The sensitivity of UK commercial property values to interest rate changes

Abstract

Duration and convexity measures are commonly applied in the management of bond portfolios to measure the sensitivity of asset values to changes in interest rates, enabling fund managers to manage their exposure to interest rate risk. Yet, there are no commonly accepted methods for applying the concepts of duration and convexity to equities and real estate, making it difficult for fund managers to analyse the exposure of multi-asset portfolios to interest rate risk (Blitzer & Dash, 2004).

This paper contributes to this underdeveloped area of interest rate risk management by assessing the accuracy of using duration and convexity to measure the sensitivity of commercial property values in the UK to discount rate movements. Simulations confirm that property has duration and convexity characteristics similar to bonds. Our estimates overlap with duration figures estimated by Cairns and Wilkie (2010) for index-linked British government bonds over 15 years but are higher than their estimates for conventional bonds and five- to 15-year index-linked gilts. Perhaps more importantly, the paper demonstrates that duration is not sufficiently reliable enough to mitigate the interest rate risk attached to a property portfolio. The inclusion of convexity is necessary for effective interest rate immunisation strategies.

Keywords:

• interest rate risk
• duration
• convexity
• asset-liability matching

Notes

1. Future income streams in Equation (1) are assumed to be annual in arrears and perpetual with default and void risks captured by the risk premium included in the discount rate. These assumptions simplify the valuation of freehold property but Adams et al. (2003) argue they do not fundamentally change the results of the analysis. In a similar way, the holding of property assets for a finite period is ignored. The growth explicit DCF model is sufficiently flexible to accommodate different holding period assumptions but this will only have a significant impact on capital values, and subsequent duration and convexity measures, if the exit yields at disposal are allowed to vary significantly from the target rate of return minus the expected growth rate. Otherwise, the sale price, usually estimated as a rack rented investment, is a close proxy for the cash flows the investor foregoes at disposal.

2. This non-linear relationship is represented by the concave curve in Figure 1.

3. Adams and Booth (1995) argue that volatility measures can provide useful insights into the sensitivity of asset and liability values to changes in interest rates but warn that the volatility of the present values of financial assets need not necessarily correlate with market price fluctuations. They cite Bulkley and Tonks (1989) as evidence that imperfect knowledge of future dividends and inefficient use of information, where it is available, give rise to volatile fluctuations in UK stock prices and enable traders to earn excessive returns based on a simple trading rule. Adams et al. (2003) note that similar market inefficiencies also generate mis-pricing in property markets where market prices deviate from the underlying worth of assets.

4. The development of the formulae for the capital value, V, modified duration, D and convexity, X, of freehold property is available from the corresponding author on request.

5. Although the explicit growth DCF model specified by Equation (1) assumes the properties are quickly re-let when leases terminate, an important point to note is that lease length can have an impact on the default risk associated with an investment, which in turn influences the discount rate. Thus, Morrell et al. (2004) cite the simulations of Crosby et al. (2004) who estimate that lease lengths of 10 years or less are likely to give rise to discount rates 2% higher than assets let on longer leases, and conclude that further downward pressure on duration is likely as existing leases terminate and are replaced with shorter leases.

6. Adapting the method advocated by Brooke et al. (2000), the real redemption yield on five- to 15-year British government bonds has been derived for the period of study by removing the 10-year moving average of RPI inflation from the nominal yield. The 10-year moving average is used as a proxy for the average rate of inflation expected over the following 10-year period.

7. CAPM is used to estimate a time varying property risk premium but readers should only interpret as illustrative. The time varying beta is estimated from recursive regression using a five-year moving window of historic returns. The expected market equity risk premium is assumed to be a constant 3.5%, in line with the higher long run risk premium suggested by Morrell (2007, 2010). This generates time varying risk premiums for the retail, office and industrial sectors with the all-property risk premium estimated as the geometric average across these sectors.

8. The average nominal implied rental growth rate over the same period has been 5.42% for offices, 3.93% for industrial units and 5.46% for retail.

9. The unit of measurement for duration is years, and represents the ratio of the percentage change in the reduction in an investment’s price to the percentage increase in the discount rate. This generally lies between 0 years and the time to maturity of the investment and, in terms of the zero-coupon bond definition given by Fabozzi, would have the same price sensitivity to interest rate changes as a hypothetical 100 years zero-coupon bond.

10. The duration of a reversionary property will also lengthen if the cash flow frequency is increased.

11. Completely mitigating inflation rate risk rests on the assumption that the second derivative is a close approximation of the mathematical relationship between changes in capital values and discount rates, and higher order derivatives are insignificant.

12. The IPD index is widely accepted as representative of the property investment market so duration and convexity measures of this portfolio in effect are representative measures of the market.

13. The phenomenon may also occur if net nominal rents rose faster than the rate of inflation. This would result in the short run inflation flow-through factor being in excess of one, resulting in the appearance of a negative duration, as discussed in Section 3. However, this is less likely to be the explanation for the UK office and industrial sectors where rental income growth either slowed or decreased.

14. Although it is difficult to see whether property behaves in the way suggested by the figures in Table 5, an interesting point to note is that the combined duration and convexity measures in nominal figures predict that a 0.5% rise in the discount rate (as at December 2006) would give rise to an 5.78% fall in the capital value of the portfolio. Bank base rates rose from 5% to 5.5% between 2006 and 2007, and over the same period initial yields rose by 0.5% and the capital value of the IPD portfolio fell in nominal terms by 7.7% (IPD, 2009). Assuming target rates of return moved by the same magnitude this suggests the measures captured only 76% of actual adjustment.