Study group report 2008: Estimating the volatility of property assets (Actuarial Profession)
This is the final report on the problem of estimating the volatility of property assets brought to ESGI64 by the Actuarial Profession. Click on the link at the bottom to download the full report as a pdf document.

Report coordinator
Melvin Brown (Industrial Mathematics KTN)

Executive summary
When an investor is allocating assets between equities, bonds and property, this allocation needs to provide a portfolio with an appropriate risk/return trade-off: for instance, a pension scheme may prefer a robust portfolio that holds its aggregate value in a number of different situations. In order to do this, some estimate needs to be made of the volatility or uncertainty in the property assets, in order to use that in the same way as the volatilities of equities and bonds are used in the allocation. However, property assets are only valued monthly or quarterly (and are sold only rarely) whereas equities and bonds are priced continuously and recorded daily. Currently many actuaries may assume that the volatility of property assets is between those of equities and bonds, but without quantifying it from real data. The challenge for the Study Group is to produce a model for estimating the volatility or uncertainty in property asset values, for use in portfolio planning. The Study Group examined contexts for the use of volatility estimates, particularly in relation to solvency calculations as required by the Financial Services Authority, fund trustees and corporate boards, and it proposed a number of possible approaches. This report summarises that work, and it suggests directions for further investigation.

Introduction

Background and motivation
Estimates of the volatility or uncertainty are currently used in property assets, as in equities and bonds, to evaluate the solvency of insurance companies and large pension schemes. In this context, solvency is defined as the excess of assets (such as equities, bonds, property and cash) over liabilities (such as insurance policies or pension payments) expressed as a fraction of liabilities. Solvency estimates are required by the Financial Services Authority (FSA), fund trustees, and corporate boards. The timescale for which solvency is evaluated may exceed 35 years. Since 2004, the FSA has required a market consistent approach to the evaluation of solvency. In this regime, solvency estimates are required to certain levels of confidence, and so they require the use of variances and covariances between different types of portfolio holdings; these can be calculated using the respective volatilities in their rates of return. In a similar way, volatilities are also required for activities such as portfolio planning. Pension fund trustees and insurance company investment managers may review their asset allocation strategy typically every three to five years. Within such periods they may also adjust their portfolios as conditions change. In both these cases, volatility estimates inform decisions in portfolio planning. For pension schemes, although there are many variable elements, there is a guaranteed element in the final pension. For life assurance companies, there is the guaranteed sum assured, but for with profits policies there are also bonuses. Property and bonds mainly are held against promises which have a guaranteed element. The tension between the guarantees and the uncertainties in the investment assets generates insolvency risk. Monte Carlo simulations are run to assess this risk, by modelling a variety of futures for the benefits i.e. the liabilities and for the growth in assets, and so evaluate the probability of insolvency, and identify asset mixes that minimise this probability. It is in this context, that estimates of the volatilities of and correlations between various asset types are required.
Estimates of solvency are highly sensitive to correlations between asset types, and they may change. For example, if equities and property act in concert during extreme economic shocks then the diversification plan for less extreme situations may not work. However, it is volatility estimates that determine the scale of uncertainties, as represented in variancecovariance matrices. A key feature of commercial property assets is that they are only valued monthly or quarterly (and are sold only rarely) whereas equities and bonds are transacted and thus priced with high frequency and recorded daily. Currently, many actuaries will assume that the volatility of property assets is between those of equities and bonds, but without quantifying it from real data. Commercial property indices are published, for instance by IPD, which use surveyors estimates. However, the volatility in such an index may not correctly represent the long-term risk, because the sale price of a property is subject to various unpredictable factors that mean it will not be directly linked to the index. This is similar to the ’thin trading’ problem for equities with small capitalisation (’small cap’ equities). They appear to have a good risk-adjusted return, because infrequent trading means that the volatility of the shares is understated. This issue has been addressed by Dimson (1979), and by Roll (1981) but there is no corresponding analysis for property assets.

Challenges for the Study Group
The challenge for the Study Group was to produce a model for estimating the volatility or uncertainty in property asset values, for use in portfolio planning and solvency assessments.
The following questions were put to the Study Group:
(a) What information do the surveyors estimates use? Are they based on commercial rents, or do they use information from property sales when available?
(b) Might other information such as returns on real estate investment trusts (REITs) be useful surrogates for estimating property portfolio volatilities.
(c) Can a model for a sale price be obtained from using the IPD index, but then also multiplying by a random factor F at the time of sale, where F has a distribution over perhaps the interval from 0.8 to 1.2? If one made such a model, is there data available that could be used to validate it?
(d) Is there data available to find what other economic variables F is correlated with?
(e) How does F change with the time horizon?
(f) Should a model for property asset values look at the extent to which similar properties sold at nearby times and locations can be used to give a more specific measure of volatility?
(g) What can be inferred from the change in variance over different time horizons, allowing for the extent to which there is serial correlation that might have an impact? (Booth & Mercato 2004)

Click on the link below to view the full report.

Download 'ESGI2008ReportActuarial.pdf' (612 Kb).