Index Investor Model Portfolios - Backtesting Analyses

The following tables present backtested real returns for our 2006 - 2007 model portfolios, which were formed in 2005. Please keep the following important points in mind when reviewing them.

First, the target return for a model portfolio represents a geometric average real (after inflation) return. We use real returns because that is what matters to an investors purchasing power. In the tables, we present results in addition to the realized geometric real return for each model portfolio. The average annual return is the simple (arithmetic average). The standard deviation measures the extent to which annual returns are disbursed around this average. The return/risk ratio is the annual average divided by the standard deviation. It is a measure of how much return is being earned from each unit of risk taken on, with the latter defined as standard deviation. Finally, as an alternative risk measure, we also present the maximum quarterly drawdown (i.e., the lowest quarterly return) for each portfolio over the 1995 - 2005 period.

Second, to form our model portfolios we used a weighted mix of asset class return assumptions. We gave a fifty percent weight to historical results, and a fifty percent weight to the forward looking output of our asset pricing model. This model assumes that financial markets are strongly attracted to market equilibrium, in which state different asset classes will earn different risk premiums above the expected return on inflation protected government bonds. Given that our model portfolios are not wholly based on historical data, there are bound be differences between their backtested results and expected future performance. For example, as you can see, the geometric realized returns (i.e., the compound average returns) do not perfectly correspond to their targets.

Third, these tables make it quite clear that geometric real returns above 6% to 7% are usually very difficult to achieve.

Fourth, we also present the results for a model portfolio that equally weights all the asset classes we use in our basic portfolios, including real return bonds, domestic investment grade bonds, foreign bonds, domestic commercial property, foreign property, commodities (as measured by the Dow Jones AIG Commodities Index), timber, domestic equity, foreign equity, and emerging markets equity. Our advanced portfolios include allocations to equity market neutral (i.e., uncorrelated alpha strategies) and equity volatility; however, due to space limitations we do not show their results here. Their addition to a portfolio usually improves performance compared to the base case. The equally weighted portfolio is appropriate for an investor who believes it is impossible to forecast (to a degree of accuracy beyond luck) either the return or risk of any asset class. This is admittedly an extreme assumption; while relative returns are indeed very challenging to forecast, the relative riskiness of different asset classes is much more constant over time. Still, the equally weighted portfolio is a very interesting point of comparison for our other model portfolios. As you can see, in most cases, we are able to achieve a superior level of return per unit of risk in comparison to the equally weighted benchmark, despite the limitations of this comparison noted above.

Finally, we (like everyone else) stress that studies have repeatedly shown that historical results are no guarantee of future success. They represent one set of returns on different asset classes that were based on underlying conditions in the real economy and financial markets that may well change in the future. As we frequently note, there is an irreducible level of uncertainty associated with investing, and fallible human judgment will always be required.

Australian Dollars	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	13.66%	15.12%	13.22%	13.09%	15.87%	11.10%	11.83%
1996	8.22%	7.96%	7.22%	11.49%	9.44%	9.11%	5.95%
1997	30.66%	29.32%	24.83%	27.16%	26.80%	20.80%	25.75%
1998	10.91%	9.49%	8.51%	8.85%	12.36%	8.24%	6.57%
1999	8.45%	8.95%	6.06%	5.13%	1.59%	1.86%	5.17%
2000	4.20%	7.47%	9.44%	10.95%	10.32%	13.41%	10.62%
2001	-2.44%	-3.44%	-1.85%	-2.76%	-1.14%	0.33%	0.32%
2002	5.21%	3.76%	7.90%	5.95%	8.88%	10.57%	2.39%
2003	-1.93%	-2.60%	-2.85%	-6.75%	-7.83%	-6.18%	-0.91%
2004	6.21%	5.82%	6.23%	3.05%	4.28%	4.03%	9.57%
Geometric Avg.	7.97%	7.84%	7.63%	7.26%	7.68%	7.08%	7.49%
Annual Avg.	8.32%	8.19%	7.87%	7.62%	8.06%	7.33%	7.72%
Std. Dev.	9.35%	9.27%	7.71%	9.33%	9.61%	7.60%	7.62%
Return/Risk	0.89	0.88	1.02	0.82	0.84	0.96	1.01
Max Quarterly Drawdown	-6.36%	-6.80%	-5.32%	-4.76%	-5.64%	-3.98%	-5.16%
Canadian Dollars	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	12.54%	12.65%	8.72%	8.72%	8.64%	2.22%	6.97%
1996	14.07%	12.60%	10.67%	9.41%	9.25%	9.40%	12.93%
1997	11.23%	9.31%	7.97%	7.30%	7.24%	5.00%	7.06%
1998	3.13%	2.97%	3.49%	4.54%	4.30%	0.46%	1.78%
1999	20.30%	15.79%	7.21%	4.50%	3.18%	2.24%	9.42%
2000	2.88%	3.81%	5.33%	5.18%	5.45%	6.78%	4.83%
2001	-5.96%	-4.14%	-1.73%	-0.62%	0.66%	1.27%	-1.09%
2002	-5.57%	-3.06%	0.08%	1.31%	2.08%	4.07%	-1.17%
2003	11.46%	9.82%	9.63%	7.93%	7.46%	9.72%	10.19%
2004	6.58%	6.16%	6.24%	5.53%	5.55%	6.79%	8.06%
Geometric Avg.	6.75%	6.40%	5.69%	5.34%	5.35%	4.75%	5.80%
Annual Avg.	7.07%	6.59%	5.76%	5.38%	5.38%	4.79%	5.90%
Std. Dev.	8.52%	6.71%	4.07%	3.19%	2.84%	3.31%	4.76%
Return/Risk	0.83	0.98	1.42	1.69	1.90	1.45	1.24
Max Quarterly Drawdown	-7.80%	-7.31%	-5.53%	-5.59%	-5.05%	-5.09%	-6.88%
Euro	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	6.79%	6.80%	8.25%	9.82%	10.71%	10.85%	7.96%
1996	20.97%	19.74%	13.50%	10.22%	8.67%	8.58%	13.80%
1997	26.05%	21.54%	15.23%	12.88%	9.79%	8.09%	13.66%
1998	6.66%	5.43%	2.34%	3.93%	4.72%	5.70%	-0.20%
1999	39.72%	35.47%	27.10%	19.95%	14.65%	10.79%	26.24%
2000	-0.86%	-0.16%	1.50%	3.90%	4.13%	5.18%	3.16%
2001	-14.70%	-11.89%	-5.93%	-3.12%	-0.92%	-0.33%	-4.11%
2002	-27.35%	-21.49%	-10.69%	-3.75%	0.07%	2.86%	-10.03%
2003	13.35%	14.52%	9.44%	5.91%	5.01%	5.08%	8.29%
2004	9.14%	11.59%	9.49%	8.04%	7.62%	7.76%	9.53%
Geometric Avg.	6.31%	6.96%	6.53%	6.56%	6.35%	6.40%	6.39%
Annual Avg.	7.98%	8.15%	7.02%	6.78%	6.44%	6.46%	6.83%
Std. Dev.	19.37%	16.57%	10.85%	7.15%	4.81%	3.50%	10.27%
Return/Risk	0.41	0.49	0.65	0.95	1.34	1.85	0.67
Max Quarterly Drawdown	-20.95%	-18.90%	-12.02%	-7.91%	-5.04%	-3.37%	-11.24%
Indian Rupees	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	5.51%	5.17%	6.25%	7.90%	7.24%	6.11%	10.71%
1996	12.30%	11.18%	10.98%	7.52%	5.04%	5.65%	9.69%
1997	12.20%	12.53%	11.26%	10.88%	11.89%	10.35%	6.42%
1998	-7.29%	-7.72%	-7.69%	-3.55%	-2.59%	-5.32%	-7.34%
1999	23.57%	24.28%	23.23%	15.04%	13.77%	13.82%	19.14%
2000	6.02%	6.68%	7.02%	7.05%	5.66%	7.81%	6.94%
2001	-1.28%	-0.66%	-1.19%	2.73%	5.64%	7.39%	-4.04%
2002	-2.32%	-0.28%	-0.09%	3.29%	4.77%	7.53%	-0.76%
2003	11.18%	10.55%	11.27%	8.09%	7.88%	8.25%	13.94%
2004	2.80%	1.25%	2.12%	0.14%	-1.40%	-1.40%	6.24%
Geometric Avg.	5.93%	5.96%	6.01%	5.78%	5.68%	5.89%	5.81%
Annual Avg.	6.27%	6.30%	6.32%	5.91%	5.79%	6.02%	6.09%
Std. Dev.	8.96%	8.94%	8.62%	5.38%	5.07%	5.53%	8.14%
Return/Risk	0.70	0.70	0.73	1.10	1.14	1.09	0.75
Max Quarterly Drawdown	-9.29%	-8.61%	-8.60%	-4.95%	-4.13%	-3.85%	-8.72%
Japanese Yen	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	13.52%	18.34%	17.80%	20.04%	17.82%	17.43%	15.39%
1996	13.23%	21.38%	20.13%	18.08%	12.69%	10.07%	12.94%
1997	7.65%	17.84%	15.73%	15.31%	11.23%	8.50%	9.69%
1998	-12.89%	-7.31%	-8.00%	-6.93%	-7.96%	-7.98%	-11.48%
1999	19.87%	12.34%	15.98%	11.08%	10.25%	8.18%	11.01%
2000	5.22%	6.14%	4.92%	6.80%	7.06%	7.88%	8.19%
2001	-4.49%	2.19%	-0.39%	1.32%	0.95%	2.16%	1.79%
2002	-11.14%	-12.19%	-12.10%	-7.59%	-4.25%	-0.74%	-5.52%
2003	19.38%	12.97%	14.96%	13.38%	11.48%	8.89%	12.67%
2004	8.76%	5.31%	5.77%	6.16%	6.14%	4.91%	6.83%
Geometric Avg.	5.29%	7.16%	6.92%	7.36%	6.26%	5.72%	5.81%
Annual Avg.	5.91%	7.70%	7.48%	7.77%	6.54%	5.93%	6.15%
Std. Dev.	11.79%	11.11%	11.34%	9.74%	8.05%	6.89%	8.70%
Return/Risk	0.50	0.69	0.66	0.80	0.81	0.86	0.71
Max Quarterly Drawdown	-13.51%	-12.84%	-13.28%	-9.15%	-6.40%	-5.58%	-7.91%
Swiss Francs	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	18.27%	18.27%	17.23%	16.08%	13.61%	10.09%	4.38%
1996	20.69%	20.69%	22.68%	21.86%	16.18%	7.98%	24.91%
1997	40.02%	40.02%	35.14%	26.73%	21.30%	10.49%	12.29%
1998	12.60%	12.60%	10.03%	9.56%	12.17%	7.04%	2.25%
1999	16.19%	16.19%	19.77%	20.57%	14.58%	-0.09%	28.03%
2000	7.34%	7.34%	10.37%	11.72%	6.25%	2.68%	3.52%
2001	-16.42%	-16.42%	-17.12%	-15.09%	-8.11%	1.71%	-6.82%
2002	-21.48%	-21.48%	-18.57%	-12.64%	-8.27%	3.49%	-13.12%
2003	16.12%	16.12%	15.59%	13.86%	9.55%	1.14%	11.86%
2004	5.89%	5.89%	6.57%	7.83%	7.62%	4.76%	8.06%
Geometric Avg.	8.52%	8.52%	8.92%	9.19%	8.07%	4.87%	6.86%
Annual Avg.	9.92%	9.92%	10.17%	10.05%	8.49%	4.93%	7.54%
Std. Dev.	17.89%	17.89%	16.78%	13.88%	9.79%	3.78%	12.69%
Return/Risk	0.55	0.55	0.61	0.72	0.87	1.31	0.59
Max Quarterly Drawdown	-19.89%	-19.89%	-18.44%	-13.93%	-8.16%	-2.45%	-12.69%
U.K. Pounds	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	11.83%	10.84%	11.39%	10.79%	9.61%	9.31%	10.05%
1996	9.92%	6.16%	5.61%	4.40%	5.70%	4.33%	6.43%
1997	10.56%	2.50%	6.59%	2.53%	4.65%	7.31%	4.21%
1998	-2.88%	-3.36%	1.49%	1.02%	-0.14%	5.16%	-5.12%
1999	16.89%	12.34%	11.35%	8.47%	8.35%	7.79%	13.32%
2000	4.36%	9.23%	6.51%	9.47%	10.13%	6.52%	9.20%
2001	-8.52%	-2.80%	-4.08%	-2.22%	-1.93%	-2.34%	-3.48%
2002	-13.93%	-4.49%	-5.61%	-0.60%	0.54%	1.20%	-5.64%
2003	18.59%	14.56%	11.84%	11.07%	11.86%	8.96%	15.96%
2004	13.55%	10.54%	8.97%	9.33%	12.18%	10.07%	13.19%
Geometric Avg.	5.49%	5.33%	5.23%	5.32%	5.98%	5.76%	5.53%
Annual Avg.	6.04%	5.55%	5.41%	5.43%	6.10%	5.83%	5.81%
Std. Dev.	11.03%	7.10%	6.28%	5.00%	5.17%	3.91%	8.05%
Return/Risk	0.55	0.78	0.86	1.08	1.18	1.49	0.72
Max Quarterly Drawdown	-12.17%	-7.41%	-6.67%	-5.30%	-5.31%	-3.49%	-7.83%
U.S. Dollars	7% Tgt.	6% Tgt.	5% Tgt.	4% Tgt.	3% Tgt.	2% Tgt.	Eq. Wtd.
1995	13.16%	14.09%	11.94%	11.20%	13.95%	8.46%	11.46%
1996	8.49%	8.42%	7.58%	7.46%	7.74%	5.53%	9.86%
1997	10.51%	9.47%	6.77%	8.74%	9.75%	5.77%	2.44%
1998	2.81%	2.17%	0.18%	0.93%	4.20%	0.11%	-1.49%
1999	11.63%	11.60%	8.64%	9.79%	4.24%	6.61%	12.95%
2000	-0.84%	1.27%	3.65%	4.14%	4.37%	6.17%	-0.40%
2001	-3.51%	-5.55%	-4.02%	-3.72%	-2.01%	-2.87%	-7.14%
2002	-3.63%	-1.15%	3.11%	3.85%	3.94%	8.79%	0.96%
2003	17.68%	17.73%	16.54%	16.73%	13.50%	13.00%	23.87%
2004	8.94%	8.22%	8.38%	7.78%	7.40%	6.94%	13.85%
Geometric Avg.	6.29%	6.40%	6.13%	6.55%	6.61%	5.77%	6.27%
Annual Avg.	6.52%	6.63%	6.28%	6.69%	6.71%	5.85%	6.63%
Std. Dev.	7.39%	7.26%	5.86%	5.70%	4.84%	4.44%	9.30%
Return/Risk	0.88	0.91	1.07	1.17	1.39	1.32	0.71
Max Quarterly Drawdown	-6.12%	-5.37%	-3.72%	-3.88%	-3.14%	-3.92%	-6.21%