Monday, September 20, 2010

Pension fund return assumptions.

Pension funds have to make assumptions about the returns that they expect over long horizons. These assumptions then form the basis for how much money the fund should invest. If the fund is run by a state, these assumptions then directly impact the state budget.

Pension funds are pretty much free to come up with whatever expected return they choose. Of course this is a decision of monumental importance. Set it too low and you have to raise taxes or cut current expenditures in other areas of state government. Set it too high and you end up with an unfunded liability.

An MBA 523 student of mine forwarded me this article from the WSJ.

The article reports that most states are using an 8% expected return and then goes on to suggest that this might be too high.

I think it is too high. Lets look at some basic numbers..

Assume that a pension fund is 50% in T Bonds and 50% in Equities.

The yield on a 30 year T Bond is about 3.9%.

We can solve for the expected return on the equity portfolio using a little portfolio math...

8% = R(TBond)*0.5 + R(Equity)*0.5
8% = 3.9*0.5 + R(Equity)*0.5
Solve for the R(Equity) = (8 - 3.9*0.5)/0.5 = 12.1

Based on my assumptions these plans are working on an expected return on equities of about 12.1%. Given a risk free rate of 3.9%, this implies an equity premium of:

(1+0.121)/(1.039) - 1 = 7.9%

The historic equity premium has been 6%. To assume near 8% is purely delusional.

However, it could be that I have my portfolio weights wrong. So lets assume a more modest equity premium of 5%. This implies an equity return of 1.05*1.039 - 1 = 9.1%

We can now solve for the portfolio weights.

8 = wRF*3.9 + (1-wRF)*9.1

Doing a little algebra, we can solve for wRF which is the weight in the risk free bond (in this case the T Bond).

We find that wRF = 21%. This implies an equity holding of 79%.

Again, for a public pension fund this seems far too high.

What can we conclude...
1. State governments are just kicking this problem down the road. Eventually taxes will have to go up to fund these plans, and/or benefits will be cut to retirees.

2. If you are in one these plans, you should be funding a 401-K or other plan as a supplement.

Finally: What return assumption are you using for your plan? Over optimistic investors end up living with their kids in their retirement.