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The Actuary The magazine of the Institute & Faculty of Actuaries

A volatile business

Henry Simmons and Lloyd Jones ask:are UK property indices misleading?


© Shutterstock
© Shutterstock

“The volatility of individual properties is hard to measure due to infrequent sales”

The valuation of the no negative equity guarantee (NNEG) for equity release mortgages (ERMs) is a hotly debated topic. The NNEG is a key feature of ERMs, ensuring the loan repayment never exceeds the value of the property – even if the loan balance is greater. It is predominantly valued using the Black model. The annualised volatility of returns is one input to this valuation when using Black for option pricing. Within its consultation paper 13/18 ‘Solvency II: Equity release mortgages’, the UK Prudential Regulation Authority (PRA) proposes a long-term property volatility estimate of 13%, derived from Nationwide, Halifax and Office for National Statistics (ONS) index data and adjusted for autocorrelation and the impact of moving to the volatility of individual property returns rather than index returns. 

The volatility of individual properties is hard to measure due to infrequent sales. We have created postcode area-level indices using Land Registry data to assess whether the volatility of granular parts of the market differs from that of the national index. Our findings suggest that local variation in volatility does not lead to materially different NNEG valuations for geographically diversified portfolios. Conversely, using a national index adjustment may lead to inappropriate volatility assumptions when applied to portfolios concentrated in certain areas of England and Wales.

House price indices by postcode

To examine local differences in volatility, we constructed a set of house price indices for England and Wales, split by postcode area – the first one or two letters of a postcode. These 104 indices were produced via the repeat sales method, using Land Registry price data from 1995 to the present day. A repeat sales index uses the price change of unique properties to determine the movement of house prices over time. This method forms the basis of the methodology behind the construction of the UK house price index (HPI) by the ONS. In simplified form, our results closely match UK HPI at the national level. The indices are plotted in Figure 1, with overall index movements in red.

Figure 1
Figure 1


Annualised volatility by geography

By creating an index for each area and looking at annual non-overlapping returns, we can calculate area-specific volatility. We find that the volatility does not vary greatly by area, which suggests there is not much to gain from valuing NNEG by area and that a constant volatility across all areas is sufficient. The range of property one-year annualised volatilities by area is shown in Figure 2, along with the England and Wales index volatility of 8% (dotted line). 

Figure 2
Figure 2


Autocorrelation in index returns

The returns of property price indices are not entirely random – they are autocorrelated, and property prices display momentum. This contradicts one of the Black method assumptions: that returns are independent. The observed annualised volatility of returns increases over longer time-frames before levelling off. The difference between the one-period volatility and this plateau is the adjustment made to account for autocorrelation.

There is a question over whether autocorrelation may also be different between areas. This would have the effect of changing the level at which the long-term volatility plateaus.

Autocorrelation varies by geography

 Autocorrelation of returns is not consistent between areas, with values ranging from 0.01 to 0.57. The volatilities of one-year returns (Figure 3) are tightly clustered around 8.0%, but due to differing autocorrelations the spread of values increases drastically when looking at 10-year returns (Figure 4). Although median value is 12.1%, slightly below the PRA’s central estimate, the increased spread of volatilities could be cause for concern.

The wider spread may not cause an issue with using national indices to set assumptions for portfolios that are geographically diverse, but may cause problems for portfolios concentrated in high volatility areas. 

Using an average volatility rather than region-specific volatility is acceptable for low loan-to-value, geographically diverse portfolios. For geographically diverse portfolios, the areas of high volatility – and therefore higher NNEG – net off against the areas of low volatility and NNEG. This netting off will be weaker for a high loan-to-value portfolio.

Figure 3
Figure 3
Figure 4
Figure 4


A worthwhile test

The adjustment required to national indices to represent volatilities of individual properties is not straightforward. One-year volatilities are similar between areas, but differences in autocorrelation of returns means that treating them all with the same adjustment factor is not appropriate. However, our results offer some consolation with respect to using single point volatility estimates. For sufficiently geographically spread property portfolios, the presence of higher volatility areas does not have a material impact on NNEG valuation, compared to using a prudent central estimate. The results also highlight how ERM portfolios that are heavily concentrated in low volatility areas, such as the South East, may need to consider whether they are overstating their NNEG by using a national property index to derive volatility and the autocorrelation adjustment. Although moving to an area-specific volatility valuation approach may not be practical in all cases, it may be a worthwhile test to assess an overall property volatility assumption.

Henry Simmons- Data scientist at Hodge

Lloyd Jones- Capital management actuary at Hodge