Simpson's paradox

Let's take a look at a simple fund management score card.

	Fund 1			Fund 2			Fund 1+2
	Return	Assets	Rate	Return	Assets	Rate	Return	Assets	Rate
Fund manager A	8	200	4,0%	72	800	9,0%	80	1000	8,0%
Fund manager B	48	800	6,0%	22	200	11,0%	70	1000	7,0%
Total Fund managers	56	1000	5,6%	94	1000	9,4%	150	2000	7,5%

Clearly Fund manager B performs 2% better in both Fund 1 and 2 than Fund manager A. However, across both funds, Fund manager A seems to perform better.

This effect is called Simpson's paradox.

Keep in minds:

• Always be critical in ranking mix funds (managers) on overall performance
• Even if the risk profiles of Fund 1 and 2 are the same, Simpson's paradox may show up
• Besides choosing the right Fund manager, choosing the right asset mix is just as important

Another nice example of Simpson's paradox is:

Good for Men, Good for Women, Bad for People

	Woman			Man			People
	Survived	# Start	Rate	Survived	# Start	Rate	Survived	# Start	Rate
Treatment A	3135	3300	95	4020	6700	60	7155	10000	72
Treatment B	7395	8700	85	650	1300	50	8045	10000	80

A cohort or a series of people receive treatment A, and another cohort receives treatment B. The survival rate of treatment A is better for woman as well as for man, but not for people!

Simpson's Paradox Actuary Links:

1. Ratemaking: The CEO asks the actuary...
2. Smokers and survival rates
3. Credit Score really explains Insurance Losses?