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.