Based on empirical analysis, Arjan van Bussel, Marija Beleska and Mike Nawas argue that Solvency II’s approach to real estate is too uniform

Despite real estate’s attractive investment features, its role in the asset allocation of insurance companies is set to deteriorate as a consequence of Solvency II. Unlike the current regulatory framework, Solvency II will relate capital requirements to the characteristics of assets and liabilities under stress scenarios. Effective asset liability management, whereby the interest rate sensitivity of assets mirrors the sensitivity of liabilities, is therefore more important than ever.

Unfortunately, the current proposals only identify a limited number of assets as sensitive to interest rate movements, and real estate is not one of them. We challenge this decision of Solvency II by analysing the interest rate sensitivity of residential European real estate. We do this by empirically deriving its duration.

Duration was introduced in 1938 in a groundbreaking work by Frederick Macaulay. Unlike maturity, duration also captures the timing of all other principal and interest payments of a financial investment. Therefore, duration is also an accurate indicator of the interest rate sensitivity of an investment.

By matching the duration of assets to the duration of liabilities, financial institutions mitigate interest-rate risk. Such an immunisation strategy requires that the interest-rate sensitivity of each investment is correctly measured and incorporated in the asset liability management guidelines. Of course, these guidelines need to tie in to the method prescribed by regulators. The problem, though, is that the parameters describing the interest-rate sensitivity of real estate investments in the Solvency II standard model are counterintuitive. Consequently, real estate is becoming a much less compelling investment for insurers.

Under Solvency I, the capital that must be held by an insurance company is simply a function of the insurance premium it receives. Solvency II endeavours to make the capital weighting more risk-based. Real estate investments will have to be stress-tested by a 25% shock to their market value. The real estate industry believes that this assumption is too severe and not in line with historic evidence.

IPD (The IPD Solvency II Review – Informing a new regulatory framework for real estate, 15 April 2011) concludes that the shock assumption should be no higher than 15%. IPD also writes that the correlation between real estate and interest rates is negative whereas the Solvency II guidelines, as currently drafted, propose a correlation of zero if interest rates increase and 0.5 if interest rates decrease. The positive correlation indicates that insurance companies have to assume that property values go down if interest rates decrease. This is counterintuitive, so we put it to the test empirically.

To demonstrate the interest rate sensitivity of real estate, we derive empirically the duration of residential real estate in five European countries.

Why residential real estate? First, residential real estate forms a very important asset class for insurance companies. Secondly, residential property returns are generated by large numbers of granular valuations that are well-suited to statistical analysis. And finally the Solvency II standard model is based on UK data including all real estate asset types except residential property, so any empirical deviation from the standard model is likely to be particularly visible in this segment.

Interest-rate sensitivity and duration
The blue curve in figure 1 shows the normal inverse relationship between interest rates and the value of a fixed-income instrument. Small interest-rate fluctuations can be approximated by the grey tangent line, the slope of which is the first derivative of the function described by the blue convex curve:
dMV = -    D     MV
    dr    (1 + r)

This equation can be rewritten as:
dMV = -    D     dr
    MV    (1 + r)

Equation (2) shows that the interest rate sensitivity is described by the Macaulay duration divided by 1 plus the interest rate. This fraction is widely referred to as the modified duration, so:
dMV = -  Dmod  dr
    MV    
whereby Dmod = modified duration

Equation (3) is commonly expressed in its discrete analogue:
ΔMV = -  Dmod  Δr
    MV    
whereby ∆MV = change in market value, ∆r = change in interest rates
Equation (4) states that the percentage change in the market value of a fixed income instrument resulting from a small change in interest rates can be approximated by multiplying the negative value of the modified duration with the absolute change in interest rates.

Unlike a fixed-income instrument whose value solely depends on interest rates and the credit quality of the borrower, the value of a real estate asset also depends on many property-specific and macro-economic variables such as location, quality of the building, tenants, remaining lease length, demographic variables and inflation expectations. For that reason the modified duration cannot theoretically be determined for a real estate asset; one has to apply empirical analysis.

To do so we use the following regression equation:
LN(MV) = α + β  r + ε

This function allows us to directly estimate the modified duration by deriving empirically the β parameter. This can be demonstrated by differentiating Equation (5) with respect to interest rates, r:
dLn(MV) = β  = dLn(MV) =   1    dMV = - Dmod
    MV    dMV    MV    dr

Equation (6) demonstrates that the first derivative of regression Equation (5) is equal to β and also to the modified duration. Equation (6) therefore proves that the modified duration equals the β parameter that will be found when regressing the natural logarithm of market values, Ln(MV), against interest rates, r. Similarly, it can be proven that this also holds if we substitute market values with price indices in the above equations.

We empirically derive the interest rate sensitivity of residential real estate by estimating the β parameter in Equation (5) for residential properties in Belgium, France, Germany, the Netherlands and the UK.

Data used
Figure 2 describes the data used. The independent variable is the 30-year euro swap rate for countries in the euro-zone, and the 30-year GBP LIBOR swap rate for the UK. Use of long-term interest rates is appropriate given the long-term nature of real estate investments.



Results of our empirical analysis

The results yield interesting similarities, but also noticeable differences. In figure 3 we show the results of the regression analyses specifically for Belgium and France, in graph format, and in figure 4 we show the results for all five countries in table format.


Solvency II prescribes that parameters have to be statistically significant at a 99.5% confidence interval over a one-year period. P-values less than 0.5% indicate that the corresponding parameters meet this requirement. As can be seen in figure 4, the estimated β parameters are statistically significant and negative, confirming the inverse relationship between interest rates and the value of real estate.

Moreover, the results in figure 4 demonstrate that residential real estate has a long modified duration, making it a very attractive asset class for any insurance company with long-term liabilities. The one exception is Germany where the modified duration is only 3.7 years. The differences in duration are most likely caused by differences between local housing markets, mortgage markets and tax incentives stimulating home ownership in each country. However, an in-depth analysis of these differences is beyond the scope of this article.

The R2 is 0.65 or above for Belgium, France and Germany, whereas it is below 0.5 for the Netherlands and the UK (An adjusted R2 of 0.65 indicates that 65% of the variation in the dependent variable is explained by changes in the explanatory variable).  An adjusted R2 of 0.65 or higher suggests a relatively strong linear relationship between interest-rate fluctuations and house prices. The lower R2 for the UK and the Netherlands shows a less clear relationship. What these two countries have in common is the relatively large contribution of the financial industry to the gross domestic product. The banking crisis may have had a more severe impact on relationships between interest rates and price movements of real assets in those two jurisdictions than in other countries.

To test this assumption, we split the analysed period into two sub-periods, with March 2009 as cut-off date, as it marks the first quantitative easing operation by the Bank of England.

Figures 5 and 6 demonstrate that the relationship between interest rates and UK house prices indeed differs substantially before and after the cut-off date. In fact, the linear relationship appears to have disappeared since quantitative easing.

We observe a similar disruption in the Netherlands. In that country, since the onset of the financial crisis, the housing market and tax-deductibility of mortgage interest have been subject to contrasting political pressures with new rules suggested and rejected at high speed. Add to this the euro-zone crisis and it is easy to see why (potential) homeowners have been playing a waiting game. House prices decreased significantly despite historic low interest rates. This is illustrated in figure 5 by the positive β parameter, and in figure 6 by the corresponding increasing trend line for the period March 2009 to February 2013.

This is in stark contrast to the negative β parameter and decreasing trend line for the period before March 2009.

Hence in the UK and the Netherlands the relationship between interest rates and house prices changed substantially during the financial crisis. Prior to the crisis the relation is in line with economic expectations and with empirical results found for neighbouring countries, but in the midst of the crisis these relationships appear not to hold in the UK and the Netherlands.

Conclusion and recommendations
Once Solvency II comes into force, the amount of capital that must be held by an insurance company will also have to reflect the riskiness of its investments. The approach that Solvency II took so far is too generic across real estate asset classes (not distinguishing between residential, retail or offices), and exclusively based on UK data.
We have demonstrated that the values of residential properties in Belgium, France and Germany are sensitive to interest rate movements similar to bonds. The same holds true for residential real estate in the UK and the Netherlands for the period January 1999 to March 2009, although no such relation was found for the UK and the Netherlands in the midst of the financial crisis when economic relationships appear to be impacted by interventions and other exogenous factors.

We argue for fine-tuning of Solvency II’s standard model by introducing different parameters for different real estate segments in different jurisdictions. After all, isn’t it precisely the objective of Solvency II to make the capital charges more risk-based and less blunt?

Alternatively, we recommend that insurance companies develop their own proprietary real estate risk model. Solvency II permits this alternative. Although not an easy endeavour for individual insurance companies, developing and validating such an internal model will most likely result in lower capital requirements under Solvency II, higher investment returns and a better risk management tool when investing in real estate.

Arjan van Bussel and Mike Nawas are partners, and Marija Beleska is a financial analyst at Bishopsfield Capital Partners

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