Cross-subsidy in DB & DC

Can somebody please comment whether my undertstanding is correct or not -

In a DC, the Cross subsidies say between a male and a female are apparent if the contribution rate is same for male and female. If the contribution rate is determined on the basis of average mortality for male and female, then the females are subsidising the males assuming that they live longer than male. This cross subsidy is adversely affecting the member (female) and not the employer because the rates of contribution paid in male's account are more than actually required and being paid less in the female's member than required.

In a DB, there would not be a cross subsidy affecting the member because his benefits are defined as % (say 1%) of salary for each year of service, so he would not be directly affected by being a male or a female. In this case the cross-subsidy is for the employer in a way that he will end up paying more pensions to a female, if two employees one male and one female have served for exactly same no. of years and salary at retirement.

Thanks

 

I'm not too convinced by your description of DC.
If one person (male) wants 5 bottles of milk and another (female) wants 7 bottles, but the stores only sells them in boxes of 6, I don't think you could say that the female is subsidising the male because she bought less than she wanted. The both received equal value for what they purchased.
In DC the subsidy only comes into play when you convert the account balances to a pension. The subsidy here depends on the relative annuity rates. If unisex rates used the male will subsidise the female because he is paying relatively more for the value he receives.

With the DB one, I don't think you can say that the cross subsidy affects only one of the parties which are paying for it. The male is paying the same as the female (even if this is nil) and receiving lower value (unless gender specific factors remove this "inequality"). Thus the male is subsidising the female.

 

Hi,

I am not sure if I can explain myself be giving reference of milk bottles but I have tried to illustrate it through a real life example -

Consider a DC scheme where the employer decides to fix a contribution rate when a member joins the scheme based on his actual age and rest of the assumptions based on actuary’s judgement. Let’s say the employer wants to target a certain level of pensions say 2/3rds of the final salary after 40 years of service and wants to adopt the EAM for keeping the contribution rate same throughout the future.

Suppose 1 male and 1 female both of age 25, join the scheme at the same time. The actuary uses the EAM SCR (with entry age 25) formula below to derive the contributions for both employees under the standard assumptions (eg no decrement pre-retirement etc). He first does calculations with the post retirement annuity based on actual gender and then based on unisex annuity rate (calculated by taking average). He gets the contributions given in the table below the formula -

EASCR =
(65-25))/60 x S x (1.04/1.06)^40x a65/(S x ā40ר

Male
a65 = 13
SCR = 14%

Female
a65 = 15
SCR = 17%

Unisex(average of 13 & 14)
a65 = 14
SCR = 16%



Therefore, if he is not calculating the annuity rates differently for males and females and calculating the rates based on an average annuity rate, he is paying 16% in male’s account as opposed to 14% required and paying 16% for female as opposed to 17% required to secure same level of pension. Assuming that for next 40 years, experience is same as assumed, both the male and female will have same pot of wealth at age 65. Now if they go to secure the annuity in the market, female will get the pension which is lower than 2/3rds of her salary because the market will price annuities differently for male and female, hence she is at loss. The male will get higher that targeted pension and hence at benefit. Effectively, the female has subsidised the male.

 

It's a valid point that a female member might regard as unfair not being able to obtain the same level of pension as a male.

Where the annuity is purchased from an insurer it's difficult to criticise the scheme however, as they are providing equal lump sums on retirement to male and female members. The perceived inequality arises from the insurer's pricing basis.

Where the annuity is purchased within the scheme it is more problematic. People may regard the scheme design as unfair if it leads to unequal pensions for otherwise identical male and female members.

I don't think it's correct to call this a cross subsidy though.

Normally cross subsidy refers to using profits from one contract to subsidise losses on another contract. In this case, if we assume annuities are priced by expected cost and that experience is as assumed on the pricing basis, there will be no profit arising on the smaller female annuity contract because the female is expected to live longer. Similarly there will be no losses arising on the larger male annuity contract. Each contract is self financing.

 

Agreed - it might be regarded as unfair but not really a cross subsidy.
The male pays 16% and gets 16% worth of benefits. The fact that this is more than he really "needs" is a different issue - he gets what he paid for.

In fact, if unisex annuity rates are used to remove this (perceived?) inequity, then there would be a cross subsidy. The males are paying more for what they get, and females less.

 

It agree that it may not be strictly regarded as cross-subsidy but it is laying a similar impact.....benefit of one at the cost of the other.It can be given the name 'unfair'. However, this 'unfair' effect is eventually leading to cross-subsidy on retirement if the unisex rates are not offered from the scheme (ignore the insurer for the moment). So, if contributions are on unisex terms and the pension payments are also on the unisex terms then it is fine and nothing unfair and no cross-subsidies.