Reference Dependence and Portfolio Management

Executive Summary

Kahneman and Tversky (1979) have provided substantial empirical evidence proving their concept of Prospect Theory, or the psychological process on making decisions in the face of uncertainty. What we have learned is that decision-makers do not view gains and losses in a symmetrical manner and reference points play a significant role in the decision-making process. In this essay we will discuss the distinct phases that a decision-maker will experience as it relates to portfolio management decisions. We will discuss how altering reference points can ultimately lead to better decisions and reduce the emotional discomfort of portfolio losses.

Phases of Decision-Making

As an individual faces a decision, there are two emotional phases used to quantify and ultimately choose from the available options (Gneezy & Epley). In the first phase, the individual will attempt to breakdown the complexity of available options into simpler ones. By creating digestible choices, one will perceive having greater control over the outcomes of the decisions. In the second phase, the individual will select the option that is perceived to be the optimal choice, not because it is the most logical solution, but because it minimizes emotional discomfort. In phase two of the decision-making process there exists two dynamics that contribute to the selection of an option, an apparent value and weight function (Barberis, 2013).

Value Function

As an individual develops the potential options during the decision-making process, they will place a value on the potential outcome of the decision. The underlying nuances in placing a value on the potential outcome tends to be centered on changes in value as opposed to absolute change. The perceived change in value is then compared directly the other available options considered. This comparison between options is the reference point and is of the utmost importance in influencing proper decision making. Once the reference point is established, all potential choices are benchmarked against it.

It is further understood that individuals do not view loss and gain in a symmetrical manner. The value function is S-shaped, meaning it is concave for gains and convex for losses as it increases and decreases away from the reference point. The pain that is felt from losses outweighs the pleasure from gains by a ratio of nearly 2-to-1 (Kahneman, 2003). This will indicate that smaller changes that are closer to the reference point are more sensitive than changes further along the value function and will have a greater impact on the decision-making process. This behavior is exhibited from the multiple examples in which an individual would be willing to travel an additional 15 minutes for a $5.00 savings on an item that costs $20.00, but be unwilling to travel the equal distance to save $5.00 on an item that costs $1000.00.

By framing a decision in a particular way, one can utilize the asymmetrical value function in order to influence better decision-making. It is this very process that Thaler and Sunstein (2009) refer to as libertarian paternalism. As an asset manager, one can act as a choice architect and nudge clients in the proper direction without taking away freewill to choose (Thaler & Sunstein, 2009).

Weight Function

As we venture further down the value function, we find that individuals that are normally risk-averse under typical circumstances actually become risk-seekers. The importance of reference points in the decision-making process, and the emotional discomfort of loss will cause an individual to overweight low-probability events while simultaneously underweighting high-probability outcomes. This weighting process combined with reference dependence often leads to less than desirable decisions.

Reference Dependence and Portfolio Management

Early in my career I noticed an unusual occurrence among my investment management peers. Within their portfolio was a consistent pattern of companies with depressed stock prices and few companies with significant gains in share price. Upon further examination, I had concluded that this was due to what Kahneman and Tversky (1979) referred to as loss aversion. The pain of selling an equity security at depressed levels, and officially booking the loss (as opposed to carrying a paper loss) was an overriding emotion. So much so that, when given the necessity to raise capital in the portfolio, stocks with marginal gains were selected for sale. This was done without consideration of future company prospects. All things considered equal, one can assume that with a depressed stock price, the outlook for the underlying company may be deteriorating while an appreciating stock price should signify corporate health. Selling the healthy corporation’s stock and holding the deteriorating ones are a clear example of risk-seeking behavior attributed to loss aversion behavior.

In the industry this is referred to as “get-even-it is” (Pompian, 2011). He states, “Get-even-itis can be dangerous because, often, the best response to a loss is to sell the offending security and to redeploy those assets. Similarly, loss aversion bias can make investors dwell excessively on risk avoidance when evaluating possible gains, since dodging a loss is a more urgent concern than seeking a profit. (P.191)”

Portfolio Adjustment Through Framing

When faced with the decision to sell the stock of a company with deteriorating fundamentals one can frame the situation in a way that alters the reference point of the decision and mitigate the emotional discomfort attached to a loss. Using a total portfolio approach to the situation has been a successful way to nudge investors towards the most logical decision without altering freewill. A total portfolio approach to selling unfavorable securities focuses less on the company in question and more towards the overall portfolio health. Consider the following example.

An investor has a $1,000,000 portfolio. There are 20 stocks in the portfolio equally weighted ($50,000 per equity holding). One of the companies in the portfolio has had a material change in its fundamental outlook. The stock drops by 20% for a $10,000 loss. The investment manager wants to replace the security with one that has brighter prospects and understands the opportunity cost of holding this particular security. When presenting the situation to the client, the client will undoubtedly feel emotional discomfort regarding taking a 20% loss and may opt to hold the stock in the company until those loses are recovered. Upon recovery, then the client may decide to sell the security in favor of another, and possibly superior investment option. This is risk-seeking behavior and is not the most logical choice but does minimize the emotional discomfort of losing $10,000.

Now consider a different way of framing the situation. Assuming the same investor with the same dilemma, it is framed as saying a company in the portfolio with deteriorating fundamentals has dropped and has cost the portfolio 1% ($10,000 loss on a $1,000,000 portfolio). The loss of $10,000 remains the same in both instances, yet the reference point has altered the value proposition in the equation. The emotional distress from the loss is reduced and the likelihood of recovering a 1% portfolio drawdown has shifted the weighting function in the decision. Through experience, I have found that the investor in the first example has a higher probability of making the illogical portfolio choice whereas the investor in the second example will make the best choice for the overall portfolio.

Joseph S. Kalinowski, CFA

Barberis, N. (2013). Thirty Years of Prospect Theory in Economics: A Review and Assessment. Journal of Economic Perspectives, 27(1), 173-196

Benartzi, S., & Thaler, R. (1993). Myopic Loss Aversion and the Equity Premium Puzzle. doi: 10.3386/w4369

Gneezy, A., & Epley, N. (n.d.). Prospect Theory. Encyclopedia of Social Psychology. doi: 10.4135/9781412956253.n424

Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality. American Psychologist 58(9), 697-720

Kahneman, D. & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica (pre-1986), 47(2), 263

Pompian, M. M. (2011). Behavioral finance and wealth management: how to build optimal portfolios that account for investor biases. Hoboken, NJ: Wiley.

Thaler, R., & Sunstein, C. (2009). Nudge: Improving Decisions about Health, Wealth, and Happiness. New York NY: Penguin Group USA