It's been a half-decade not to own large-cap equities.
Ex-post measures are not benchmarks.
Tracking errors and information ratios4
| year | TE.466/.534 | IR.466/.534 | ||
| 1999 | 4% | 0.8 | ||
| 2000 | 8% | 1.1 | ||
| 2001 | 8% | -0.1 | ||
| 2002 | 8% | 0.5 | ||
| 2003 | 8% | 1.1 | ||
| 99-03 | 7% | 0.6 |
The lower the tracking error, the less misleading the information ratio.
I started with performance against a basic basket of indexes: non-US/small/large equities and non-US/US bonds:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0031 0.0030 1.0 0.31
GFD.WdxUS 0.0534 0.1594 0.3 0.74
Russ.2k 0.5141 0.0750 6.9 7e-09 ***
S.P.500 -0.0443 0.1162 -0.4 0.70
ML.C.G 0.0155 0.3335 0.05 0.96
ML.GG 0.5532 0.2755 2.0 0.05 *
---
Multiple R-Squared: 0.73, Adjusted R-squared: 0.7
F-statistic: 30 on 5 and 55 DF, p-value: 1.9e-14
Note immediately that the intercept (alpha) here has a one-in-three chance of being greater than zero only by chance. An accurate reflection of uncertainty and rightly humbling, I think. Note also that I have not constrained coefficients, and so get both negative numbers (a small short of large-caps) and a net investment greater than 100%.
Digging through anova tables shows the intuitive parsimonious submodel using only small-caps and global bonds works:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0030 0.0028 1.1 0.3
Russ.2k 0.5220 0.0424 12.3 <2e-16 ***
ML.GG 0.5976 0.1467 4.1 1e-04 ***
---
Multiple R-Squared: 0.73, Adjusted R-squared: 0.72
F-statistic: 78 on 2 and 58 DF, p-value: <2e-16
Scaled down to 100% invested, this is the source of the otherwise-inexplicable ex-post blend index. It's not a real benchmark.
As analysis, these regressions were a mixed bag. They capture some truths: alpha while positive is not significant, holdings indeed favored non-dollar-denominated fixed income and small stocks. However, the large real allocation to foreign equities is not seen.
Here are the residuals of the parsimonious regression, month by month.
There may be some time dependence, but an eyeball judgement is not enough. Here's a look at the estimated autocorrelation function.
There is more time structure than you want to see, but nothing pops over the significance bands. Durbin-Watson statistics for the first several lags similarly are not significant:
lag Autocorrelation D-W Statistic p-value 1 0.1573 1.68 0.166 2 -0.1657 2.30 0.178 3 -0.0396 2.01 0.712 4 -0.1418 2.20 0.280 5 -0.1571 2.21 0.140 6 -0.1599 2.20 0.150 Alternative hypothesis: rho[lag] != 0
Interesting that first-order autocorrelation is positive. Albeit too weakly to be significant, on a one-month basis the trend was my friend. Thereafter performance appears to have been as weakly mean-reverting.
1This page is not a formal presentation or an advertisment of any kind. I am not an investment firm. I have no composite. This page is for illustrative purposes and comes with no guarantees of any sort. I endeavored to follow calculations standards and have tried to make "every reasonable effort to assure that [my] performance information is a fair, accurate, and complete presentation of [my] performance." That said, I very explicitly have not prepared or presented this information in compliance with the Performance Presentation Standards of the Association for Investment Management and Research (AIMR-PPS®), the U.S. and Canadian version of the Global Investment Performance Standards (GIPS®). AIMR has not been involved in the preparation or review of these performance calculations or this presentation.
In re the size and density of that footnote, better safe than sorry.
2 Growth of $100 represents the hypothetical return to $100 using monthly total returns of portfolios and indexes. Return vs volatility is annualized five-year total returns vs annualized five-year standard deviations of the returns. Ex-Post Regression shows ordinary least-squares fit to monthly portfolio risk premium versus ex-post blend RP.
3 .466/.534 ex-post index blend represents a monthly total return blend of 46.6% Russell 2000 and 53.4% Merrill Lynch Global Government Bond indexes.
4 Risk premium (RP) is the monthly total return in excess of T-Bill return, a proxy for the true risk-free return. Tracking error (TE) is the standard deviation of monthly out-/underperformance versus a benchmark index. Information ratio (IR) is the out-/underperformance versus the index divided by the tracking error.
5 Regressions and other detailed statistics calculated with R.
