More than you ever wanted to know about conditional value at risk optimization 289
around mean returns), downside risk measures focus exclusively on losses (often
defined as shortfalls below a given target return). This sounds in line with a more
layman interpretation of risk (risk only arises from unexpected losses not from
unexpected profits), but it carries some underappreciated side effects. First, this
view ignores the fact that any asset that goes up a lot might also go down a lot.
We might not have seen losses in a particular asset for a long time (Japanese equity
market between 1975 and 1992), but that does not mean we are not exposed
(Japanese equities fell about 70% in the following 3 years). In other words, what
can go up can go down. CVaR will not realize that large upside deviations from
average growth are a sign of volatility and should not be ignored in risk consid-
erations. Second (and very much related to the point above), CVaR will create a
bias toward momentum investing. 7 Assets that show positive momentum will not
only exhibit positive returns, but also lower risks as a sequence of positive returns
will reduce the measured downside risk. What is hoped to be a more appropriate
risk measure will tend to load up on a momentum factor. Backtests on realized
return data claiming the superiority of downside risk measures relative to disper-
sion measures should be very mindful to this and might give a misleading picture.
7 While it is true that momentum will also cause autocorrelation in returns and therefore lead to
an underestimate in volatility, this effect is much less pronounced.
Figure 12.1 Are deviations from symmetry stable? In order to assess the stability of
estimates for nonnormality, we split the sample into two 10-year periods and estimate
the excess skew for each series and time period. The solid line represents fitted values
from Equation (12.10).
Excess semivariance (t)Excess semivariance (t+1)- 0.0018 –0.0016 –0.0014 –0.0012 –0.0010 –0.0008 –0.0006
–0.004–0.003–0.002–0.001Oil and GasBasic MatsIndustrialsCons GdsHealth CareCons SvsTelecomUtilitiesFinancialsTechnology