The Mentality Of An Average Investor, Part I

by: Yicheng Lin


Being "rational" in Neo-Classical Economics and St. Petersburg Paradox (1738).

Allais Paradox show that most investors do not belong to one type of risk preferences.

Are investors "loss averse" instead of "risk averse".

The Mentality of An Average Investor series will talk about the biases and heuristics of average investors. This series will mostly use interesting surveys conducted by readers to show common misconceptions and biases. Most of the material is taken from the behavior finance course taught by Ling Cen at University of Toronto. Although the entire series are written by me, I would like to credit my professor for the valuable life lessons and investment ideas in this series.

The series will start off with various definition of terms to guide the readers through the article. Do not worry if the terms seem to be confusing and vague in the beginning. You can always look back if there are things that you don't understand. After you read through the article and finish with the surveys, the idea and thesis behind should be straight forward. I hope the articles will provoke interesting thoughts and comments from the readers.

Neoclassical economics:

Neoclassical economics dominates micro economics, it is a set of solutions to economics focusing on outputs through the determination that individual are rational and follow utility maximization.

Utility: describes the satisfaction received from consuming a product.


Neo-classical economics like to assume that people are rational. And they defined rational as having three layers:

1) People have rational preference across possible outcomes or state of nature

2) People maximize their utility and firms maximize profits under constraints

3) People make independent decisions based on all relevant information

Rational Preference:

weak preference: agent prefers X at least as much as Y.

strict preference: agents strictly prefers X than Y.

Indifference: agent is indifferent between X and Y.

Although, utilities are ordinal(general choices) instead of cardinal(numbers), here we will assign function form for utilities for the sake of comparison.

Completeness: for any pair of choices, a choice must be made: whether X is preferred as to Y, Y is preferred compared to X or X and Y are indifferent.

Reflexivity: X must satisfy X=X or X=>X

Transitivity: If X>Y, Y>Z, then X>Z.

Now that we are done with the boring definition, we can begin the interesting discussions

Expected Utility as a function of expected value of outcomes?

There is misconception that expected value or the expected return is the same or should be treated as same as expected utility. For example, a 50% chance to win a 100 dollar lottery has an expected return of $50 and therefore its expected utility is $50.

St. Petersburg Paradox (1738)

If this is the case, what is the value of the gamble described here? (Spoiler) Click to enlarge

The expected outcome= (1/2)x2+(1/4)*4+(1/8)*8+...=1+1+1+...=\infty \,.

If the expected value is equal to the expected utility then why does it seems that no one is willing to pay infinite for this gamble?

Researchers then modified expected utility to include risk (random states of outcome with known probability distribution) and uncertainty/ambiguity (random states of outcomes with random probability). And different investors have different risk attitude such as risk averse, risk seeking and risk neutral.

Click to enlarge

Allais Paradox

Please complete the following survey. It has two questions.

Results (Spoiler)

Question 1 A B
Pay off with probabilities 1,000,000 with 100% probability

0 with probability of 1%, 1,000,000 with probability of 89%

and 5,000,000 with probability of 10%

Click to enlarge

Most people in the experiment choose A, which means:

U(1,000,000)>0.89U(1,000,000)+0.1U(5,000,000) and U(0)=0

Organize this expression, we get


Question 2 A B
Pay off with probabilities 0 with probability of 89%, 1,000,000 with probability of 11%

0 with probability of 90%, 5,000,000 with probability of 10%

Click to enlarge

Most people in experiments choose B*, which means 0.11U (1,000,000)<0.1U (5,000,000).

Click to enlarge

The result contradicts itself

Question 1 function(0.11U(1,000,000)>0.1U(5,000,000)

Question 2 function (0.11U(1,000,000)<0.1U(5,000,000)

The terms in the both functions are exactly the same. However, the result contradict with each other. What could be the reason?

Prospect Theory (1)

Survey (Spoiler)

Results: Most of the people choose A and B*.

Observation: People tend to be risk aversion when it comes to winning and risk seeking when losing. People's risk preference depend on gains and losses relative to a reference point, which is usually the status quo.


People do not display a clear line of risk preferences, and a definite utility function. It seems that the measurement for expected utility changes as the status quo changes. When people are winning, they like to be risk averse and when people are losing, they are desperate to get back to where they started. An interesting research done by Odean also shows that investors are reluctant to realize their losses as an average holding period for a winning stock is 102 days and losing stocks is 124 days (source: research paper), which is in-line with our conclusion.

I believe that studying our human nature and other investors' biases can help us make better investment decisions and avoid pitfalls in our perceptions. In the world of investing, the biggest enemy is likely to be ourselves. I would like to leave you with the quote from Warren Buffett.

It seems to be some perverse human characteristic that likes to make easy things difficult. --Warren Buffett

Finally, congratulations for making it to the end! If you like what you are seeing, please click the follow button, so you don't miss the next part of the series. Hopefully my surveys are as entertaining as the SeekingAlpha community.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.