When the probabilities are given, what would you choose?
Let’s start measuring, shall we
In the last post we learned about risk appetites and then we described capacity. A good and honest fiduciary knows there’s a difference. They’re out there but they’re difficult to find. A good fiduciary also knows that your capacity to take on additional risk and your appetite for it tends to change over time. The big banks will have you thinking otherwise. Remember their goal is achieving higher AUMs. Yours is financial freedom; and many times, those goals conflict with one another.
That post is here if you need a refresher.
Risk tolerance is what industry insiders tend to call it so appetite and capacity tend to get lumped into one. Appetite is willingness. Capacity is ability. When the bank sees your large capacity to take on risks, they’ll assume you’re also willing to take it on. So that random call on a Friday that came out of nowhere isn’t so random after all. It’s them seeing you with a large book so they can pad their AUM at the end of week just before a long weekend. Don’t fall for it.
When I ended that post I promised to give you a measurement. Not a feeling. Not “rate yourself seven out of ten.” A set of tickets you can actually take.
Well, this is that post. So here it is in all its splendor.
A quiz is not a bet
A brokerage form asks how you would feel if somehow you lost twenty percent of your portfolio’s total value. The form prints moderate-aggressive and a model portfolio. Why? Because you were asked during a good month and you feel good about your chances. That is a sale. It is not a measurement.
Asked again but this time when the market is actually bleeding twenty percent and I bet your answer will be wildly different.
A questionnaire set up as a bet is different. It’s more thoughtful. Is it still emotionally biased? Sure. But less so than the brokerage form we just went over.
I’m confident that it is because it requires self-reflection and introspection. Taken seriously enough it eventually produces consistent results. It’s the Myers-Briggs test on how you handle risks (it’s a stretch I know, but it’s a cool analogy). All it takes are two sleeves with known odds. This is best taken when real dollars are on the line but lab dollars work too. You are given one sleeve at a time. The sleeves are two choices (a.k.a. Choice A and Choice B) each with its own payout and known probabilities. You pick one sleeve. Then you pick again. You keep picking until you’ve done it ten times. The odds change. The sleeves do not.
You are not forecasting the market. You are not sizing a 401(k). You are answering a narrower question: when p is written on the page, which pair will you sit with.
The two sleeves
Let’s go through a working example to make this clear. The questionnaire that I’m presenting here is actually based on a real lab experiment called the Holt-Laury Procedure. It is a widely used experimental method in economics created by Charles Holt and Susan Laury. It has practical implications to the investment management industry and is therefore useful in measuring one’s appetite (or lack thereof) for risk.
The dollar payouts they used in the lab experiment aren’t large but since we’re a serious shop we’ll use meaningful dollars. The nice thing about the experiment is that the amounts within the questions can scale and so do the results.
The first question goes like this:
The probabilities in both of these cases are p = 10%, where p is the probability of a good print; and (1-p) = 90%, where (1-p) is the probability of a bad one.
Sleeve A (or Choice A) is the tight pair. It pays $10,000 or $8,000. The good print is not spectacular but the bad print is not a wreck and the spread is only $2,000.
Sleeve B (or Choice B) is the wider pair. It pays $19,250 on a good print or $500 on a bad one. The good print is a real ticket. The bad print, not so much. That floor is the whole point of the instrument. If you take B, you have agreed to underwrite $500 and you might be considered a gambler. Why? Because the stakes are much higher.
Let’s do the math to make it clearer. Remember when we calculated expected values from this post. We have to do it here again.
Sleeve/Choice A: EV = p1v1 + (1-p1)v2 = (0.10)(10,000) + (0.90)(8,000) = 8,200
Sleeve/Choice B: EV = p1v1 + (1-p1)v2 = (0.10)(19,250) + (0.90)(500) = 2,375
Now you see why choosing Sleeve B on the first row makes you a gambler. Astute investors don’t just look at high payouts; they also look at spreads and they look at expected values. Each sleeve has it. Only in doing the math will you be able to see it. Just remember that expected value is not a real payout. It’s a probability weighted value. Knowing it allows you to compare one choice versus another. Spread is perhaps more important than the payouts themselves and it has another name. It’s called volatility.
Remember that’s how you win in this game in the long-run. You manage risks, not gains. In a long enough timeline, a good risk manager always beats a phenomenal gambler.
So that’s how the quiz goes and you do it ten times over.
On every row the probability is the same on both sleeves. Call it p. p is given. Row 1 is 10 percent. Row 10 is 100 percent — two sure amounts. We do this so the rational choice is clear. Even the most risk averse investor chooses the higher payout when it’s a sure thing.
Each row is its own bet. You do not carry a position from row 3 into row 4. You may switch sleeves once as p rises.
The risk neutral investor
We went over the calculation of Expected Value in the earlier section. The table below summarizes the resulting values.
A has the higher expected dollars on rows 1 through 4. B has them from row 5 to 10. The flip is not a personality. It is arithmetic and switches over at Row 5.
A picker who only maximizes expected dollars switches at row 5. That picker has a name in the experiment. Risk-neutral. Most households are not that picker. That is the point of the list.
The ten tickets
| Row | p | Sleeve A | Sleeve B | Higher EV | Gap (EV_B – EV_A) |
| 1 | 10% | 10% of $10,000 and 90% of $8,000 | 10% of $19,250 and 90% of $500 | A · $8,200 | ($5,825) |
| 2 | 20% | 20% of $10,000 and 80% of $8,000 | 20% of $19,250 and 80% of $500 | A · $8,400 | ($4,150) |
| 3 | 30% | 30% of $10,000 and 70% of $8,000 | 30% of $19,250 and 70% of $500 | A · $8,600 | ($2,475) |
| 4 | 40% | 40% of $10,000 and 60% of $8,000 | 40% of $19,250 and 60% of $500 | A · $8,800 | ($800) |
| 5 | 50% | 50% of $10,000 and 50% of $8,000 | 50% of $19,250 and 50% of $500 | B · $9,875 | $875 |
| 6 | 60% | 60% of $10,000 and 40% of $8,000 | 60% of $19,250 and 40% of $500 | B · $11,750 | $2,550 |
| 7 | 70% | 70% of $10,000 and 30% of $8,000 | 70% of $19,250 and 30% of $500 | B · $13,625 | $4,225 |
| 8 | 80% | 80% of $10,000 and 20% of $8,000 | 80% of $19,250 and 20% of $500 | B · $15,500 | $5,900 |
| 9 | 90% | 90% of $10,000 and 10% of $8,000 | 90% of $19,250 and 10% of $500 | B · $17,375 | $7,575 |
| 10 | 100% | 100% of $10,000 and 0% of $8,000 | 100% of $19,250 and 0% of $500 | B · $19,250 | $9,250 |
Row 5 is highlighted because that is where expected dollars change sides. It is not the “correct” row. It is the baseline.
How to read a switch — without a letter A
If you jump to B while A still has the higher expected dollars, you are paying for the $19,250. You like the upside enough to take the cheap floor early.
If you stay on A after B has the higher expected dollars, you are paying to avoid the $500. That is the risk-averse tell. You are leaving expected dollars on the table to keep the floor at $8,000.
The quiz is designed such that even the most risk averse investor eventually chooses B because it’s a sure 10,000 versus a sure 19,250. You always take the higher guaranteed payout. Always. If you never leave A, including row 10, you are not using expected dollars at all. You either misunderstand the game and you shouldn’t be playing at all. There’s nothing left to fear.
Write your ten letters down. A or B. One per row. That list is appetite on this instrument. It is not capacity. It is not a mix. It is not a score yet.
What this is not
This isn’t a score yet. I promise that’s coming. This is the quiz that gets you to that score. In order to get there, we need data and this quiz is what gives us that.
In the next post we will turn the switch into an interval. Not an exact number, an interval. Like everything in investing (and in life for that matter), this is an estimate, not a guarantee.
This is not advice. A desk that turns your ten letters into a target allocation this afternoon is doing the thing this series refuses to do.
Next
You now have a switch. Next post that switch becomes a range on A. Not a model book. Not a product.
Stay tuned!
