The equally weighted seven-asset withdrawal portfolio performed the best at protecting the portfolio against losses.

Of the portfolios in this study, the seven-asset portfolio has the best risk/return combination.

This study examines the benefits of low correlation in retirement portfolios during the distribution phase, when money is being systematically withdrawn. Given that many retirees are concerned about outliving their incomes, it's surprising that little analysis has focused on portfolio durability post-retirement. In fact, the vast majority of mean-variance research has been based on buy-and-hold portfolios during the preretirement accumulation phase, despite the fact that a portfolio in withdrawal mode is far more sensitive to portfolio volatility (i.e., account value losses) than a buy-and-hold portfolio.

Specifically, this analysis looks at the impact that low correlation among a portfolio's assets has upon the standard deviation of annual returns, internal rate of return, maximum portfolio drawdown in any single year, frequency of loss and probability of portfolio recovery following a loss.

Background

The time frame covered in this study is the 37-year period from 1970 to 2006. 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. The 37-year historical performance of large-cap U.S. equities is represented by the Standard & Poor's 500 Index, while the performance of small-cap U.S. equities is captured by using the Ibbotson Small Companies Index from 1970 to 1978, and the Russell 2000 Index from 1979 to 2006. The performance of non-U.S. equities is represented by the MSCI, Europe, Australasia, Far East (EAFE) Index. U.S. intermediate term bonds are represented by the Ibbotson Intermediate Term Bond Index from 1970 to 1976 and the Lehman Brothers Intermediate Term Bond index from 1977 to 2006.

The historical performance of cash is represented by three-month Treasury bills. The performance of real estate is taken from the National Association of Real Estate Investment Trusts (NAREIT) Index (annual returns for 1970 and 1971 were estimated as the NAREIT Index did not provide annual returns until 1972). Finally, the historical performance of commodities is measured by the Goldman Sachs Commodities Index (GSCI), now called the S&P GSCI Commodity Index. The primary data source for this study is Morningstar Principia. Additional raw data comes from Stocks, Bonds, Bills, Inflation by Ibbotson Associates.

At least one caution is in order. The time frame of this analysis (1970 to 2006) was a period of robust returns across the board. Equities averaged in excess of 11% annually, intermediate bonds averaged over 8%, commodities generated over 11% and REITs returned roughly 13.5%. These levels of performance may not persist, but the benefits derived from building low correlation portfolios will always be in demand regardless of the performance level of various assets.

The Results

Now, to the findings. We examine a portfolio in the post-retirement distribution phase (i.e., a withdrawal portfolio). A starting balance of $500,000 is assumed, with an initial withdrawal at the end of the first year of 5% of the starting portfolio balance (in this case, $25,000), and an annual increase in the withdrawal of 3% to account for annual inflation. Thus, the second-year withdrawal in this analysis was $25,750, the third-year withdrawal was $26,523, and so forth.

The step-by-step results of building increasingly diversified portfolios are shown in "Correlation Scorecard," above. The most dramatic impact occurs when adding commodities as the seventh asset class. This multi-asset portfolio comprised large U.S. equity, small U.S. equity, non-U.S. equity, U.S. Int. term bonds, cash, REITs and commodities-each asset having a portfolio weighting of 14.3%.

At 11.25%, the seven-asset portfolio has the highest internal rate of return (IRR is a measure of the annualized rate of return that can accommodate uneven cash flows), the lowest standard deviation of return (8.67%), the lowest aggregate correlation (.128), the smallest maximum one-year drawdown (-10.2%) and a zero frequency of a 10% loss (as measured by IRR) over one-, two- and three-year periods.

The location of the seven-asset portfolio in "Seeking the Northwest Corner," right, is significant inasmuch as the upper left hand corner represents the ideal combination of risk and return. In this case, the Y-axis represents the 37-year IRR of each portfolio during the withdrawal phase, whereas the X-axis shows the worst single percentage loss in the portfolio during the 37-year withdrawal period.

In this withdrawal portfolio scenario, the probability of recovery from a 10% loss within three years is lowest in the five-asset and seven-asset portfolios. The key point here is that highly diversified portfolios with low aggregate correlation tend to avoid losses, which essentially negates the need for a high recovery probability. In sum, the probability of recovery from a 10% loss within three years is slightly lower in the more diversified portfolios, but the frequency of 10% or higher losses is essentially eliminated.