

$\%$

The average of the return in the differential series is

$-$Select$-$

the difference in the arithmetic means.

Choose the correct graph of the return differential series.

A$.$

B$.$

C$.$

D$.$

The correct graph is

$-$Select$-$

$.$

The average return differential from part $($b$)$ is one way of calculating the risk premium associated with a value investment factor. Interpret this risk premium statistic and explain how it can be seen as the average annualized return earned by a hedge fund following a strategy to go long in value stocks and short in growth stocks. Do not round intermediate calculations. Round your answers to two decimal places. Negative values, if any, should be indicated by a minus sign.

A hedge fund that was following a strategy to go long in value stocks and short in growth stocks would

$-$Select$-$

quite profitable. The hedge fund would have

$-$Select$-$

the average annualized return in the Value Index of

$\%,$ thus

$-$Select$-$

it the additional risk premium of

$\%.$

Compute the percentage of the months in the two$-$year sample period when the rolling average annualized return to the growth index was actually larger than that for the value index. Do not round intermediate calculations. Round your answers to two decimal places.

$\%$

What, if anything, does this tell you about the reliability of the value risk premium over time?

This means that the value risk premium of

$\%$ was reliable for over

$\%$ of the time in the period studied.