The downside distribution is more punishing on the low end. For people who need ...

chii · on Oct 2, 2020

> a 90% probability of losing half your wages is generally not worth a 10% probability of making 7x your wages.

this is a fairly bad expected value: 10% * 7 * wages - 90% * wages/2 = 25% * wages

So you expect to lose 75% of your wages! Nobody is gonna agree to do that!

A more realistic scenario is 10% * 100 * wages - 90% * wages/2 = 955% * wages

vkou · on Oct 2, 2020

Your math is wrong.

0.5 * 90% + 7 * 10% = 1.15 average.

Tomminn · on Oct 2, 2020

For the record, the correct way of doing the first math, centered such that 0 represents no change to your wages, is as follows:

0.1 * 6 - 0.5 * 0.9 = 0.15.

That is, a 10% chance of a 6 fold gain, and a 90% chance of a 50% loss (-50% gain), gives an expected value of a 15% gain.

Your math is correct also, and has 1 represent no change to your wages instead.

vijayr02 · on Oct 2, 2020

Actually, it's a bit more involved than that...

The gain is a one time amount

Wages are recurring income. So when wages fall by 50% you need to value an annuity with half the cashflows as before. The PV of your wage income stream over some time horizon can then be compared with the one time gain.

Otherwise you are comparing a stock concept (wealth) with a flow concept (income)