314 The Basics of financial economeTrics
summarize the performance of some of the representative portfolios from a
study conducted and updated by Ma in 2005 and 2010.^13
It is not surprising that higher excess returns are generally associated
with higher correlation between successive returns. More importantly,
higher risk seems to be also related to higher statistical significance of the
relationship (correlation). The bottom line is that an acceptable level of risk-
adjusted excess return, in the form of information ratio (e.g., 1), cannot
always be achieved by statistical significance alone. A more striking obser-
vation, however, is that, sometime without conventional statistical signifi-
cance, the portfolio was able to deliver superior risk-adjusted returns. While
the driving force may yet be known, evidence is provided for the discon-
nection between statistical significance and abnormal risk-adjusted returns.
Investment Strategy Process
Once the quantitative research process is completed, implementing financial
econometric results involves the investment strategy process. As can be seen
in Figure 15.1, this involves two phases:
- Estimating expected returns
- Independent risk control.
We describe each below.(^13) Ma, “How Many Factors Do You Need?”
taBle 15.3 Statistical Significance and Economic Profits
Correlation
Coefficienta t-Valueb
Annual
Excess
Return (%)
Annual
Standard
Deviation (%)
Information
Ratio
0.10 2.10b 0.50 2.17 0.230
0.25 3.78b 1.82 4.06 0.448
0.50 7.15b 3.71 4.25 0.873
0.15 1.20 0.58 1.10 0.527
0.35 2.93b 1.98 4.55 0.435
0.60 2.75b 3.80 4.55 0.835
aSignificant at the 1% level.
bt-value is for the significance of correlation coefficient.
Source: Christopher K. Ma, “How Many Factors Do You Need?” Research Paper
#96-4, KCM Asset Management, Inc., 2010.