Ch 18, Section 1.2 - Market Consistency

I am confused by the core reading on page 9 of chapter 18 (Setting Assumptions - Investment Return - Market Consistency).

The first paragraph says:
"If a market-consistent approach (as described in Section 3 of Chapter 15) is used, either deterministically or stochastically, then the expected investment return can be set as the risk-free rate, irrespective of the actual underlying assets held (this is the "risk neutral" calibration approach)."

However, in the next paragraph it appears to contradict itself:
"However, if the stochastic approach is adopted, then the investment return volatility and correlation assumptions do remain dependent on the actual underlying asset type(s)?"

Reading through Chapter 15 Section 3, it doesn't appear to mention anything about a stochastic market-cosistent approach...

Could someone help to clarify what the core reading is trying to say here?

Thanks!

 

Hi

Good question/challenge.

Short answer

There's a distinction between a central/expected scenario and the distribution around the central scenario. The former can be determined irrespective of the actual assets held; the latter must consider the actual assets held.

Long answer

1. The investment return volatility and correlation assumptions will affect the DISTRIBUTION of the results around the central/expected scenario. The distriution of the results will therefore be affected by the underlying assets held.

2. However in a market consistent world we KNOW what the value of the asset is; it's the market price. Therefore whether a deterministic or stochastic model is used doesn't matter because we are constrained (in a central scenario) by the knowledge that the market has already told us what the price is.

3. For e.g, take two assets: equity & government bonds both valued at £100. In a market consistent world both would be recorded at £100 on the balance sheet (the fact that one is riskier than the other is irrelevant). However, both would have very different DISTRIBUTIONS because equities are riskier than gov. bonds.