Morris: How to Win Your Bonus
Sometimes rules set up to achieve one result can have exactly the opposite result.
You are a financial trader.
Your company has a bonus scheme, just to make sure your personal interests and the greater good are aligned. As if that were necessary!
Let’s see just how that bonus scheme works.
Ten percent of the company’s profits are paid in bonuses to its traders. Of course if there is no profit then no one gets a bonus.
Each trader’s bonus is in proportion to their profit. Only traders that make a profit are included.
There are 100 traders in the company, including yourself. Every trader has the same $100 to invest.
Let’s look at how this could work out:
80 traders trade in company A and double their money. Total profit = 80 x $100 = $8,000
20 traders trade in company B and lose their stake. Total loss = 20 x $100 = $2,000
Overall profit = $6,000
10% of profit available for bonuses = $600
80 traders qualify for bonuses. As they have achieved the same profit they each get the same share.
Bonus for each profitable trader (80 traders) = $600/80 = $7.50
It all seems to be working fine so far, the traders who made the good trade made money for the company and got a bonus.
How could this possibly go wrong?
Suppose that the other 99 traders all trade in Company C. If it does well they will double their money. If it does badly they will lose their stake. Each is equally likely, it is as though they were all betting on the same coin-flip coming up heads.
You are a bit better than the other guys. But can you turn it to your advantage?
You have spotted Company D and have worked out that it has a 75% chance of success. Again if it does well you double the money, if it does badly you lose the original stake.
What should you do? Should you follow the crowd and trade in Company C or take the better trade in Company D?
What difference does your choice make to your bonus and to the company’s expected profit? Are they actually aligned as intended?
Thanks to Paul Wilmott on More or Less for this great insight into the current financial meltdown excitement.
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jyoak said,
March 20, 2009 at 11:45 pm
Show Spoiler ▼
Stephen Morris said,
March 30, 2009 at 6:36 pm
jyoak, that’s exactly the solution I had!
Show Spoiler ▼
Can anyone see another way to make this work?