Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

The Windham Portfolio Advisor 101

should an unpleasant loss occur, they will not be unduly surprised and act to
reduce risk out of a misguided perception that the nature of their investment
strategy has changed.

4.4 Risk regimes

4.4.1 The problem

It is well known that volatilities and correlations are unstable. They may differ
significantly depending on the sample used to estimate them. This instability
may lead investors to underestimate their exposure to loss and to form portfo-
lios that are not sufficiently resilient to turbulent markets.

4.4.2 The WPA solution

The WPA includes a methodology for partitioning historical returns into dis-
tinct samples that are characteristic of quiet markets and turbulent markets. 4
This separation enhances risk management in several ways. It enables investors
to stress test portfolios by evaluating their exposure to loss during turbulent
conditions. It enables investors to structure portfolios that are more resilient to
turbulent markets. And it enables investors to shift their portfolios ’ risk pro-
files dynamically to accord with their assessment of the relative likelihood that
market conditions will be quiet or turbulent.
The WPA uses a statistical procedure to isolate periods in which returns are
unusual either in their magnitude or in their interaction with each other. For
example, a period may qualify as unusual because two assets whose returns are
positively correlated generate returns that move in the opposite direction. These
periods with unusual returns represent statistical outliers, and they are typically
associated with turbulent markets. The WPA creates subsamples of these out-
liers and estimates volatilities and correlations from these turbulent subsamples.
It also estimates volatilities and correlations from the remaining returns, which
represent quiet markets.

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0

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Conventional Continuous

5:1 7.5:1 10:1 15:1

Figure 4.5 5% value at risk, 3-year lockup period.

4 See Chow et al (1999) and Kritzman et al (2001) for a description of this methodology.