# Framing: Part I of a Series on Utility Theory

Jan 29, 2007 by

1. Which of the following options do you prefer?

A: Getting \$200 for sure

B: Having a 1/3rd change of getting \$600

2. Now, imagine that I gave you \$600 and the following choices. Which would you prefer?

C: Losing \$400 for sure

D: Having a 2/3rds chance of losing \$600

According to Daniel Kahneman and Amos Tversky, most people would prefer options A and D. All of the above options produce an expected return of \$200. However, options A and C are risk-free, while options B and D are risky. According to Kahneman and Tversky, people tend to be risk-seeking when facing loses, and risk-averse when facing gains. Note that since in the second problem, the person had been given \$600 beforehand, the two possible outcomes would have been the same as in the first problem.

Now, imagine two more scenarios:

3. Imagine that you were playing a two-stage game. There is a 25% chance that you win the first stage, at which point, you advance to the second stage. If you lose the first stage, you get nothing. Once arriving at the second stage, you can choose between \$3,000, or an 80% chance at winning \$4,000. Which do you pick?

4. Imagine that you were offered a choice between two gambles: a 20% chance at winning \$4,000 or a 25% chance at winning \$3,000. Which do you pick?

According to Kahneman and Tversky, most people pick the sure \$3,000 in the first game, and the 20% chance at the \$4,000 in the second game. These choices are not consistant. The chance of winning \$3,000 in the first game is 25% * 100% = 25%, just as it is in the second game. The chance of winning \$4,000 in the first game is 25% * 80% = 20%, just as it is in the second game. However, when we separate the game into stages, we isolate the risk of the first stage, and ignore it. Most people would rather have something for certian, than a risk of having nothing, so they choose the sure \$3,000. However, when the chance of winning either prize is far from certain (20% and 25%), and the differences between the probabilities of winning appear to be small, people opt for the bigger prize. This is a sort of monetary optical illusion.

What does this mean for the average investor? When making investment decisions, consider how you are framing them, and how your options are being presented to you. Would you respond differently if things were presented to you as loses instead of gains, or vice-versa?

Here is a scenario involving making an investment decision for one year:

Imagine that I have two investment options: placing \$2,000 in CD, at a bit below the risk free rate (receiving -1% real growth for sure), or placing \$2,000 in XYZ Index Fund, which has a 50% chance at gaining 10% in real value, and a 50% chance at losing 12% in real value. In this scenario, the XYZ Index Fund sounds superior, as people are risk averse when facing loses.

Now, let’s rephrase the problem. Imagine you were given two new options: placing \$2,000 in a CD at a growth rate (5%) a bit below the nominal interest rate (6%), or placing \$2,000 in XYZ Index fund, which has a 50% chance of a 8% gain in nominal value, and a 50% chance of a 2% gain in nominal value. In this scenario, most people would prefer the CD, as it provides more stable returns. Given a sure shot at growth, it is not worthwhile to take a risk to earn a higher rate of return.

The moral of the story is that you can reframe one investment decision in multiple ways, and come to multiple conclusions as a result.

For the interested reader: The first four examples presented above are based upon those used by Daniel Kahneman and Amos Tversky in the essay Prospect Theory: An Analysis of Decision Under Risk

### 1 Comment

1. I’d be interested to see how this dichotomy plays into people’s degree of reluctance to buy vs. to sell. Really, if you are risk averse, you should be reluctant to put your money into the market at all, yet most people assume investing with risk as a given. However, personalities react very differently when deciding when to take money OUT of the market, whether to minimize losses or to maximize gains. Which is a more powerful force, the desire to get out of an investment before it sinks to the floor or the impulse to stay in a rising stock to wring out every penny?