Optimal valuation of noisy real assets

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.