Traditional risk measures are wealth agnostic. An individual losing $1,000 on his $10,000 portfolio is treated the same as one losing $1 million on a $10 million portfolio. Most say that these losses are equally as painful, though it may well be the $10,000 investor suffers the greater pain.

This might be true for different investors, but what if we're talking about the same investor at different stages in his or her life, who is invested in a target-date fund? Here's the point. A wealthy individual feels more pain today losing $1 million on a $10 million portfolio than he or she did losing $10,000 on a $100,000 portfolio 20 years earlier. Similarly a less wealthy person feels more pain losing $1,000 today on a $10,000 portfolio than he or she felt 20 years earlier losing $10 on a $100 portfolio. Risk in this context is not wealth agnostic.

Anup Basu and Michael Drew in their “Portfolio Size Effects in Retirement Accounts: What Does it Imply for Lifecycle Asset Allocation.” published in the spring 2009 issue of the Journal of Portfolio Management, contend that a glidepath that increases equity exposure through time dominates the traditional glidepath, which has decreasing equity exposures. This contrarian path delivers greater ending wealth 90% of the time, with about the same risk, they found, leading to a characterization called “almost statistical dominance.” ASD means the contrarian path is better most of the time in both risk and reward.

So what is wrong with this picture? Few if any would recommend 100% equity exposure at retirement. Yet traditional risk and reward measures indicate that a glidepath with increasing — rather than decreasing — equities results in greater wealth with about the same risk. It's a significant winner. In other words, our intuition tells us that retirees can't “afford” that much risk taking, but traditional unweighted risk measures argue otherwise. I believe the problem lies in the unweighted risk measure.

We need an alternative risk measure that captures the importance of protecting account balances near retirement, if for no other reason than retirees have limited opportunities to make up losses by working longer. That is, we need a risk measure that is weighted by either account value and/or time remaining to retirement.

There is a disconnect between ending wealth, which is very much dependent on the “size effect” described by Messrs. Basu and Drew, and risk measures that do not reflect the size effect. As Thomas Klepsch, vice president, State Street Bank & Trust Co., Boston, puts it, we need a risk metric that captures the “path dependency of a recurring investment with time variant objectives.” For example, a dollar-weighted risk measure reveals that the contrarian glide path is in fact 75% riskier than the traditional glide path.

In a recent article, “Should Investors Hold More Equities Near Retirement, or Less?” published in August by Advisor Perspectives, an online publication, I measure risk as dollar-weighted downside deviation, where the dollar weights are account balances through time. This captures the size effect. In that article I find that the contrarian approach of increasing equity exposures has a dollar-weighted downside deviation of 7% per year on average over the 44 40-year periods that I examined. By contrast, the downside deviation of the traditional glidepath, with its decreasing equity allocation, is 4.2%. In other words, the contrarian glidepath is 75% riskier than the traditional. Not surprisingly, average ending wealth of the contrarian glidepath is also higher, averaging $631,000 vs. $516,000 for the traditional path. So the contrarian produces 22% more wealth. Reward-to-risk ratios using these results are $90,000 per unit of risk for contrarian, which compares with $123,000 for traditional. So I conclude that traditional is 37% more “efficient” than contrarian, defining efficiency as reward per unit of risk. So much for ASD.