Kevin questioned yesterday whether the deferment rate is affected at all by any illiquidity premium. Here is a mathematical approach to the same question.
We have discussed here and elsewhere (for example in the Eumaeus Guide) how the deferment rate is mathematically connected with the net rental yield. The key is the assumption that the value of the property S is the present value of all net rental receipts, so the following equation holds:
S=d × y × (1+y+y^2+y^3…) = d × (y+y^2+y^3…) = d × y/(1-y)
where y = (1+g)/(1+r+π), d is the net rental, r is the risk free rate, π is the risk premium required by investors in residential property, and g is growth of net income (e.g., dividends or net rental, not property price). Then it is easily shown that d/S= q, i.e. the deferment rate q1 is simply the net rental divided by the market observed value of the property. You don’t need to know the rental growth, the risk free rate or the risk premium to establish the deferment rate.
We can easily extend this reasoning to show that any illiquidity premium is also irrelevant to the value of the deferment rate, an exercise which I shall leave to the reader.
In other news, the IFoA paper is featured in an article in InsuranceERM here.
As two of the fiercest critics of the industry’s approach, Kevin Dowd and Dean Buckner, comment in their own analysis of the Working Party’s paper: “There is no point worrying about theoretical possibilities that don’t apply in the real world. But we are talking about actuaries here.”