The CW portfolio underperformed the EW portfolio by 170 bps, but volatility of return (as measured by standard deviation) was reduced by 268 bps. While a reduction in volatility is intuitively desirable, it is proposed that the other three measures in Figure 4 are more compelling to the average investor.

For instance, the CW portfolio had only two years with a negative return, whereas the EW portfolio had four years with a loss. The worst one-year return was only -2.23 percent for CW compared with -5.34 percent for EW. Finally, the worst three-year cumulative return in CW was 6.43 percent versus 2.09 percent in EW. It is instructive to note that the multi-asset portfolios (EW and CW) had significantly better downside protection than the two-asset portfolios (moderate 60/40 allocation and conservative 40/60 allocation). Downside protection is a direct benefit of assembling portfolios with more diverse assets.

The risk/return characteristics of the individual assets and the four portfolios are shown in Figure 1. The EW portfolio is shown by the beige square, CW is the orange square, the 40/60 portfolio is the plum square, and the 60/40 portfolio is the dark blue square. Each individual asset is shown by a different-colored dot.

As shown in the scatter graph, there is meaningful correlation between performance and risk. Risk is measured by worst three-year cumulative return. The individual assets (represented by different-colored dots) depict the classic upward sloping shape of the risk/return frontier. Assets that provide higher return potential tend to expose the investor to larger worst-case three-year losses. Asset allocations of 100 percent bonds or 100 percent cash eliminated large portfolio losses over any three-year period, but their performance was significantly lower than the individual equity assets and the four portfolios. Without sufficient growth, the likelihood of outliving one's retirement portfolio obviously increases.

The benefit of creating diversified portfolios is demonstrated by the location of the squares. For example, the seven-asset portfolios (beige square and orange square) eliminated negative returns over any three-year period during the 38-year time frame of this study. Importantly, the seven-asset portfolios avoided prolonged losses while maintaining a level of performance that was comparable (or superior) to most of the individual equity assets.

With this connection between performance and worst-case three-year cumulative return in mind, the information presented in Figure 1 is more persuasive. For example, a 25 percent loss in a *distribution portfolio* will require a 19.4 percent annual return over the subsequent three-year period to restore the loss compared with "only"; a 10.1 percent needed annual return over the next three years in an *accumulation portfolio*. It is important to note that five of the individual assets in this study had worst-case three-year cumulative losses in excess of -25 percent (large U.S. equities, small U.S. equities, non-U.S. equities, REITs and commodities). Indeed, three of the individual assets had worst-case three-year returns below -37 percent. (And this is assuming a buy-and-hold portfolio. In distribution portfolios, market losses are magnified because of money being withdrawn). Recovering from losses of this magnitude is far more problematic in a retirement portfolio than in a preretirement accumulation portfolio.

**Postretirement Distribution Portfolio**

In analyzing a retirement distribution portfolio, a starting balance of $500,000 was assumed, with an initial withdrawal at the end of the first year of 5 percent of the starting portfolio balance (in this case, $25,000), and an annual increase in the withdrawal of 3 percent 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.

As shown in Figure 6, the first distribution portfolio analyzed consisted of 100 percent cash. Understandably, this portfolio allocation may not represent a typical retirement portfolio. It is included in this analysis simply as a starting point. The 38-year IRR of the 100% cash portfolio was 7.04 percent with a standard deviation of 3.08 percent. The worst-case one-year portfolio drawdown (i.e., the percentage change in portfolio account value from year-end to year-end) was -13.9 percent, which occurred in 2007 (as the account value began to plummet). The frequency of loss for the all-cash portfolio (i.e., the percentage change in account value from year to year) was 53 percent -or in 20 out of the 38 years. In those 20 years, the average loss was -4.4 percent.