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Problem 11-09

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 (%)
1		9.28	%	10.03	%
2		17.19		18.26
3		27.85		29.70
4		17.51		13.44
5		18.33		16.43
6		18.42		16.73
7		18.50		11.49
8		17.23		9.88
9		18.23		11.11
10		21.53		14.87
11		28.74		23.53
12		22.79		17.03
13		26.65		22.89
14		22.45		16.32
15		24.40		18.92
16		25.33		25.39
17		25.78		27.36
18		27.00		29.49
19		16.98		21.31
20		24.27		25.71
21		21.89		20.65
22		16.93		18.75
23		15.51		19.14
24		25.25		23.88

The Value Index: %

The Growth Index: %

The -Select-Growth IndexValue IndexItem 3 appears to have outperformed the -Select-Growth IndexValue IndexItem 4 over the 24-month period by %.

1. 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.

2. For each month in this sample period, compute the difference in annualized returns between the value index and the growth index (R_value - R_growth). 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-less thanmore thanthe same asItem 31 the difference in the arithmetic means.

3. 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-have beennot have beenItem 33 quite profitable. The hedge fund would have -Select-earnedlostItem 34 the average annualized return in the Value Index of %, thus -Select-earninglosingItem 36 it the additional risk premium of %.

4. 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.