In the previous post, we investigated whether outperforming funds report their results earlier in the month, and whether that induces a systematic bias into the early reported hedge fund indices relative to the finalized values at the end of the month. The table below shows my measurements of the Dynamic Trading Risk Factor, as estimated through the procedures outlined on this blog, as determined according to a fairly ad-hoc updating schedule determined by my commitments to other projects.
| Mark Date |
Initial Latency Days |
Initial Rate of Return/% |
Initial Sample |
Final Latency Days |
Final Rate of Return/% |
Final Sample |
Corrected Estimate/% |
Residual/% (H0) |
Residual/% (H1) |
| 08/31/2009 |
16 |
2.26 |
1545 |
35 |
1.94 |
2622 |
2.05 |
0.32 |
0.12 |
| 09/30/2009 |
3 |
3.99 |
2 |
37 |
3.25 |
2621 |
3.49 |
0.74 |
0.24 |
| 10/31/2009 |
2 |
2.05 |
10 |
30 |
-0.47 |
2577 |
1.55 |
2.51 |
2.02 |
| 11/30/2009 |
30 |
1.47 |
1 |
36 |
1.40 |
2634 |
0.97 |
0.07 |
-0.43 |
| 12/31/2009 |
5 |
2.24 |
4 |
33 |
2.25 |
2567 |
1.74 |
-0.01 |
-0.51 |
| 01/31/2010 |
2 |
-0.53 |
55 |
38 |
-0.11 |
2012 |
-1.02 |
-0.42 |
-0.91 |
| 02/28/2010 |
8 |
0.89 |
151 |
10 |
0.81 |
1178 |
0.45 |
0.08 |
-0.36 |
For each month we present the first recorded estimate of the factor return, the final recorded estimate of the factor return, and a “corrected estimate” or forecast final value based upon our bias expression from the prior post and the initial estimate. We compute residuals for two hypotheses:
- the null, H0, that the early measurement is an unbiased estimate of the final value; and,
- the alternate, H1, that the corrected estimate is a better forecast of this final value.
We can compare these hypothesis by evaluating their forecasting skill, which gives a 23% edge to the corrected estimate. This skill is usually defined by the following equation, where MSE means mean square error.
}{\mathrm{MSE}(H_0)})