Academic journal article Real Estate Economics

Optimal Valuation of Noisy Real Assets

Academic journal article Real Estate Economics

Optimal Valuation of Noisy Real Assets

Article excerpt

We study the optimal valuation of real assets when true asset values are unobservable. In our model, the observed value cointegrates with the unobserved true asset value to cause serial correlation in the time series of observed values. Autocorrelation as well as total variance in the observed value are used to calculate an efficient unbiased estimate of the true asset value (the time-filtered value). The optimal value estimate is shown to have three time-weighted terms: a deterministic forward value, a comparison of observed values with previously determined time-filtered values, and a convexity correction for incomplete information. The residual variance measures the precision of the value estimate, which can increase or decrease monotonically over time as well as display a linear or nonlinear time trend. We also show how to revise time-filtered estimates based on the arrival of new information. Our results relate to work on illiquid asset markets, including appraisal smoothing, tests of market efficiency, and the valuation of options on real assets.


Real asset value is typically estimated with error. This is because real assets have unique locational, physical, and contractual-relational characteristics that cannot be replicated--either physically or synthetically--by comparable assets. When these characteristics are priced, payoffs to the nontraded asset will also be difficult to replicate, thereby resulting in value estimation error (Case and Shiller 1989, Vandell 1991). Even a sale of the asset will be noisy because of liquidity and other private demands of investors, as well as bilateral bargaining outcomes in nondealer-intermediated markets (Quan and Quigley 1991).

To understand the setting we have in mind, consider the valuation of commercial real estate that is unique in its location and physical design. The asset need not be highly unusual--only slight variations in location and physical design may result in a real asset whose characteristics are nonreplicable. Furthermore, the leasing contracts that determine the revenue flows to the asset are likely to be nonstandardized, with a set of tenants that vary in their space demands and credit quality. This heterogeneity further complicates the replication problem.

Now suppose that there is a sale of the commercial real estate at time zero and that it is nontraded for a period of time after the sale date. Further suppose that the asset sells at a variance to its true value. This implies that the initial observed value is noisy. After sale date, suppose that the initial observed value is updated based on two complementary information sources: (a) a continuous flow of relevant macroeconomic data, and (b) sporadic comparable asset sales. With only the macroeconomic data, the initial noise will generally persist and even accumulate over time, in the sense that "a drunk tends to wander further and further from his starting point" (Black 1986, also see Case and Shiller 1989).

Counteracting the tendency for noise to accumulate is information derived from comparable asset sales. Provided that these comparable sales contain information that is specific to the subject asset, they will tend to pull the value estimate back towards its true value. Comparable asset sales therefore cause noise to dissipate over time. However, despite all efforts to uncover the true value, unobserved differences between the subject asset and comparable assets suggest that estimation error cannot be eliminated and therefore that noise will persist over time.

This paper extends our previous work in this area (see Childs, Ott and Riddiough 2001) by developing a formal model that addresses the economic setting described above. At any given time, noise hinders observation of the true asset value. We allow for noise in the initial observed value (possibly resulting from an asset sale) as well as in subsequent periods when the asset does not trade. …

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