Problem description:
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 will 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.

There are commercial property indices available, for instance the IPD series, 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 capitalization (``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 [1], and by Roll [2] but there is no corresponding analysis for property assets. Some of the issues to be addressed are:

1. What information do the surveyors' estimates use? Are they based on commercial rents, or do they use information from property sales when available? Other information available would be return information from real estate investment trusts (REITs).
2. 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? Is there data available to find what other economic variables F is correlated with?
3. How does F change with the time horizon?
4. 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?
5. 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?

References:
[1] Risk measurement when shares are subject to infrequent trading. Elroy Dimson. Journal of Financial Economics 7, 197-226, 1979.
[2] A possible explanation of the small firm effect. Richard Roll. The Journal of Finance, 36, 879-888, 1981.