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At the end of this article you can find details on the 44 40-year calendar periods from 1926-2008 displayed in a table.   There is a lot to be learned from this table. Here are some highlights:

• Dollar-weighted downside deviation for the backward path is substantially higher in all periods, averaging 75% higher than the Forward path. Compare the last column in the table to the column just left of it.
• Dollar-weighting risk reduces the forward path’s downside measure below its equal-weighted number, and increases the backward path’s risk. This approach converts risk from a measure of fractional loss to one of wealth loss. Compare columns FDown and BDown to $FDown and $BDown. 

In other words, increasing one’s equity allocation creates 12.5% (the professors’ result) to 22% (my research) greater wealth, but at a whopping 75% increase in risk.  That’s a lot of pain for not all that much gain.

Some believe that I’ve concocted a measure – dollar-weighted downside deviation – to make a point, but that’s simply not true. I want to use a metric that captures the risk of loss of wealth rather than the fluctuation in returns. Although the unweighted volatility of returns for the backward path is similar to that of the forward path, the volatilities of wealth along the glide paths are quite different. We know that the backward approach is a higher risk wealth path because it exposes assets to more risk when account balances are high. Unweighted return volatility does not capture this fact; dollar weighting does. After all, isn’t it wealth that concerns us most?

The following exhibit summarizes the key conclusions.

In a similar vein, some have suggested what I would call “contingent glide paths,” designed to react to the investment and savings experience, specifically targeting objectives. You take less risk if your objectives have been achieved, and more risk if they have not. This may make sense, but can only be applied to individual accounts. The Pension Protection Act of 2006 specifies three Qualified Default Investment Alternatives (QDIAs): Target Date Funds, Balanced Funds, and separate accounts. The first two QDIAs – Target and Balanced – are comingled vehicles (mutual funds and commingled trusts).

Separate accounts are individualized and could adopt a contingent glide path. These solutions are usually more appropriate for the wealthy, since they typically have significant minimum account balance requirements.    

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