Minimizing Regret: an Alternative Approach to Controlling Risk

Minimizing Regret: An Alternative Approach to Controlling Risk
by Harindra de Silva

Consider two hypothetical pension plans, the first with a benchmark of 80% equities and 20% fixed income, the second a benchmark of 40% equities and 60% fixed income. Based on their view of the prospects for each asset class, both plans choose a 50/50 allocation. Both portfolios now have the same expected risk and return.

Suppose now that stocks return 10% and bonds return 12%.1 The plan with the 80/20 benchmark feels pride for having made this decision--the asset allocation shift results in a gain of 60 basis points (bps) versus the benchmark. The sponsor with the 40/60 benchmark, however, feels regret; its portfolio has a loss of 20 bps versus the benchmark.

Deviating from the norm, as defined by a benchmark or other comparable plans, is a choice that fiduciaries often have to make. This choice and the accompanying responsibility bring the pain of regret when the choice turns out badly. Aversion to regret often leads to poor choices as it leads to a preference for staying with the benchmark portfolio or status quo.

Our primary thesis is that investors are more concerned with controlling regret than minimizing the variability of returns, the basis of most risk management techniques. Incorporating this fact directly into the risk management process leads to better investment decisions in the context of the actual objectives of the typical plan sponsor or investor.

Scenario analysis2
One way investors can select among competing allocations is to evaluate the level of regret in various scenarios. For example, imagine a fund that has the current allocation shown in Exhibit 1 and is considering changing to Option 1, Option 2, or remaining with the current allocation.

In order to evaluate the merits of each allocation, the plan sponsor evaluates the likely performance of the plan in various economic scenarios and corresponding asset returns, as shown in Exhibit 2:

The first scenario is based on the long-run premiums of each asset class over the risk-free rate. The second scenario corresponds to their typical performance in a deflationary environment. The low-return scenario captures the mean reversion in return after the stellar performance of the equity markets in the '90s, and the recession scenario is based on current economic expansion coming to an end. These scenarios, while not exhaustive, capture the set of most likely outcomes over a three to five-year horizon.

We can now simulate the performance of the various allocations to assess their desirability. In addition, if a probability is assigned to each scenario, an expected return and volatility can be computed for each port-folio, as shown in Exhibit 3. For simplicity, we assume that each scenario is equally likely.

Option 1 has the highest expected return and the lowest volatility. In both dimensions it appears to be superior to the current allocation and to Option 2. A plan sponsor, based on this analysis, would therefore likely choose Option 1--with the nagging feeling that Option 1 has less equity exposure than the standard plan. This discomfort would likely manifest itself in the actual allocation being split 50/50 between the current allocation and Option 1.

But what if the plan sponsor focuses on regret, where regret is defined as the performance relative to the standard plan? This focuses the allocation decision on outperforming the standard plan. The performance relative to the standard plan in each of the scenarios is shown in Exhibit 4.

Both the current allocation and Option 1 result in regret in one of the scenarios--when returns match their long-run means. In contrast, Option 2 causes no regrets! While Option 1 has a higher expected return, it produces regret if returns are as forecast in the long-run scenario. Option 2 has a higher expected return than the current allocation and produces no regrets; for most sponsors this would be the preferred choice.

1. Bonds do outperform stocks on rare occasions!
2. The scenarios and decision-making process illustrated here are based on the actual experience of the author with a large plan sponsor.

Harindra de Silva, Ph.D., CFA, is president of Analytic Investors, Inc. in Los Angeles, California.

Contex Group