Implementing Withdrawal and Savings Strategies

Over the past year, a number of readers have written to us asking if we had ever written about the best way to withdraw or add money to a portfolio. Up to now, we have not. In our modeling, we had assumed that funds withdrawn from or added to a portfolio were divided across different asset classes in proportion to their portfolio weights. Clearly, this was a simplifying assumption that was, in many cases, impractical (or at the very least, expensive) to implement in practice. In response to our readers' requests, we have recently completed an analysis of different strategies that could be used to annually withdraw or add funds to a portfolio.

We tested three different strategies, as shown in the following table:

All our analyses were run in U.S. dollars, using the same asset class real return, risk, and correlation assumptions we used to develop our model portfolios. For each withdrawal strategy, we ran 10,000 simulations of our model to estimate the impact of the withdrawal strategy over a wide range of possible future conditions.

Withdrawal Strategies

Our initial analysis focused on a retirees with a twenty year time horizon who wanted to leave a bequest equal to 100% of the portfolio's starting value, while also withdrawing 4% of the portfolios value (in real - that is, inflation adjusted - terms) each year. As we were focused on the impact of different withdrawal strategies, we started with an equally weighted asset allocation across eleven different asset classes (real return, domestic and foreign bonds; domestic and foreign securitized commercial property; commodities and timber; domestic, foreign and emerging markets equity; and equity market neutral, our proxy for uncorrelated alpha strategies.) To minimize the potential impact of our rebalancing strategy assumption, we set our portfolio rebalancing trigger at 20% -- that is, an asset class would have to be either 20% above or below its target long-term weight to trigger a general rebalancing of the portfolio. Finally, we set the rebalancing adjustment factor equal to zero. To refresh readers' memories, the adjustment factor is designed to take advantage of mean reversion when portfolios are rebalanced. Rather than rebalancing all asset classes back to their target weights, the most overweight asset class is rebalanced to its target weight less the adjustment factor, while the most underweight asset class is rebalanced back to its target weight plus the adjustment factor. Given the similarity to the logic that underlies the winners and losers withdrawal strategies, we did not include a rebalancing adjustment.

At this point, you may be thinking that the analysis we undertook sounds a lot like the three dimensional chess Commander Spock used to play on Star Trek. As it turned out, that is a pretty good description of the dynamics we found.

Our fitness criteria was the probability that our investor would achieve his or her bequest goal. Using the equally weighted portfolio, we found that the "sell your losers" strategy had a very slight advantage over the other two approaches (a 1% higher probability of achieving the bequest goal). When we further analyzed the dynamics involved, we found that the impact of the withdrawal strategy selected was almost completely overwhelmed by the year-to-year changes in asset class and overall portfolio returns. The impact of the choice of withdrawal strategy was also dampened by the rebalancings that occurred over the 20 year period covered by our simulations.

Given this, we ran two further analyses, using equally weighted mixes of low and high volatility asset classes. In the former case, we gave 20% weights to real return, domestic and foreign bonds, along with timber and equity market neutral; in the latter, we used foreign commercial property, commodities, and domestic, foreign and emerging markets equity. We should also note that the higher volatility mix generated about a 7% higher probability (across all three cases) of achieving the bequest goal, compared to the low volatility mix. In the case of the high volatility portfolio, we found a slight disadvantage for the "sell your losers strategy" (about a 1% in terms of the probability of achieving the bequest goal) compared to the sell your winners and sell an equal mix of both strategies. In contrast, in the case of the low volatility portfolio mix, no withdrawal strategy had an advantage over the others.

Our next step was to raise the target annual withdrawal to 6% of the portfolio's initial value. In this case, for the low volatility portfolio, the sell your losers strategy had a 1% advantage over sell and equal mix of your winners and losers, and a 3% advantage over sell your winners. In the case of the high volatility portfolio (which had about a 20% greater chance of achieving the bequest target, compared to the low volatility mix), sell your losers and sell an equal mix of winners and losers each had a 1% advantage over sell your winners. When we extended the time horizon for this case to thirty years, the relative advantage of the sell your losers strategy increased to 5% over sell your winners (based on an equally weighted portfolio), and 2% over the sell equal amounts of winners and losers approach.

On balance, our analysis of different withdrawal strategies led us to two key conclusions. First, given the assumptions that underlie our model (e.g., about asset class risks, returns and correlations, and rebalancing strategy), the impact of different withdrawal strategies on goal achievement (measured by the probability of achieving a target bequest) was relatively low compared to the impact of other decisions (e.g., asset class weights and rebalancing strategy). Second, the impact of the withdrawal strategy chosen increased with the size of the income target, length of the time horizon, and expected level of portfolio volatility. Finally, if taxes were not a consideration, the sell your losers approach is generally preferred to the others. However, its advantage over the sell equal amount of winners and losers may be offset by the tax benefits from the latter strategy.

Contribution Strategies

In comparison to a retired investor, an investor who is still in the accumulation stage of life faces a relatively easy problem. In essence, a retired investor makes his or her investment problem harder each time he or she withdraws funds from his or her portfolio. In contrast, an investor saving for retirement makes his or her investment problem easier every time he or she contributes new money to his or her portfolio. That being said, our accumulating investor can still gain an additional edge by carefully choosing the contribution strategy he or she will use.

Our analysis was based on the situation facing an investor with thirty years remaining until retirement, who wanted his portfolio to increase by a multiple of 10x over its starting value. Each year, he also contributed 7.5% of the portfolio's initial value in the form of additional savings. Once again, we started with an equally weighted eleven asset class portfolio, and set our rebalancing trigger to 20% and our rebalancing adjustment factor to zero. Under these circumstances, the choice of contribution strategy had no impact on the probability of achieving the investor’s accumulation goal, as it was overwhelmed by the inflow of new savings and fluctuation in asset class returns over time.

In our next analysis, we shifted to the five asset class "low volatility" portfolio. In this case, buying an equal mix of winners and losers had a 1% advantage (in terms of the probability of achieving the accumulation goal) over the buy winners strategy, and a 5% advantage over the buy losers strategy. We then analyzed the impact of switching to five equally weighted high volatility asset classes. Again, we found that buying an equal mix of winners and losers was the superior approach, with a one percent advantage over buying winners and a four percent advantage over buying losers. This was also the case when we cut the annual savings rate from 7.5% of the original portfolio value to 2.5%. In sum, we found that when contributing funds to his or her portfolio, an accumulating investor is well advised to buy an equal mix of the asset classes that are most over and underweight in his or her portfolio.

| This Month's Issue: Key Points | This Month's Letters to the Editor: FT Articles: Commodity Index Funds' Future Contract Rollovers and VIX and Barclays' Water iShare | Global Asset Class Returns | Asset Class Valuation Update | Implementing Withdrawal and Savings Strategies | The Potential Benefits from MacroShares | Style Rotation With REITS | Product and Strategy Notes: Recent Research Reports and STILL more ETF Products | 2006-2007 Benchmark Portfolios - All Currencies |