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My Little Experiment

First of all, I’d like to thank all the participants to my little experiment with a special mention for those who helped me to get answers beyond the narrow circle of my followers. As I am writing this, the number of answers has just crossed the 201 mark — which is, to be honest, much more than what I expected.

That was a test. I’m not working on an academic research paper (as some of you rightly noted, the panel of respondents would have been highly biased toward economists and financial markets professionals) but on pedagogical tool I intend to use with my students. I was just trying to come up with something workable and needed a little bit of user testing: I had much more than this since some of you (I don’t know who, by the way) provided me with a number of very useful suggestions. So, again, thank you everybody!

Spoiler alert: if you want to do the test, do it before reading what follows.

The raw data is there. I have just removed the answers to the last question (“According to you, what was that all about?”) to protect everyone privacy (there was a number of personal messages in there) as well as three answers (a troll and two obvious jokes). You may play with if you want but keep in mind that the panel is biased.

So, what was that all about?

The first question was, of course, about time preference or, to be more specific, about time-value of money. To put it simply it means that, for “normal” homo sapiens, a dollar today is worth more than a dollar at any distant date in the future. Since I was assumed to be a borrower of an unquestionable creditworthiness (a Lannister) offering to pay back 100 dollars, any strictly positive amount below 100 dollars was therefore a consistent answer. For instance, if you have offered 80 dollars, it basically means that, in one year from now, you’ll get your 80 dollars back plus 20 dollars of interest — that’s a 25% interest rate (100/80-1=0.25). If your answer fits in that range, I considered it as a “valid” answer.

Of course, since you had no reason to question my ability to pay my debt, a 25% interest rate was completely off current market conditions. For instance, as the questionnaire was circulating, the 12-months USD LIBOR rate was around 0.83% and the 1-year T-Bill rate was 0.34% — therefore, a realistic price would have been somewhere between 99.18 and 99.66 dollars (one respondent bided 99.66115 dollars exactly — unsurprisingly, he rated himself 9 in finance and economics).

If you’ve answered zero, it means that you are discounting future amounts with an infinite interest rate. In other words, you think that any future payment is worthless which means, for instance, that you would refuse any wage-paying job unless your boss agrees to pay you on a continuous basis — e.g. you want a cash transfer for every second of work. If you have bided 100 dollars or more, it means that your discount rate is equal to zero or negative. The latter doesn’t make sense (most people answering this ranked themselves poorly in finance/economics and even sometimes in English) while the former is probably a moral condemnation of interest (typically people who see financial markets as a “useless casino for the wealthy”). These answers fall in the “out of range” category.

Table 1
Bids in auction #1

Range ($) Number
[99:100[ 12
[90:99[ 124
[75:90[ 22
]0:75[ 21
Out of range 22

The second question was, as many of you guessed, about risk aversion and the risk premium. Results are a bit trickier to interpret since they must be analyzed with respect to your first answer. For instance, if you have bided 80 on the first auction (meaning that your one-year risk-free rate is 25%), you are expected to bid a lower amount (a higher yield) on the second option because it’s riskier. Out of the 179 valid answers to the first question, an overwhelming majority of respondents got it right (171 or 95.5%).

In real life, the situation where a borrower is not able (or not willing) to meet its obligations is called a default. As it is, of course, extremely difficult to assess someone’s creditworthiness [1], I’ve created a similar risk (you don’t get your money back) that is easy to measure, known in advance and does not depend on interpretations. With the “roll-a-dice” thing, we know exactly all possible outcomes (1, 2, 3, 4, 5 or 6) and their associated probabilities (1/6th each). From this, it is fairly easy to compute the expected reimbursement amount: 83⅓ (100*5/6).

This is where it starts to be interesting. Assuming you have bided 80 dollars on the first auction (e.g. your one-year, risk-free interest rate is 25%), the mathematically perfect bid for the second option is 66⅔. Why is that? Because by lending 66⅔ dollars at 25% you would get exactly 83⅓ dollars after on year — which is the expected reimbursement amount. In other words, your bid hedges your risk to the penny: you’re risk neutral [2]. You may easily compute the risk-neutral bid given your first bid ($x$) with the following formula: $(83+\frac{1}{3}) \times \frac{x}{100}$.

Now, using the same example, if you paid more than 66⅔ dollars, you’re basically requiring a lower interest rate to participate in a risky project than what you asked to lend me money without any risk. For instance, if your second bid is 70 dollars, your risk-adjusted rate of interest is 19.05% (83⅓/70-1) to be compared with the 25% you required in the risk-free auction. You’re a risk lover (or risk seeker) meaning that you have a preference for risk; you’re willing to make less money in percentage terms to play the risky game.

Lastly, you may also have bided a lower amount in which case you’re said to be risk-adverse. For instance, if you only paid 60 dollars, you’ll get a 38.89% interest rate which is much higher than the risk-free 25%. It basically means that, explicitly or intuitively, you required an extra discount, an incentive, to participate to the risky auction. In finance and economics, the difference between the risk-adjusted interest rate you require to participate in a risky project and the risk-free rate (38.89%-25%=13.89%) is known as a risk premium.

If you’re risk neutral your risk premium is equal (or very close) to zero, risk lovers have negative risk premiums and risk-adverse people have a positive risk premium. The next table summarizes the implicit risk premiums extracted from the bids of the 171 respondents who made it through the first two filters.

Table 1
Risk premiums in auction #2

Range (%) Number
Risk-lovers (below -1%) 24
Risk-neutral (-1% to 1%) 28
- of which [-0.01%:0.01%] 13
Risk-adverse (above 1%) 119
- of which > 10% 85

Well, that’s typically what was expected: most people are risk-adverse. I’m afraid it’s nothing new: remember I’m just trying to explain the concept to my students.

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[1] That’s the business credit rating agencies such as Moody’s or Standard & Poor’s are in, by the way.
[2] Alternatively, you’re good at maths and you wanted to prove it.

Now, if you’re a teacher and if you want to use something like this for your students, maybe we can join forces and build something more robust. Just tell me.

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