Discount Rates for Smoothed-Return Pension Liabilities

Summary

The document asks which discount rate is appropriate for market-consistent valuation of liabilities when an insurance arrangement uses return smoothing. The setup distinguishes general assets earning a risk-neutral rate from insurance capital whose return follows a smoothed process, with mutual own funds supporting the smoothing mechanism.

The response uses a pass-through vehicle analogy to connect asset returns, borrowing costs, and weighted asset discount rates when the vehicle has no equity. It then contrasts that case with a similar structure whose borrowing is guaranteed by a sovereign, where the borrowing rate is described as risk-free. The short answer does not directly resolve how the smoothing mechanism affects liability valuation, nor does it provide a valuation framework or supporting calculations. The analogy highlights the relevance of capital structure and guarantees, but further actuarial or market-consistent valuation analysis is needed to determine the appropriate liability discount rate.

Key ideas

• The question concerns liability discounting when assets and insurance capital follow different return processes.
• A pass-through structure without equity is used to relate asset returns and borrowing costs.
• A sovereign guarantee is described as making the borrowing rate equal to the risk-free rate.
• The response does not directly determine how return smoothing should enter the liability discount rate.

Tags

# Market consistent valuation of a pension scheme with return smoothing


# Market consistent valuation of a pension scheme with return smoothing












Assume we have an insurance company that is valued under a risk-neutral probability measure. Further assume that the company, for simplicity, only has return smoothing based insurance. Assets return with the risk neutral rate while the insurance capital returns with the smoothing based return. The own funds are mutual and are used for return smoothing mechanisms among other things.

What discount rate should one use to do a market consistent valuation of the liabilities? The risk-free rate or the implied from the return smoothing? The different return processes of the general assets and insurance capital make me a bit confused which one should choose.

## Answer by Sergei Rodionov (score 1, accepted)

https://quant.stackexchange.com/a/61484

Imagine a pass-through investment vehicle that invests into various asset classes with different risk/return profiles. Assume now that this vehicle has no equity. The interest on these bonds, as well as WACC, as well as the weighted discount rate on its assets will be all the same.

Now imagine that the corporate structure is the same but the borrowings are guaranteed by a sovereign. In this case the interest will be equal to the risk free rate.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.