Longevity risk solved

Holiday news today...

An unknown Dutch actuary (don't quote me !) claims to have found the definitive solution for what's called 'longevity risk'.

Instead of a traditional non-comprehensive actuarial equation, the proof is one of those rare, and sometimes dangerous or wrong, visual proofs in (actuarial) mathematics.



Anyway, have a nice holiday!

Klantenmonitor Zorgverzekeringen®

Resultaten onderzoek Klantenmonitor Zorgverzekeringen® :

gemiddelde marktscore voor:
- dienstverlening aan klanten: 7,4 (2006:idem)
- probleemafhandeling: 4,9 ( 2006: 5,5)

Eindoordeel dienstverlening
Verzekeraar	2007	2008
Pro Life Zorgverzekering	8.0	8,1
De Friesland Zorgverzekeraar	7.7	7.9
Azivo Zorgverzekeraar	7.5	7.8
DSW Zorgverzekeraar	7.8	7.7
IZA	7.5	7.7
ONVZ Zorgverzekeraar	8.2	7.6
Univé Verzekeringen	7.4	7.6
Zorg en Zekerheid Zorgverzekeraar	7.4	7.5
IZZ	7.4	7.5
FBTO	7.5	7.4
Agis Zorgverzekeringen	7.4	7.4
Groene Land Achmea	7.4	7.4
OHRA	7.4	7.4
CZ	7.3	7.4
Trias Zorgverzekeraar	7.4	7.3
Zilveren Kruis Achmea	7.2	7.3
De Goudse	7.4	7.2
AnderZorg	7.3	7.2
VGZ	6.9	7.2
Avéro Achmea	7.0	7.1
Menzis	7.2	7.0

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?