discounting pension liabilities: what rate do we use?

Hi! 2010 AM mock for level 3 states in question 6C: liabilities should NOT be discounted using the zero coupon bond, they should be discounted by the IRR on the immunised portfolio. Volume 2 reading 15, end of curriculum question 4 reads: “pension liabilities are long term. the discount rate used to discount pension liabilities is the rate at which high quality bond such as the long treasury bond are quoted”. Isn’t this contradictory? Thanks, Olivia


I think not. It mentions “the rate. . . at which the . . . bond is quoted.” " Rate", singular: they’re talking about the YTM, which isn’t a spot rate; it’s a par rate.

You’re welcome.

Shouldn’t liabilities be valued using the immunized target rate of return? If the yield curve is upwards sloping, then the YTM is not equal to the immunized target rate of return.

They should be discounted at . . . the rate CFA Institute says to discount them.

I haven’t a copy of the curriculum, so I cannot check this; I’d encourage you to do so.

(I agree with your approach in the real world. Separate that from this exam.)

you are mixing reporting a liability and monitoring a LDI strategy

Pension liabilities should be discounted with AAA/AA curve this is required by law ( at least in canada ) and this is for reporting purposes

the other case you are reffering to is a case of a cashflow matching MONITORING ( not reporting ),

if you match every cash flow of your liability and you want to monitor the market value of asset vs the present value of liabilities, you should use the same IRR since everycash flow is matched so you want to expose them to the same yield curve ( or single rate ). Its not because their is a yield change somewhere on the yield curve that your cash flow match is not good anymore ( since both has the same cash flow at the exact same date)

but, if you use the same IRR and PV is not the same, then something is wrong with your cash flow match, some cash flows are not match somewhere.

big story short, yiled use for REPORTING a liability and yield used for MONITORING a strategies are not the same thing.

ex : at my job when I do a LDI portfolio for a pension plan liability, i do not use the same yield curve as the one I use to evalutate the reporting liability value.

you can read about it page 45 book 4 under MONITORING

if you have a pension plan (in any state of funding - fully or under funded) - starting rate = Discount rate for the liabilities (used by Actuaries).

If the plan is fully funded - they can afford a stretch target - higher that rate to calculate pv (liabilites) [rate used to calculate the PBO/DBo - in order to 1) earn pension income. 2) reduce future contributions.

Is this a par curve or a spot curve?

I’d suspect the former.

spot curve always.

the thing with the Canadian AAA/AA curve is that bond with maturity over 25yrs pretty much doesnt exist on the market. pension liabilities have 60 + yrs of expected cash flows. so we try to compensate with provincial spread for those years but it is far from perfect.

AAA/AA market in the US is awesome and liquid. so you can go straight with the actual AAA/AA spot curve.

another fun fact :

for a pension liability the mandate may be :

Edge the Solvency Basis of the liability : this will edge the volatility of required contribution to fund the funding gap since the required contribution are based on a solvency calculation of the liability. This use gov yield + annuity purchase rate for discounting ( your are required by law to fund the solvency funding gap over 5yr in canada )

Edge the financial report basis : they may want to have less variation on their financial statement no matter how much the solvency change. this is based on a AAA/AA curve

Edge little bite of both : use a mix curve, add corp bond to the portfolio of provincial + gov bonds.