Prospect Theory Vs. Expected Utility Theory

As you begin thinking about how you might advise clients in diffucult situations, consider the differences between each theory.

Eric and Josie seem to display the behavior explained in the Prospect Theory. Prospect theory is an alternative framework for how people make decisions under uncertainty. This framework is built on the expected utility theory, which assumes the main driver of happiness is one's level of wealth, although it is considerably different. The prospect theory assumes that people derive happiness from wealth changes rather than their wealth levels. Eric and Josie’s portfolio has taken a hit and their happiness has fallen drastically because of their change in wealth. If I were their portfolio manager, I would explain the risk of under-diversification and biases that lead to it, figure out what their investment horizon and goals were, and optimize a portfolio that assessed the risk with no biases.

“Prospect theory is an alternative framework for how people make decisions under uncertainty. This framework is built on the expected utility theory, which assumes the main driver of happiness is one's level of wealth, although it is considerably different.”

I would look at which stocks make up their portfolio and re-evaluate whether these are the right stocks for their investment goals. Many times investors choose stocks because of biases such as local, familiarity, house money, self-attribution and social. The disposition effect explains how investors behavior after experiencing a gain or loss. It is when investors are reluctant to sell their loser to avoid a feeling of regret, while selling off their winners too early. Self‐Attribution Bias is when investors intentionally avoid selling losers to avoid a negative feedback. Occasional positive returns due to high volatility and biased self‐attribution can induce a non‐negative image of the loser stock. It can lead to investors believing that negative returns are due to random events. Investors believe in mean reversion, especially if they are overconfident in their stock picking ability. I would explain how these biases can affect your investment decisions. You usually lose much more than they could have by holding on to the bad stocks. If the stock has potential, then you could keep it and possibly lower the portfolio weight on it and hope for a turnaround. The next step would be to find an optimal portfolio mix that met their investment horizon and goals. After their portfolio was allocated correctly, I would explain to them the common mistakes investors make when their portfolio is down. Many of our decisions can be explained in the prospect theory. The prospect theory is in fact a family of heuristics concerning how people make choices when confronted with risky options. Evidence has been provided that the weighting function shifts farther away from linearity (i.e. probability-weighting) as the context of the choice becomes more emotion-laden. Humans change how they make decisions in different ways, depending on the change in wealth from your reference point. As we gain money, we become risk averse, whereas when we are losing money, we become risk seeking. Eric and Josie are probably under-diversified. Research has found that most individuals (90.47%) seem to hold portfolios that are below the Capital Market Line. There are various behavioral biases that could explain why people are under-diversified. Some are overconfidence, local bias, trend-chasing, or gambling motives.

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***Prospect Theory

The bottom line is that under-diversified investors are less sophisticated. The annual cost of under-diversification is about 2.3% (risk-adjusted). The problem is stronger among investors who demonstrate stronger local bias and greater overconfidence. Many investors stay away from index funds because they do not give them the same thrill as choosing stocks on your own that could have high returns. Overconfidence in investors leads to an under-diversified, high risk-low return portfolio. Another common mistake investors make is changing their risk levels depending on if they have made money or lost money from the investment. When we go into loss territory we go from risk aversion to risk seeking. For example, if I bought my shares at $25 and they are trading at $35, I may decide that I want to realize the gain even though I don’t think they are overvalued. Now if you bought the same shares for $45 and they were at $35, you become risk seeking because you bought them at $45. You expect the shares to exceed your purchase price because humans tend to be overconfident in their abilities and tend to believe in mean reverting. Instead of comparing the new price to the price you paid, you should look at the fundamentals of the stock and sell it, even if it means you realize a loss. Sometimes it's better to accept a sunk cost, rather than watch it slowly go to $0. Ultimately, I would help Eric and Josie understand how certain biases can affect your investment decisions, re-access their portfolio risk and reallocate their investments to find an optimal portfolio.