Considering Black Swan Events For Decision Making

Ödön Heller [Public domain], via Wikimedia Commons

Sleep per Day: (Target) 7h30m / day (Actual) 7h18m  / day (64 day average)

**I wrote an article that pointed out the flaws of my thinking of this article, you can read it by clicking here.**

I was talking to a friend who just became an insurance agent, and I initiated the discussion of critical disease illness.

For me, a critical disease insurance is very attractive since even though the probability of getting a critical disease is low for my age group, once it does visit me, it would absolutely cripple me financially.

But that’s System 1 thinking, a more educated decision requires sitting down to think about the question in terms of probability and expected utility value, which is essentially “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.

One of the most well known diseases covered by critical disease illness is cancer, which as a male, I statistically have a 43.31% chance to catching one in my lifetime. However, as a below 45 year old male, I have a 6.23% chance of getting cancer at this stage of my life.

What this implies is that critical diseases such as cancer is common enough among humans to be taken seriously, but that over-fearing isn’t warranted.

With cancer treatments usually lasting 4-6 months, and cancer treatments costing 10,000 USD or more / month, the cost of cancer treatment may cost from 40,000 USD to 138,000 USD.

So the decision of whether to buy critical disease illness (if cancer is the only concern) would boil down to whether I can afford the expected utility value of cancer treatment (probability of getting cancer at current age * cancer treatment cost), and if I can’t then how much should I pay in terms of insurance premium?

The expected utility value of cancer treatment for male below 45 year old is $8,597.40 USD [1], which I could afford right now.

But the critical disease insurance covers up to 39 more situation besides cancer. What this means is, if the expected utility value of every other 39 situations is 50% [2] of expected utility value of cancer treatment, then the total expected utility value for critical diseases is 176,246.70 USD, which is something I can’t afford as of now.

So faced with a 176,246.70 USD expected utility value of critical disease treatment, how much should I pay for insurance premium? Since the payout ratio of claims to insurance premium is around 1000:1, the amount I should be willing to pay is 176.25 USD, which is around 1374.75 HKD.

The same decision making process can be made in terms of what market conditions is most favorable to invest for investors who are just starting out and have shorter investment horizons (eg. <= 3 years).

Historically, the average duration of bull markets is 68 months, while the average draw downs during bear markets is 35.88%.

The decision for whether a investor who is just starting out would be basically boil down to the probability of a bear market to happen * the average draw down – the probability of the bull market to keep going * the average investment return possible in a bull market.

Since the last part of the component is susceptible to your investment strategy (average investment return possible in a bull market), the question needs to be inverted to see whether the average investment return is realistic or not when making an informed decision to enter the stock market or not.

So an example would be if probability of a bear market to happen is 50%, the average draw down is 35.88%, the probability of bull market to keep going is 50%, then the investment return needed to make investing sane would be at least 17.94% for the remainder of the bull market.

Another way to look at this question is how long will it take to break-even the the average draw down.

In order to break-even a 35.88% loss, a 55.96% return needs to be achieved before the next loss is occurred. If the bull market is expected to continue for 2 years only based on historical pattern, then an average return of 24.88% required would put into perspective whether it is realistic that the investor can generate this amount of returns before the next bear market hits.

But of course, the present doesn’t always repeat exactly what the past has done, but it’s always important to use these historical probabilities as a reference point if there’s no substitute for accurately predicting the probability of certain events happening.


[1] 6.23% chance of below 45 year old male getting cancer * 138,000 USD cancer treatment

[2] I don’t have the time to research the probability of being in the 39 other situations besides cancer and the cost of treatments for these 39 situations, but quite a lot of them seem to have a lower probability than cancer by gut feeling, so a conservative 50% discount is used for each of the 39 other situations.


Not advice. No offer. Do not rely. May lose value. Risky. Conflicts hidden/obscured. (Borrowed from Terrence Yang‘s Disclaimer on Quora)


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