Our research into regret risk has focused on the asset allocation process, with the goal of helping clients avoid “timing the market” based on emotional responses to the volatility of their chosen strategy. Unusually-large returns sometimes bring on feelings of regret, resulting from losses in value, or from missing out on extraordinary gains in assets not held in the portfolio. These emotions sometimes trigger decisions to exit or enter the market, deviating from the long-term strategy that is the most important source of investment return. This violates one of the key assumptions of the investment plan: establishing and maintaining a well-diversified asset allocation. Sadly, this type of reactive trading often produces a “whipsaw” of ill-timed trades, resulting in underperformance relative to having simply maintained the strategy. This is well-documented, with the client’s portfolio underperforming the assets it contains.
In our effort to control this risk, we created a method for quantifying regret, while customizing its measures that describe each client’s personal preferences and unique perspective on acceptable and bearable investment performance. Our “regret triggers” identified the range of losses and gains that would likely induce feelings of regret. By measuring the severity and the likelihood of regret in each strategy, we were able to match clients to strategies that they could sustain throughout the market cycles they would likely experience. The result is greater confidence in their ability to stick with the asset strategy, and a higher likelihood of achieving the expected return from bearing market risk.
But what about the regret risk from the active investments that make up the actual portfolio?
The typical investment portfolio holds actively-managed funds that hope to exceed the returns on their respective market segments, after adjusting for their own unique performance risk (and net of their fees.) This idiosyncratic risk is the source of the “excess return” that clients hope to achieve, and it carries its own uncertainty. It also brings its own sense of regret. After all, no process works all the time, and even funds with long-term outperformance experience periods of underperformance. Funds also experience times when their approach may simply be “out of favor.” This underperformance often elicits feeling of regret, which may bring on thoughts to abandon the fund – potentially right before a “reversal of fortune” restores lost active value. On the “flip side” we see funds that experience a period of tremendous outperformance, which encourages investors to “chase” this performance, right before a mean-reverting correction brings on an offsetting period of underperformance. This is the danger of trading based on regret, where investors “buy high and sell low” in terms of their active performance.
We see the need to evaluate the regret risk inherent in the “team of funds” and its expectation of earning excess returns that help clients meet their financial goals. In effect, we intend to help clients make well-informed decisions and stick with them. This increases their likelihood of success from both sources of return: market exposure and active returns. We now shift our emphasis from market return to idiosyncratic excess return.
Our analysis takes two approaches. The first is an examination of the total return of the portfolio, which is the sum of the investment strategy return, combined with the additional return contributed by its active funds. By comparing the regret of the portfolio and its benchmark return, we extract the “active regret effect” produced by the fund team. The second analysis of regret is applied to each fund individually. We compare the results of both approaches to evaluate the benefit that “alpha diversification” had on minimizing active regret. By understanding these dynamics, we hope to increase confidence in the benefit derived from the active interactions between the funds, resulting in the portfolio’s “regret adjusted return” exceeding both its benchmark and the average performance of its funds.
This case study starts with a 60-40 portfolio of global equity and bonds, in a hierarchy of three major asset groups and seven asset segments. Each segment uses a single fund.
Our performance results were drawn from an actual portfolio over a 12-year period of monthly net returns. Using the summary statistics of mean return and standard deviation, we created a Monte Carlo simulation of 1,500 paths of 30 annual returns. These formed the set of returns that were the basis for our analysis of regret.
We used the same “return triggers” from our analysis of regret in the context of asset allocation. Our lower trigger (the regret from “despair” over losses) was set at -12% while our regret from “envy” (missing out on large gains) was set at +25 percent. We calculated the average of the regretful returns that exceeded these triggers and grouped them by deciles to understand the severity and the likelihood of regret for both our active portfolio and its benchmark.
The regret penalty continues to be the combined effect of severity and likelihood of occurrence for the extreme returns. This penalty is subtracted from the expected return to give us the regret-adjusted returns.
Our results reveal a few useful insights:
The combined effect of these factors produces a regret-adjusted return for the portfolio that exceeds the benchmark return (adjusted for its own regret.) The 30 bps difference in regret (between the portfolio and the benchmark) is added to the 128 bps excess return, producing a regret-adjusted excess return of 158 basis points. In effect, we created a higher-returning portfolio with a higher likelihood of being maintained, relative to taking a passive approach for this strategy.
Since our portfolio reflects lower return uncertainty than the benchmark (given its lower standard deviation of returns) our portfolio has a higher risk-adjusted return. This risk adjustment increases our return by almost 40 bps. We then adjust for lower regret, and our “regret-adjusted alpha” increases to almost 200 bps over the benchmark. Even more impressive is the increase in the Information Ratio, as we adjust for both risk and regret: from 0.88 to 1.35 (a relative increase of more than 50 percent.)
Our alpha diversification from the team approach to fund selection produced a higher-returning portfolio with lower volatility risk and less regret risk. In addition to better performance statistics, we have a portfolio of funds that is more likely to be maintained through periods of stressful active performance.
Our analysis now shifts from the portfolio’s total return to its active return, as measured by its annualized mean return minus the mean return of the benchmark. Using this excess return as the basis for our analysis, we evaluate the effect of regret for the total portfolio, its major segments (US Equity, Foreign Equity and Bonds) and for the individual funds within these segments. We run the same Monte Carlo process we used for the total portfolio analysis: 1,500 scenarios of a 30-year path of randomly-generated returns, this time using excess return and tracking error as the input variables.
Our regret triggers differ with each level of detail, but we maintain a consistent approach by setting the “despair” trigger at zero (i.e., matching the benchmark return) and the “envy” trigger at twice the expected excess return. For example, the total portfolio despair trigger is zero, and its envy trigger is 250 bps (approximately twice its excess return of 128 bps.) We applied this approach to the major groups and then to each fund, with the respective triggers reflecting the expected return and tracking error of each component asset of the portfolio. This incorporates the unique characteristics of these components, while ensuring a consistent approach to the regret triggers. This could be modified for different clients, given their individual perspectives on regret.
The first key insight is found in comparing the levels of regret and their effect on regret-adjusted return for each level of this hierarchical analysis. The portfolio reflects the smallest level of regret (82 bps) while regret for the portfolio’s asset segments nearly doubles to 159 basis points. Regret for the funds is nearly three times the total portfolio’s regret penalty.
What are the effects on regret-adjusted excess returns?
Only the portfolio maintains a positive excess return after considering its regret. The segment-level analysis of regret lowers the portfolio’s regret-adjusted return from a positive 46 bps to a negative 31 bps, and the regret-adjusted excess return for the funds is nearly minus 100 basis points.
This may appear to be a deterioration of results, but the opposite is true. At the individual fund level, relative tracking error is typically a multiple of excess return, reflecting a wide range of values that brings a very high level of regret. This is also reflected in a negative excess return at high levels of confidence. That may be considered “the bad news.”
The “good news” is the effectiveness of “alpha diversification” that we used in creating the “fund team.” This true portfolio construction approach eliminates most of the tracking error inherent in the individual funds, along with the regret that this volatility brings. This positive active diversification effect increases as we move up the hierarchy of assets.
Because of their high tracking error (typically at least a 3x multiple of their excess returns) individual funds rarely have statistically significant excess returns at high levels of confidence. This is also true for their regret-adjusted returns, as shown in the next two exhibits. Only two of the seven funds in the portfolio (foreign equity and high-quality bonds) have positive excess returns at a 95% confidence level. And only one fund (high-quality bonds) has a positive regret-adjusted return.
Fortunately, the excess returns of our fund team have a low correlation to each other, creating strong alpha diversification effects that reduce both tracking error and regret. The result is a portfolio with a positive value for both high-confidence excess return and regret-adjusted return.
While we may not have high confidence in any individual fund, we have a reasonable basis for confidence in the total portfolio and its ability to deliver positive excess returns, after adjusting for both tracking error and regret.
Clients have unique perspectives on risk, and this drives different tolerances for regret. Understanding regret tolerance is a critical aspect of matching a client to an active fund team. As with asset allocation, it is essential to continue holding the funds in the team through their individual “ups and downs” so that we avoid making ill-timed exits and reentries that erode performance. Our goal is to sustain our exposure to the fund team through its downturns so that we can enjoy the recoveries that follow. By maintaining confidence in the strength of the fund team, the client is encouraged to sustain exposure to the team’s individual funds. Advisors should encourage their clients to focus on the strength of the fund team, rather than focusing on its separate pieces.
Our analytics help clients understand regret risk by examining it across the various triggers that define regret tolerance. We also provide insight into the sources and effects of regret. As regret tolerance increases, the experience of regret decreases, resulting in higher regret-adjusted returns. The result is sustaining an active portfolio by understanding its likely behavior.
Our next chart illustrates the inverse relationship between regret tolerance and regret experience. Regret is a penalty that subtracts from return. The regret triggers indicate each client’s degree of emotional response to the uncertainty of active management. When clients can tolerate short-term underperformance, they are more likely to achieve the expected outperformance from the fund team. This chart may also be used to set the regret triggers that must be tolerated to earn a satisfactory regret-adjusted return.
The first chart emphasizes the trend of these factors; the second focuses on the relative size of each factor.
The regret penalty is driven by the severity of the regret and its likelihood of occurrence. We noted that clients with high regret sensitivity experience a higher level of regret, and they experience it more frequently. This produces a high regret penalty that is subtracted from the fund team’s expected excess return. The most regret-sensitive clients should expect the lowest regret-adjusted returns, as noted in the next chart.
We see both the “average regretful return” and its likelihood decline as the client’s regret tolerance increases. As shown below, the regret return declines from 116 to 32 bps, and the likelihood of experiencing regret declines from a high of 67% (i.e., two out of three years) to a low of 11% (1-in-9 years.) The product of these two factors results in regret penalties that decline significantly as regret tolerance increases, producing increasingly higher regret-adjusted returns. The regret-adjusted excess return is the expected excess return minus the regret penalty.
This approach allows us to set reasonable expectations when participating in active management, given its inevitable emotional component. This is a truly customized approach, since the methodology can be adapted to the values in the regret triggers that align with each client’s unique risk perspective. In our example, only the two most regret-sensitive clients would likely find investing actively unattractive, given the paltry excess returns they would earn (adjusted for the regret they would bear.) Those clients who could tolerate higher levels of regret could expect to earn excess returns in the range of 50 bps to 100 bps (net of fees and the regret they would bear.)
In practical terms, these clients would commit to maintaining their fund team when a “bad year” produces no excess return. They also commit to refusing to “chase the hot dot” by swapping some of the team’s funds for others that outperformed over the short term. These are the times when clients are most vulnerable to the temptations to abandon their active strategy, with the “whipsaw” risk of potentially ill-timed trades.
We create a tangible active discipline, with clear guidelines that help prevent making long-term fund selection decisions based on short-term performance results.
The value of the active investment process will continue to be a hotly-debated topic in the field of investment management. There are many facets to this discussion, and there is no lack of diversity and creativity in the analytics underlying these discussions. The part that remains underserved is the component of emotions experienced by investors. While the field of behavioral finance has alerted us to the need to address this issue, it has provided little insight into quantifying or controlling the ill-timed trading that is often driven by these emotions. To address this gap, we introduced the notion of regret.
Our initial insights into regret were applied to the asset allocation process, helping clients to sustain their investment strategy throughout the inescapable volatility of the markets. By acknowledging emotion and its responses, we provided a set of guidelines to help clients avoid being “triggered” by short-term market returns that fall within a set of reasonable expectations. The result should be a higher likelihood of achieving the benefits of maintaining the investment strategy.
This second examination of regret focuses on the more visible and frequent occurrence: the hiring and firing of fund managers, as clients experience below-benchmark returns in some of their funds, while feeling disappointment from substantial outperformance in funds they do not own. Without any discipline around controlling these sources of regret, clients will continue the process of making emotionally-driven changes in their fund lineup, many of which are likely to be unnecessary and ill-timed, leading to additional regret.
Our disciplined process accomplishes three necessary tasks:
This case study demonstrated our method of measuring regret from each client’s unique perspective, as reflected in their emotional responses to various levels of the “envy and despair” that drive regret. By focusing on the set of regret penalties and its effect on “regret-adjusted excess returns” we provide an objective way to evaluate each client’s ability to bear the regret of their active investment process. This also provides useful guidance on the degree of regret a client must be willing to bear if they want to sustain their active process.
If you want your active process to succeed, you must be smart about it… and you must be disciplined.
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Written in partnership with Stephen Campisi