Anon

136 The Basics of financial economeTrics

tAble 6.3 (continued)
Mutual Fund
Month
Ended rM rft

Dummy

Dt

rM – rft =

xt Dtxt

A

rt

B

rt

A

yt

B

yt

12/31/2003 5.24 0.08 1 5.16 5.16 4.87 4.77 4.79 4.69
01/31/2004 1.84 0.07 1 1.77 1.77 0.87 2.51 0.80 2.44
02/29/2004 1.39 0.06 1 1.33 1.33 0.97 1.18 0.91 1.12
03/31/2004 –1.51 0.09 1 –1.60 –1.6 –0.89 –1.79 –0.98 –1.88
04/30/2004 –1.57 0.08 1 –1.65 –1.65 –2.59 –1.73 –2.67 –1.81
05/31/2004 1.37 0.06 0 1.31 0 0.66 0.83 0.60 0.77
06/30/2004 1.94 0.08 0 1.86 0 1.66 1.56 1.58 1.48
07/31/2004 –3.31 0.10 1 –3.41 –3.41 –2.82 –4.26 –2.92 –4.36
08/31/2004 0.40 0.11 0 0.29 0 –0.33 0.00 –0.44 –0.11
09/30/2004 1.08 0.11 0 0.97 0 1.20 1.99 1.09 1.88
10/31/2004 1.53 0.11 0 1.42 0 0.33 1.21 0.22 1.10
11/30/2004 4.05 0.15 1 3.90 3.9 4.87 5.68 4.72 5.53
12/31/2004 3.40 0.16 1 3.24 3.24 2.62 3.43 2.46 3.27

Notes:

1. The following information is used for determining the value of the dummy variable for the first three months:

rm rf rm – rf
Sep–1994 –2.41 0.37 –2.78
Oct-1994   2.29 0.38   1.91
Nov-1994 –3.67 0.37 –4.04
Dec-1994   1.46 0.44   1.02

2. The dummy variable is defined as follows:
   Dt xt = xt if (rM – rft) for the prior three months > 0
   Dt xt = 0 otherwise

For both funds, β 2 i is statistically significantly different from zero.
Hence, for these two mutual funds, there is a difference in the βi for up and
down markets.^5 From the results reported above, we would find that:

Mutual Fund A Mutual Fund B

Down market βi (= β 1 i) 0.75 0.75

Up market βi (= β 1 i + β 2 i) 0.93 (= 0.75 + 0.18) 0.88 (= 0.75 + 0.13)

(^5) We specifically selected funds that had this characteristic so one should not infer
that all mutual funds exhibit this characteristic.