Which one of these two gambles is best?
$75,000 with probability 50%
$25,000 with probability 50%
$100,000 with probability 98%
-$1,000,000 with probability -2%
Sometimes as part of my job, I have to review the academic literature to find some support for an argument that we are trying to make. From time to time, I look at the top papers at the Social Science Research Network and see if anything catches my attention. A few days ago, I came across What Happened to the Quants in August 2007? , a paper with around 11,000 downloads, making it practically viral for the world of academia.
The authors examine the week of August 6, 2007 when several long/short equity market neutral hedge funds experienced huge losses. In a section about managing risks, the authors present the two gambles.
The answer is that there is no best gamble. The first gamble has an expected return of $50,000 but has lower risk than the second gamble which has an expected return of $78,000. The answer is based solely on an individual’s level of risk aversion and which answer you choose has a profound impact on what choices you should make as an investor.
This simple question elegantly illustrates two points:
- Investors are risk averse and and investors have different levels of risk aversion. Even though Gamble 2 most likely will make more money in the long run, the risk of a large draw down may make investors prefer Gamble And the fact that different individuals choose different gambles implies that everyone has different levels of risk aversion. Modern portfolio theory makes this assumption and it is reassuring to know that it is reflected in reality.
- Which gamble you choose should inform you on what kind of investor you are. If you choose Gamble 1, you are slightly more risk adverse. This means you should consider a portfolio that consists of fixed income and dividend-paying stocks. If you choose Gamble 2, you are less risk adverse. You can look into vertical put spreads or even writing naked calls.
I personally think Gamble 2 is better. Which gamble would you choose? Please reply in the comments.