Prospect Theory - How We Really Make Decisions
This is a retelling of Chapter 6, Part 2 (sections 6.7-6.9) from “Behavioral Finance for Private Banking” by Thorsten Hens, Enrico G. De Giorgi, and Kremena K. Bachmann (Wiley, 2018).
In Part 1, we covered the basics of decision theory and expected utility. Now we get to the good part. What happens when you actually try to build a portfolio using these different theories? The answer is: you get very different portfolios. And that matters a lot.
The Two Fund Separation Theorem (And Why Advisors Ignore It)
Traditional finance has an elegant rule called the Two Fund Separation Theorem. It comes from Tobin (1958) and says something simple. All investors, regardless of how risk-averse they are, should hold the same mix of risky assets. The only thing that changes is how much you put into that risky mix versus cash.
Conservative investor? Put 80% in cash and 20% in the risky portfolio. Aggressive investor? Borrow money and put 120% into the same risky portfolio. But the risky portfolio itself? Same for everyone. The mix of stocks, bonds, and other assets inside it does not change based on who you are.
Here’s the problem. Financial advisors don’t actually do this.
The book shows data from Fidelity, Merrill Lynch, Jane Bryant Quinn, and the New York Times. All of them recommend different mixes of risky assets depending on the investor type. Conservative clients get more bonds relative to stocks. Aggressive clients get more stocks relative to bonds. The ratio of bonds to stocks changes from about 1.5 for conservative investors down to 0.25 for aggressive ones.
This directly contradicts the Two Fund Separation Theorem. According to traditional finance, those advisors are all wrong. But here’s the thing. Maybe traditional finance is the one that’s wrong.
What Prospect Theory Does Differently
When you switch to prospect theory, you measure risk and reward differently.
In the traditional approach, reward means expected return and risk means volatility (standard deviation). Simple. Clean. And incomplete.
In prospect theory, reward is your “average gain.” That is the weighted sum of all returns above your reference point. Risk is your “average loss.” The weighted sum of all returns below your reference point. The reference point is personal. For some people it’s 0% (just don’t lose money). For others it might be the risk-free rate or inflation.
This creates what the authors call the Behavioral Efficient Frontier (BEF). It’s like the classic efficient frontier from Markowitz, but customized for each investor based on their loss aversion and reference point.
And here is the important part. The BEF and the traditional efficient frontier are not the same. A portfolio that is optimal under mean-variance analysis might be suboptimal for everyone under prospect theory. The theory you use to evaluate preferences directly changes which portfolio you recommend.
Same Client, Three Different Portfolios
The book gives a very clear example that shows this in practice. Imagine you have a client choosing among five asset classes: bonds, stocks, commodities, and two hedge funds. Four possible economic scenarios with different probabilities.
You ask the client one simple question: “An investment offers a 50% chance to double your money. What is the maximum loss you would accept in the other case?”
The client says: “I can handle a 20% loss.”
Same answer. Same client. But watch what happens when you interpret that answer through three different theories.
Mean-variance analysis: The 20% answer gives you a risk aversion parameter of 1.11. The optimal portfolio? 71% stocks, 29% bonds. Nothing else.
Expected utility theory: That same 20% answer translates to a risk aversion of -2.76 (different math, different meaning). The optimal portfolio? 44% stocks, 46% bonds, and 10% hedge funds.
Prospect theory: The 20% answer gives you a loss aversion of 4.12. The optimal portfolio? Even fewer stocks, more bonds.
Three theories. Same client. Same answer to the same question. Three very different portfolios.
Why This Matters for Real Advisors
So here’s what happened. If an advisor uses mean-variance and ignores loss aversion, they put the client into 71% stocks. But the client’s real psychological tolerance, the one prospect theory captures, says that is too much. When the market drops and losses hit, the client panics and sells. The advisor didn’t recommend a bad portfolio in theory. They recommended a bad portfolio for that specific human being.
The wrong theory leads to unsatisfied clients. Unsatisfied clients leave. And the advisor-client relationship, which should be long-term, breaks down.
The authors are direct about this. Advisors should be very careful when choosing which theory to use. The consequences are practical, not just academic.
The Diversification Puzzle
There is another interesting difference. Traditional finance says diversification is always good. Spread your money across many assets, reduce your overall risk. This is practically a religion in modern portfolio theory.
But here’s the problem. Real people don’t diversify as much as the theory says they should. Their portfolios are concentrated. They hold fewer assets than the models recommend.
Prospect theory explains why.
Consider two assets that are mirror images of each other. When one goes up 60%, the other goes down 60%. A mean-variance investor would split 50/50 between them because that combination gives zero risk. Perfect diversification.
But a prospect theory investor looks at this differently. Asset 1 has positively skewed returns (small chance of a big win). Asset 2 has negatively skewed returns (small chance of a big loss). Because prospect theory overweights extreme outcomes, the investor strongly prefers Asset 1 and avoids Asset 2 entirely. Mixing them would reduce the chance of that big win.
The result? The prospect theory investor holds only Asset 1. No diversification. And research by Mitton and Vorkink (2007) confirms this is what real households actually do. People tend to hold fewer assets with positive skewness rather than well-diversified portfolios.
Traditional finance calls this a mistake. Behavioral finance calls it a predictable consequence of how humans evaluate risk.
Comparing All Three Theories
The chapter ends with a clean comparison table. Three criteria: is it rational, is it behavioral (matches real behavior), and is it intuitive (easy to explain)?
Expected utility theory scores rational: yes. But behavioral: no. And intuitive: no. It follows the axioms of rational choice perfectly. But people systematically violate those axioms (Allais paradox). And the math is hard to explain to a client sitting across the desk.
Mean-variance analysis scores rational: no. Behavioral: no. But intuitive: yes. It uses a simple “reward versus risk” picture. Everyone gets it. But it fails on rationality (violates independence and monotonicity axioms). And it fails on behavior (people prefer assets with same mean and variance but different loss characteristics).
Prospect theory scores rational: only sometimes (when reference point is fixed and probabilities are not weighted). Behavioral: yes. And intuitive: yes (it can be shown in a reward-risk diagram using gains and losses).
The authors’ recommendation? Use prospect theory with a fixed reference point and without probability weighting. This gives you a theory that is rational, matches real behavior, and can be explained to clients using a simple chart.
The Conclusion Nobody Expected
The chapter ends with a surprising twist. All these theories assume you know the probabilities. Banks have investment committees that estimate scenario probabilities so they can build optimized portfolios. Individual investors don’t have those resources.
So you would think individual investors are doomed to underperform. But a study by DeMiguel, Garlappi, and Uppal (2009) found something unexpected. Simple heuristics, like equally distributing your money across a group of stocks, perform just as well as the sophisticated optimized portfolios from banks.
Think about that. All the math, all the optimization, all the investment committee meetings. And a simple “split it equally” rule does just as well.
Sometimes the most sophisticated answer and the simplest answer end up in the same place.
My Take
This section of the book is where theory meets practice. And the practical lesson is clear: the framework you choose to evaluate a client’s risk tolerance directly determines the portfolio you build. There is no “neutral” theory. Every theory comes with built-in assumptions about what risk means, and those assumptions lead to different real-world outcomes.
For advisors, the takeaway is straightforward. Mean-variance is easy but wrong in important ways. Expected utility is theoretically clean but disconnected from how people actually behave. Prospect theory, despite being newer and more complex under the hood, actually matches real human decision-making better than either of the older approaches.
And the diversification result is worth remembering. When your client holds a concentrated portfolio, don’t just assume they’re making a mistake. They might be responding to skewness in a way that prospect theory predicts and traditional finance cannot explain.