NNEG: Rental yields versus imputed yields

My Kent colleague Radu Tunaru’s recent report for the Institute and Faculty of Actuaries (IFoA) on valuation of no negative equity guarantees was discussed at a meeting at Staple Inn last Thursday.  A controversial element was the adjusted rental yield calculation of 0.2 x 5% = 1%, where 5% is the observed gross yield on rented properties and 0.2 represents the proportion of houses in the UK which are rented out. I was initially sceptical myself: the objections from “some actuaries” enumerated as (a) and (b) on p33 of the paper correspond closely to my initial comments (and no doubt others too). This blog explains why I’ve (partly) changed my mind.

Houses are unusual assets in that roughly 20% have an observed rental yield and 80% don’t (20% are held as financial assets and 80% as consumption assets). There is no precise analogue of this when pricing options on individual shares or bonds.  But here’s something close: many companies which could pay dividends choose not to do so. For pricing options on shares in these companies, we don’t make any reference to a “potential yield” which the company could pay if it so chose. And this seems correct, because when a company retains earnings, those earnings are embedded in the share price. The price generating process for the underlying share is different because the company returns earnings. (Modelling all prices as geometric Brownian motion sort of glosses over this, but the economic logic seems clear.)

Now on p33 of the report, Radu is trying to price a put on the house price index, not on an individual property. The price generating process for the index is one where only 20% of the houses in the index generate a yield.  The lack of yield on the other 80% is embedded in the price generating process. Stated like this, I can see the point.

Whilst I can (belatedly) see the point of adjusting the observed rental yield, I’m still not sure I fully agree with the adjustment down to 1%. A useful comment at the IFoA discussion meeting on 28 February was that perhaps the 80% isn’t 0.8 x 0, it’s 0.8 x something. The “something” is the “utility yield”, reflecting the benefit the owner occupier derives from living in the house.  In economics, a more common term seems to be “imputed rent”, so let’s call it the “imputed yield” from owner occupation. 

The imputed yield is unobservable, but there are several reasons for thinking it might be lower than the observed rental yield: (a) mortgage finance is significantly cheaper for owner occupiers than for most landlords (b) all imputed rent is untaxed (c) owner-occupiers don’t have management expenses, voids, don’t require a profit margin from renting, etc.

As I said, p33 Radu is pricing a put on the index. When we move on to individual properties, and assuming the imputed yield is less than the observed rental yield, the argument suggests that a put on an individual property is worth less if it’s owner-occupied than if it’s rented.  This initially seems odd. But it’s also consistent with the idea that an owner-occupied house receives better maintenance, so that the price generating process for an owner-occupied house is nudged upwards compared to that for a rented house, like the share price of a company which retains earnings compared to an equivalent company which pays dividends.

However for NNEG there is a further twist. NNEG holders aren’t typical owner-occupiers; they’re owner occupiers who have entered into a contract which may weaken their incentives to maintain the property, and so perhaps nudges the price generating process back towards the one for rented houses. But still not the same as for rented houses.[1]Contra this argument of weakened incentives for maintenance, there are reports that more than half of equity release borrowers use the proceeds at least partly for home improvements.  eg UK … Continue reading

Note that the underlying phenomenon here is very general: the existence of a loan secured against an asset, or option on the asset, can change the value of the asset. Most financial theories seem to neglect this point.

If the above argument isn’t persuasive, here’s an alternative. Imagine a rental-only world in which owner occupation is not permitted; every house has to be either rented or left empty. Many people own one house and rent another to live in.  Or perhaps more likely, housing ownership becomes more concentrated on very rich individuals and institutions. But in that world, the demand, supply, availability of mortgage finance and political intervention in the housing market would all be different; and so the yield and price generating process for housing would be different. It’s not obvious that the observed rental yield from the 20% in the extant market provides a good estimate of what would happen in a rental-only market.

In summary, imputing a zero yield to the 80% of owner occupiers seems questionable (as the report admits – see p32), but so does imputing 5% without further thought and adjustment.  So even if I don’t ultimately agree with the 0.2 x 5% + 0.8 x 0% calculation, it highlights an important point, which I hadn’t thought of before.

Sandcastles in the air

The discussion above doesn’t touch on more fundamental doubts about the hedging approach to NNEG valuation. Another useful comment at the IFoA meeting was a fleeting allusion to “sandcastles in the air.”  The basic constructs on which Black-Scholes type option pricing depends – most fundamentally, liquid markets in forward contracts – are not even approximately operative for housing. So why are we even thinking of using option pricing models based on hedging, to value a guarantee which just isn’t hedgeable?

It might be better to include housing in a real-world economic scenario generator (ESG), and set the reserve to be sufficient for some low quantile or conditional tail expectation of the simulations. I don’t know of any extant ESG’s which include house prices, but there doesn’t seem to be any technical reason for this; it’s just because institutions haven’t historically invest in housing. This approach would be more computationally intense, but that’s always a declining problem (so far).  Perhaps this is the way it will be done in ten years’ time.   

Finally, two points of personal context. First, my comments on the report are those of an interested reader; I am not part of the Kent Business School team commissioned by the IFoA (my affiliation is with another department at Kent). Second, despite recent characterisations as “firm-friendly”, my views are not reliably pro-industry; just look at some of my other work, starting with why insurers are wrong about adverse selection or the book at top right of this page!


1 Contra this argument of weakened incentives for maintenance, there are reports that more than half of equity release borrowers use the proceeds at least partly for home improvements.  eg UK Equity Release Monitor Key Retirement 2018.  So maybe ERM houses get good maintenance at early durations, albeit perhaps not at long durations. 

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