Measuring Values of Illiquid Asset Portfolios: A General Model

This paper proposes a model for the estimation of time series returns of illiquid asset portfolios. The model has four major advantages. First, the estimators are arithmetic averages of individual asset returns (or their proxies), so they strictly correspond to the portfolio returns. Second, the model is able to estimate returns of arbitrary-weighted portfolios, including equalweighted, price-weighted, and value-weighted portfolios. Third, the model is very general and accommodates methods proposed in previous research. Fourth, the model is able to use both price data and data of asset characteristics to improve efficiency of estimators. It is also able to correct for the sample bias problem that transactions may take place more likely on over-valued assets. Simulations with actual data of Dow Jones Industrials show that this model supplies superior estimators than a simple benchmark method. ∗ Department of Economics, and International Center for Finance, Yale University, New Haven, CT 06520-8281 ([email protected]). 2 Measuring values of illiquid asset portfolios is important because many important assets transact infrequently. For example, the real estate, art, and bond markets are generally illiquid. In real estate and art markets, assets tend to be held for years or even decades between sales. In United States bond markets, less than 10% of bonds transact daily. The equity markets also have infrequent trading problem to researchers who work with high frequency transaction data. The global equity market, if considered as an integrated market, is actually illiquid. While the global equity market is considered open, equities in a regional market may not be tradable at all because this regional market is close. Not only many existing asset markets are illiquid; many to-beestablished markets might be so. For example, for the new macro markets originally proposed by Shiller (1993a), such as national income and labor income markets, the underlying cash market prices may be observable only infrequently. Repeat sales regression (RSR) is a broadly used method for estimating the returns of illiquid asset portfolios. It estimates the time series returns using the observed transaction prices for a subset of assets. First suggested by Bailey, Muth, and Nourse (1963), RSR has had a lot of modifications and variants since then. For example, Case and Shiller (1987, 1989), Goetzmann (1989, 1992), Goetzmann and Peng (2000), Goetzmann and Spiegel (1995, 1997), Shiller (1991, 1993b), Webb (1988). The original RSR model has two serious limitations. First, its estimators are geometric averages of cross-section individual asset returns, while the true returns for a portfolio, no matter an equal-weighted or a value-weighted one, are always arithmetic averages of individual asset returns. Goetzmann (1992) proposes a correction method that approximates the arithmetic average given the geometric average, under the assumption that the asset returns in each period are identically lognormally distributed. This method works well in 3 simulations. However, this method needs to estimate unobserved cross-sectional variances, which may not be easy in some cases such as when time series data are heteroskedastic. As an alternative, Goetzmann and Peng (2000) propose a method that directly estimates the arithmetic equal-weighted portfolio returns. The second limitation of the original RSR method is that it actually supplies estimators for equal-weighted portfolio returns only. In many situations, researchers may be more interested in price-weighted, value-weighted, or other special-weighted portfolios. Shiller (1991) proposes estimators, either price-weighted or equal-weighted, that are analogous to the original RSR estimators but are arithmetic averages. However, more flexible method that could estimate returns of arbitrary-weighted portfolios would be desirable. Researchers have proposed methods using both transaction data and data of asset characteristic to estimate returns of infrequent-traded asset portfolios. For example, Case and Quigley (1991), Case et al (1992), Clapp and Giaccotto (1992), “hedonic repeated measures” method (HRM) by Shiller (1993b), and “distance-weighted repeat-sales” procedure (DWRS) by Goetzmann and Spiegel (1997). The primary methodological advantage of using both transaction and characteristic data lies in its ability to explore stronger correlation between price paths of assets with more similar characteristics. Limitations of these methods are that they may not supply return estimators for arbitrary-weighted portfolios, and their estimators may not have natural interpretations, such as being arithmetic means of individual asset returns. In this paper I propose a model for the estimation of time series returns of illiquid asset portfolios. My model has four major advantages. First, it is very powerful: it supplies