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When are two portfolios better than one? A prospect theory approach

Consider an investor receiving a statement of portfolio outcome. The portfolio is very likely to have both winning and losing assets. What would be the best way to show the portfolio’s performance - does the investor prefer these outcomes to be pooled or presented separately? In this paper, we study when and under what conditions presenting two portfolios would be better than one.

Though how come the presentation of a portfolio is important? The answer has roots in how we view and compare the information. We tend to compare the results of the portfolio with the market, or with the options and strategies, we didn’t follow. Such comparisons can lead to regret and acting emotionally in adjusting the portfolio. So the idea is to minimize the regret and its emotional side effects by showing the portfolio differently.

In one of his interviews held in 2018, the prospect theory author and Nobel prize winner Daniel Kahneman proposed a “regret-proof policy,”: a behavioral portfolio policy that an investor can live with when things go badly. The idea is for investors to have two portfolios: one risky and the other safer, which are managed and reported separately.

In practice, investors hold only one portfolio, however, holding two portfolios can feel safer. Because at each time one of the portfolios is performing better than the market or the other one.

In this paper, we investigate whether the display of portfolio performance matters and how prospect theory can explain peoples' preferences. To that end, we ran a survey experiment in which we presented various portfolio presentations to individuals. Our findings reveal that individuals' preference for portfolio outcome presentation is in line with the mental codings proposed by (Thaler, 1985; Thaler and Johnson, 1990).

We also found that when the outcome of the portfolio is negative, the segregated presentation of the portfolio with two mixed (negative and positive) sub-portfolios led to more satisfaction and a higher rating for the advisor. The satisfaction for segregation presentation is lower when the outcome of the portfolio is positive.

Overall, we propose that the segregation of outcomes restricts individuals from fixating on one outcome. The mechanism under which regret-proof policy presentation works involves shifting attention to both gains and losses.


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