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2.4. PERFORMANCE MEASUREMENT: SHADOWING
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0.55
0.65
0.75
Correlation: shrink with realized
Figure 2.10: Quarterly correlations shrinkage versus realized: 120/20.
07Q1
2.4
07Q2
07Q3
07Q4
08Q1
08Q2
08Q3
08Q4
Performance Measurement: Shadowing
Section 2.1 presents the static method of performance measurement. While
that method is more powerful than peer groups and benchmarks, we can often
do even better. If we know some or all of the positions of the portfolio at
the beginning of the test period, random portfolios can give us a much more
sensitive test of performance.
The information that we need for this method is:
• the constraints under which the fund operates
• some or all of the positions at the start of the time period
• the known or approximate turnover of the fund throughout the period
With this method we imitate the trading of the fund throughout the period.
We get one random portfolio by means of a series of random trades starting
with what we know about the initial portfolio. We then repeat that a number
of times.
Let’s revisit the example we saw in Section 2.1. We know the full portfolio
at the start of the period, and we know the typical daily trading. We use this
knowledge to get the distribution of returns with zero skill.
Figure 2.11 shows the results for the year 2007 with 200% turnover, while
Figure 2.12 shows the 2007-2008 results for 200% turnover. The strategy is
very clearly outperforming chance. The results are even more extreme for 400%
turnover. Table 2.2 shows the numerical results.