Risk Tolerance vs Risk Aversion

I was looking through the learning objectives, and the idea of risk tolerance is listed separately from risk aversion. I’m not sure if I could articulate the difference between these two concepts.

Risk Tolerance is how much risk a person can stand to accept. It is difficult to quantify. You can use questionnaires to categorize an investor as conservative, moderate, or aggressive.

Is the difference that risk aversion is quantified with a coefficient, rather than a more generalized bucket?

If two investors had the same amount of money to invest, wouldn’t the one with the lower aversion coefficient always be willing to tolerate more risk? It seems like two slightly different ways to describe the same underlying investor attribute.

I am having trouble distinguishing these two ideas.

Learning Objective A.1 - BKM Chapter 6

from google: Risk tolerance measures how much risk a trader is able to stomach within his or her portfolio. Risk-tolerant traders are willing to take on higher risks in return for maximum returns, while risk-averse traders avoid risk, even if that means missing out on higher returns .

I don’t know what your text says, but to me:

Like risk tolerance is related to pricing (I’d take on any risk for the right return), and risk aversion is related to underwriting (a binary yes/no decision based on a risk threshold)

If I am a rich, skinflint my risk tolerance would be high, risk aversion high
rich, spendthrift, tolerance high, aversion low
poor, spendthrift, tolerance low, aversion low
poor, skinflint (or even realist) tolerance low, aversion high

I see
Risk Aversion is an attitude
Risk Tolerance is a capability

This is a good point. Although I think tolerance incorporates both attitude and capacity. Your risk aversion coefficient really says nothing about your capacity.

From BKM text:

Assessing your risk tolerance, however, can be tricky. You must consider not only how much risk you can afford to take but also how much risk you can stand to take.
Determining how much risk you can stand—your temperamental tolerance for risk—is more difficult. It isn’t easy to quantify.

So without the starting constraint that two investors have the same amount to invest, it could be true that even an extremely risk averse investor could still tolerate more total risk than a risk loving investor (if the risk lover had significantly less money in their portfolio).

Just based on this.

In a scenario where you can either

  1. have a 50/50 chance of winning -100 or 200
  2. have a 100% chance of winning 50

a risk averse person would pick 2, whereas a risk tolerant person would likely weigh his capacity for a loss of -100 and potentially go with 1.

Another way to look at this is to consider the following table of potential investment options.

Risk averse investors will look “first” to the last column and automatically rule out the largest and look only at the smaller number(s); risk tolerance for this person is a matter of how large of a number in that last column they’re “comfortable” with and then make a (final) decision based on the guaranteed return.

Non-risk averse investors will likely do some combination of looking at all columns after removing options that they don’t have enough funds for.

min invest amt ($) guaranteed return (%) expected return (%) max return (%) Prob of failure (%)
10k 3.0 4.5 7.0 10
25k 2.5 4.5 7.5 5
100k 2.7 5.0 7.5 10
100k 6.0 11.5 25.0 35
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Been a while since I took this exam, but the only person who should choose option 1 is someone is who risk-seeking, i.e. their risk aversion is negative(or less than 1? I don’t remember). Someone who is truly risk-neutral would be indifferent between the two, since the EVs are the same. But in practice, everyone wants some greater expected return for that increased level of risk.

Someone who is not very risk averse, would choose option 1 if the EV is only slightly higher, (e.g. payout 201 on a win). Someone who is very risk averse would require a much higher payout to compensate for that level of risk. That is what the risk aversion coefficient is trying to measure.

When I think about risk tolerance, I think more about a firm’s management acceptable risk. e.g. structuring your reinsurance so that you only have a 1 in 250 probability of default, or impairment, or downgrade or something along those lines. It’s an aggregate measure and not necessarily about any one particular transaction.

I disagree. Option 1 is the only possibility where you would ever get a $200 return. If say, you need $200 to buy a train ticket home, then that really is your only option. Tail return comes into play for some people, not just the EV (this is the whole spirit of risk capital).

Assuming that you don’t have the $200.

But if all you have is $100 (so that you have a choice in your scenario) and are risk-averse, far better to take the latter as you still have to get other necessities. (Assuming overall ethical behavior.)