Optimizing for Anxiety

Summary

• When carried through a traditional mean-variance optimization process, J.P. Morgan’s capital market assumptions imply a significant overweight to satellite bonds.
• Investors can suffer from behavioral biases – particularly around reference points ­– that can make normative optimal portfolios sub-optimal in practice.
• By accounting for these reference points, resulting optimizations hold significantly more weight in traditional asset classes, but satellite bonds remain a fixture.

In last week’s commentary (J.P. Morgan Outlook Implies Satellite Bonds Are King), we evaluated the portfolio allocation implications of J.P. Morgan’s current capital market assumptions.

When carried through a portfolio optimization process, J.P. Morgan’s assumptions for major asset class returns, volatilities, and correlations point squarely in one direction: the opportunities for both return enhancement and risk mitigation lie beyond traditional stock and bond portfolios.  In the allocation scheme designed to match the volatility of a traditional 60/40 stock/bond portfolio, U.S. equities received only a 2% allocation, while satellite fixed income received a cumulative 57% recommendation.

We received several emails about last week’s commentary, all raising points we thought worth addressing.  To paraphrase the most common two lines of questions:

• “How can I account for the fact that my clients benchmark to U.S. equities when the 60/40 portfolio only recommends a 2% weight?”
  
• “How should I think about moving my non-qualified accounts towards this optimal portfolio given they have significant embedded capital gains from the last 7 years?”

The first is a discussion of behavior management, while the latter is a discussion of tax management.  We believe both of these points warrant their own separate discussions, and so in the next two weeks we’ll be tackling these points. 

This week, we want to address the balance between the long-term normative optimal portfolio and the short-term behavioral distortions that can lead the best laid financial plan astray.

Anxiety Management

In many ways, the problem in hand is one of anxiety.  If investors are benchmarking their portfolios to traditional U.S. asset classes (e.g. stocks and bonds), but their portfolio actually holds very little of either of these asset classes, there will likely be a significant mismatch in expectations and realized performance. 

One way to address this issue is through education.  However, daily stock market performance updates in the news can create reinforced reference points that can be hard for an investor to shake (especially when they are underperforming).  Sufficient negative deviation from these reference points in the short-term can cause the investor to abandon their plan. 

So while the results we generated last week may be normatively optimal, they may not be behaviorally optimal.  To quote Davies and Lim (2013)[1]:

“However, anxiety will induce interim decisions that cause the investor to deviate from the normatively optimal portfolio (portfolios with too much anxiety along the journey will be unattainable in practice).  The rational investor will therefore take account of his own behavioral distortions and seek to reduce anxiety by choosing normatively sub-optimal portfolios, which nonetheless offer the best attainable result.”

In other words, optimal in theory and optimal in practice may be distinct when we account for preferences and behavior.  Given that most investors exhibit a significant home market equity bias, the 2% allocation to U.S. equities in the optimal 60/40 portfolio may cause so much tracking error that few investors will have the fortitude to endure. 

A second means of dealing with this issue is to actually account for these reference points in the portfolio optimization itself. 

Reference Portfolios

As investors, we have behavioral responses to outcomes along our investment journey.  Empirical evidence suggests that our recent experiences can induce reference dependent responses, changing our perceptions of risk and reward.

Prospect Theory, established by Daniel Kahneman and Amos Tversky in their seminal 1979 paper, gives us one such way to model this relationship.  Prospect Theory states that investors make decisions based on the potential value of losses and gains, rather than the final outcome. 

Traditionally, the value function that passes through the reference point is s-shaped and asymmetrical, being steeper for relative losses than gains. 

The benefit of this model, for our case, is that we can model investor utility as being relative to the performance of the traditional stock/bond portfolio they are implicitly benchmarking to.  So instead of trying to maximize return per unit of risk, as we do with traditional optimization, we can try to maximize relative outperformance versus underperformance (taking into account the asymmetric preferences) subject to a return or volatility target.

So, for example, an investor that considers themselves risk-seeking may benchmark to a 100% U.S. Large-cap equity portfolio.  Prospect Theory tells us that outperforming this portfolio is preferred, but not underperforming is critical. 

It is worth noting that an optimization that simply returns a portfolio that is 100% U.S. Large-cap equities, therefore, is perfectly suitable for this investor based on their reference point.  A portfolio that deviates from this reference portfolio, then, must offer significant assurances (based on the capital market assumptions) of relative outperformance.

We can see that taking these preferences into account results in a very different recommendation set:

The new recommended 60/40 portfolio, accounting for a reference point of 60/40 U.S. Large-cap equity / U.S. Barclay’s Aggregate bond portfolio, recommends a significantly higher weight to U.S. equities than before.  Instead of the 2% recommended prior, the optimization now recommends a 31% allocation.

While the allocation to core U.S. equities was significantly increased once we accounted for reference point preferences, satellite bonds remain a fixture within the portfolio with a 36% recommended allocation.  The size of this allocation, despite a reference portfolio that holds zero satellite bonds, is a testament to the relative certainty of enhanced return and reduced volatility potential that J.P. Morgan has ascribed these assets.

Client Talking Points

• Based on J.P. Morgan’s outlook, investors looking to maximize success over the next decade must look beyond core stocks and bonds.
  
• For these forward-looking investors, satellite fixed income asset classes like high yield bonds may offer valuable diversification without necessarily sacrificing return since they offer attractive yields.
  
• A plan is only optimal if we can stick with it.  While these asset classes may offer us more favorable expected returns over the long run, in the short-run they can meaningfully deviate from the performance of traditional stocks and bonds.  Maintaining an allocation to U.S. stocks and bonds, then, is one way for us to help ensure we stick to our plan.

[1] Davies, Greg B. and Lim, Antonia, 2013, Managing anxiety to improve financial performance: Don’t let the best be the enemy of the achievable.