The PRA’s Consultation Paper CP 7/19 makes some sensible points on a number of issues, but one proposal is a bit bonkers. We refer to S2.4 where it proposed “to take account of movements in real risk-free rates when setting the deferment rate,”’ in order to prevent variability in the real risk-free rate causing variability in the forward rate:
The PRA would increase (reduce) the deferment rate if the review shows there has been a material increase (reduction) in long-term real risk-free interest rates since the last update.
In an earlier post, however, we showed that the deferment rate is equal to the current net rental yield, i.e. the nominal net rental payment divided by the current nominal house price. The real risk-free rate does not even enter into it!
So what is going on here? Well it would appear that the PRA proposal implicitly depends on some assumed relationship or equivalence between the deferment rate and the real rate of interest, but no further details are given.
Digging deeper, it turns out that there is an equivalence, but only under conditions that do not hold. We start with the dividend discount equation:
(1) q+g=r+π
where q is the deferment rate, g the growth of nominal net rental, r the risk free rate and π the risk premium. Now assume first that the property investment is risk free, i.e. that there is no risk premium π. Then make Assumption 1:
(A1) π=0
Substituting into (1) we obtain
(2) q+g=r
Second, assume that g, the imputed growth in net rental, is equal to the general inflation rate i:
(A 2) g=i
Hence
(3) q+i=r
Finally, assume (as stated in CP 7/19 para 2.5 that the nominal rate r is the sum of the expected general inflation rate and the real rate rr, a relationship known as the Fisher Effect:
(A3) r=i+rr
and where
(A4) E[i]=i
i.e., we assume that expected and actual inflation are the same. Substituting and subtracting both sides of (A3):
(4) q+i=rr+i
Hence
(5) q=rr
Given those four assumptions (A1-A4), it follows that the deferment rate and the real interest rate are identical.
The only trouble is that those assumptions don’t hold. First, a property portfolio is clearly not risk free. An investment in a housing portfolio is commensurate to an investment in a risky index-linked bond, as opposed to an investment in an index-linked gilt, which is virtually risk free. This consideration suggests π>0, so that the risky deferment rate will be higher than the real risk-free rate. Moreover π may vary through time.
Second, while rental inflation and general inflation are likely to be correlated, they are not the same. Nominal rentals will tend to go up line with inflation, indeed rental costs are part of the UK Consumer Price Index, 1 but as Figure 1 below shows, rental inflation and CPI are far from 100% correlated. There are long periods, such as 1991-2004, when rental inflation is consistently higher than CPI.
Figure 1: UK Consumer Price Inflation versus UK Rental Inflation, 1970-2017
Source: OECD
Third, Assumption 3 above depends on the unobservable quantity, the expected future rate of inflation. This variable, as the Bank of England well knows, is difficult to predict with any certainty, and hence is difficult to monitor. 2 By contrast, the net rental yield, which we proved in our previous posting to be mathematically identical with the deferment rate, is relatively simple to observe.
Hence, if the PRA wants to monitor the deferment rate – which we think is a reasonable idea – then it should monitor developments in the net rental yield. 3
But monitoring an irrelevant variable like the real risk-free rate makes about as much sense as monitoring the frog population to see how the llamas are getting on.
- Historical data from ONS 1988 – 2004 can be found here.
- It is possible that the PRA intends to monitor market expected real interest using the return on index-linked gilts. However, returns on index-linked gilts have been negative in the 2010s, whereas it is impossible for the deferment rate to be negative. The CP also notes (S2.4) that the deferment rate will always remain positive, in order to comply with Principle III of SS 3/17, but gives no rationale of why this should be so.
- Note that the mathematical equivalence of the deferment rate and net rental yield also depends on the dividend discount model, but without additional assumptions like (A1)-(A4) above.