# The Benefits Of Low Correlation: Round II

October 21, 2008

This article is an update of an article published in the November/December 2007 issue of the Journal of Indexes titled "The Benefits of Low Correlation." Please see the introduction and literature review of the original article.

Description And Justification
This study examines the aggregate correlation among various assets and the corresponding impact on portfolio performance as measured by standard deviation of annual returns, internal rate of return (IRR), worst one-year portfolio drawdown (or loss), worst three-year cumulative return, and frequency of portfolio loss. These last three measures will prove to be more compelling performance measures than standard deviation of return.

Worst one-year portfolio loss is a measure of the percentage change in the portfolio account value from one year to the next. When examining a withdrawal portfolio during retirement, this measure also takes into account the increasing annual withdrawals that occur at the end of each year. Frequency of portfolio loss is a measure of how often the portfolio lost value from year-end to year-end.

It is proposed that three measures of portfolio risk-worst one-year portfolio loss, frequency of loss and worst three-year cumulative return-are more intuitively useful (and compelling) to the average investor than is standard deviation of return.

Analysis
We first consider a fundamental difference between a buy-and-hold accumulation portfolio and a retirement withdraw-mode portfolio. As shown in Figure 1, the mathematics of recovery from a loss are much more severe in a retirement distribution portfolio than in a preretirement accumulation portfolio. For instance, if an accumulation portfolio sustains a 10 percent loss, it only needs a 3.6 percent average annualized return over the next three years to restore its pre-loss account balance. In a retirement distribution portfolio, the needed average annualized return to recover from a 10 percent loss within three years following the loss is 11.5 percent.

If the loss is 25 percent, the preretirement accumulation portfolio must generate a 10.1 percent annualized return over three years, whereas the required annual return in a distribution portfolio is nearly double at 19.4 percent. Notice that a distribution portfolio is forced into "recovery mode"; even if the return that it is recovering from is positive (5 percent, 2 percent) or 0 percent. This is due to the fact that the required return must exceed the withdrawal rate that is increasing each year.

As clearly seen by the required returns to restore losses, recovery is considerably more challenging in a distribution portfolio. In light of that, avoiding large losses in a retirement portfolio is the highest priority-as demonstrated by the raw mathematics of recovery.

The time frame covered in this study was the 38-year period from 1970-2007. Assets included in this analysis were large-cap U.S. equities, small-cap U.S. equities, non-U.S. equities, U.S. intermediate-term bonds, cash, real estate and commodities (see Figure 2). The 38-year historical performance of large-cap U.S. equities is represented by the S&P 500 Index, while the performance of small-cap U.S. equities is captured by using the Ibbotson Small Company Index from 1970-1978, and the Russell 2000 Index from 1979-2007. The performance of non-U.S. equities was represented by the Morgan Stanley Capital International EAFE Index (Europe, Australasia, Far East) Index. U.S. intermediate-term bonds were represented by the Ibbotson Intermediate Term Bond Index from 1970-1976 and the Lehman Brothers Intermediate Government Bond Index from 1977-2007.

The historical performance of cash is represented by three-month Treasury Bills. The performance of real estate was measured by using the annual returns of the National Association of Real Estate Investment Trusts (NAREIT) Index (annual returns for 1970 and 1971 were regression-based estimates inasmuch as the NAREIT Index did not provide annual returns until 1972). Finally, the historical performance of commodities was measured by what is now known as the S&P GSCI.

The bivariate correlations between each asset are reported in Figure 2. For example, the 38-year average correlation between large U.S. equities and small U.S. equities was 0.739, or 73.9 percent. The correlation between U.S. intermediate-term bonds and commodities was -0.210. The aggregate correlation for the entire seven-asset portfolio (as calculated by computing the average of the 21 bivariate correlations) was 0.127.