246 Performance Measurement in Finance
thereby implying misspecified models. Our testing framework demonstrates
the dependence of spanning tests on joint rationality restrictions and makes
the importance of rationality restrictions clear. It is entirely possible for nei-
ther spanning restrictions nor rationality restrictions to hold, for both to hold,
or for either set of restrictions to hold. A well-specified system should span
the asset universe and meet prescribed rationality conditions.
9.5 EMPIRICAL ANALYSES
9.5.1 The asset and instrument data
The data consists of 14 monthly excess return series that are used as assets in
the multivariate analysis, along with nine series that are used as information
instruments. Data is from January 1965 to December 1999; because of the use
of up to 12 lags of return variables, the analysis period is 1/1966 to 12/1999,
inclusive. As in Fama and French (1989), we choose assets to develop a
continuous maturity structure IOS that occurs in an integrated financial market
of short- and long-term debt and equity markets. The 14 assets include excess
returns of one month holding period returns on the following assets; US
Treasury bills with three months to maturity, five year Treasury bonds, 30 year
Treasury bonds, the CRSP value weighted index and ten equal weighted size-
based decile portfolios.
17
Table 9.1 reports summary statistics of sample means, standard deviations,
skewness and kurtosis for each of the assets. The first two columns show
the unconditional sample means and standard deviations for all excess return
series. As expected, the Treasury bill series displays a relatively small uncon-
ditional sample mean and standard deviation. The value weighted equity
Table 9.1 Summary excess return statistics for the sample period from January 1966 through
December 1999
Asset series Mean*10
2
Std. dev.*10
2
Standard
skewness
Kurtosis Normality
test
R
TB3t
0.0513 0.1081 40.698 374.99 0.00
R
5Bt
0.1229 1.6910 0.0251 2.985 0.00
R
30Bt
0.0944 3.1178 0.0031 2.999 0.00
R
Et
0.5335 4.5091 0.0042 2.999 0.00
Sample means, standard deviations, skewness, and kurtosis are presented for one month holding
period, excess returns on three month Treasury bills, R
TB3t
, five year Treasury bonds, R
5Bt
,thirty
year Treasury bonds, R
30Bt
, and the CRSP value weighted index, R
Et
, respectively. The final
column reports p-values from Bowman and Shenton (1975) tests for normality.
17
The asset set is similar to the set in Evans (1994), who studies the ICAPM.
The intertemporal performance of investment opportunity sets 247
portfolio shows a substantially larger portfolio mean and standard deviation.
This sample period produced smaller 30 year bond portfolio performance than
the five year bonds. This smaller sample mean comes without a substantial
reduction in the unconditional standard deviation. Short maturity Treasury
bills tend to be the most right skewed relative to the small skewness in the
remaining assets. All excess return series display marked leptokurtism relative
to the normal distribution. The final column of the table reports the Bowman
and Shenton (1975) test for normality, which is distributed as a χ
2
random
variable. In general, we conclude that the excess return series have significant
departures from normality.
We choose a large set of information instruments to proxy for the infor-
mation set facing investors at the beginning of any investment period. Our
conditional moment estimates are directly influenced by the instrument set
used. We seek information instruments that are economically meaningful as
found in previous research. In addition, we include time series instruments
to proxy for missing economic variables and to mitigate possible microstruc-
ture effects. All information instruments used as conditioning information in a
month t conditional moment equation, are known at the beginning of month t.
Economic information instruments for conditional mean and volatility
equations include a constant, the first difference in one month Treasury bill
returns, the excess junk yield on corporate bonds rated Baa by Moodys, one
lag of Standard and Poors 500 dividend yield, the first difference of the lag
of the natural logarithm of total volume on the NYSE and a January dummy
variable.
Existing literature using variants on these economic regressors is well
established. Previous research examining changes in the riskless rate include
Campbell (1987) and Schwert (1989). In our context, this variable measures
changes in the continuous risk structure vertex location from one period to
the next. Yields on long-term bonds and spreads between high-yield debt and
comparable Government debt have been included in various forms in many
studies requiring economic motivations for conditional asset means (c.f. Chen,
Roll and Ross (1986), or Fama and French (1989)). Lamoureux and Las-
trapes (1990) find contemporaneous volume may be used as a regressor in
conditional volatility equations to eliminate ARCH effects. We include first
differences of lagged volume as information instruments in both mean and
volatility equations to accommodate both information arrival and microstruc-
ture explanations for volume. Lagged volume is also motivated by the findings
of Gallant, Rossi and Tauchen (1992) and Conrad, Hameed and Niden (1994).
Further discussion of important predictor variables can be found in Keim
and Stambaugh (1986), Breen, Glosten and Jagannathan (1989) Kandel and
Stambaugh (1989) and Jegadeesh (1991).

Get Performance Measurement in Finance now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.