A statistical examination of the risk-reward trade-off for high-risk assets. Ron Surz is president of PPCA, a San Clemente, Calif.-based software firm that provides performance-evaluation and attribution analytics, a principal of RCG Capital Partners, a Denver, Colo.-based fund-of-hedge-funds manager, and a co-founder of target-date index maker Target Date Analytics.

In a recent article in the Journal of Portfolio Management, Michael Drew and Anup Basu argue that -- contrary to conventional wisdom and the practice of lifecycle funds -- portfolio risk should increase as retirement nears, rather than decrease. Their April 2009 paper "Portfolio Size Effects in Retirement Accounts: What Does it Imply for Lifecycle Asset Allocation?" describes research that concludes that investors with 40-year horizons are 12.5% richer on average with a "glide path" that operates in the opposite direction of lifecycle funds, increasing rather than decreasing equity allocation through time. They also conclude that there is a 90% probability of ending up richer with an increasing equity glide path.

Drew is a professor of finance and economics at Griffith University in Brisbane, Australia. Basu is a lecturer at Queensland University of Technology, also in Brisbane. They based their conclusions on 10,000 simulations of 40-year returns, using data from 1900 to 2004.

"Risk, after all, has a friend called pain," Russell Investments strategist Don Ezra told the U.S. trade publication Pensions & Investments last month in reaction to the findings of Drew and Basu.

In other words, the co-authors of "Portfolio Size Effects in Retirement Accounts" have re-discovered that investors, gratefully, tend to be rewarded for taking risk. After all, if risk weren't rewarded on a reasonably regular basis, no one would ever take it.

Degrees of loss

The important thing here is whether a given reward is commensurate with the risk taken to acheive it.

To examine this trade-off, I've evaluated the increase in risk that accompanies an increasing equity allocation. I take the position that the amount of a potential loss is what matters, rather than the percentage of loss. By this light, losing $100,000 in a $1 million portfolio is substantially worse than a $1 loss on a $10 portfolio, even though both are 10% losses. I also define risk to be the risk of loss, rather than volatility.

Combining these concepts, I have calculated the dollar-weighted downside deviation of returns over 40-year periods using glide paths that progress forward through time with decreasing equities, and contrast these to the same glide path executed in reverse with increasing equity allocations. I use the PlanSponsor On-Target Index (OTI) glide path, which is entirely in risky assets for the first 20 years and then moves to zero during the next 20 years. The proxy for risky assets is 70% S&P500 stocks and 30% Citigroup High Grade Bonds. The proxy for risk-free is Treasury bills, and downside deviation is measured as return below Treasury bills. The investor is assumed to contribute $1000 initially and to increase this $1000 by 3% per year.

This table provides details on the 44 40-year calendar periods from 1926-2008 -- and please don't be alarmed: an explanation of the columns follows.

|image1| The columns in the table are as follows.

Fwealth: Ending wealth when the glide path moves Forward, ending at zero in risky assets Bwealth: Ending wealth when the glide path moves Backwards, ending at 100% risky assets Fret: Annualized return using the Forward glide path Bret: Annualized return using Backward glide path FDown: Equal-weighted downside deviation for Forward path BDown: Equal-weighted downside deviation for Backward path $Fdown: Dollar-weighted downside deviation for Forward path $Bdown: Dollar-weighted downside deviation for Backward path

And here are some observations about the table.

Average ending wealth for the Backward path of $630,940 is 22% greater than the corresponding $515,570 ending wealth for the Forward path. This is even larger than the professors 12.5% result. Forward beats Backward in 13 of the 44 40-year periods, which is 30%, substantially greater than the 10% in the article. Annualized returns and equal-weighted downside risks are about the same moving forward or backward. Dollar-weighted downside deviation for the Backward path is substantially higher in all periods, averaging 75% higher than the Forward path.

In sum, the increasing equity-allocation approach creates 12.5% (as Drew and Basu find)) 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.

Here's an illustration of this point.

|image2| 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. The idea is that you take less risk if your objectives have been achieved, and more risk if they have not.

This may make sense, but it 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 commingled vehicles, namely mutual funds and commingled trusts. Separate accounts are individualized and could adopt a contingent glide path. As usual, these solutions are usually better for the wealthy. Separate accounts are typically used by company executives.

In my simple way of thinking, I get used to having $500,000 if that's roughly what I've had for the past 5-10 years as retirement approaches, so I plan around that number. If the number is 20% higher at $600,000 I'm probably not that much happier because I haven't been assessing my situation relative to the $500,000 alternative path. I deal with the current reality, and adapt to it.

But, in either case, a 20% loss is devastating -- much more so than a 20% loss would have been 30 years earlier. The challenge is to create a risk measure that captures this spirit. I think that dollar-weighted downside deviation accomplishes this, because account balances are higher as retirement nears.

Perhaps you have a better measure. -FWR

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