Unsmoothing valuation-based indices using multiple regimes

Valuation error and valuation index smoothing have been the subject of a great deal of recent research efforts, largely due to concerns over the quality of investment decisions that can be made using valuation-based data. To date, unsmoothing models have assumed that the variances in valuation noise and market noise are at a constant ratio, producing a constant unsmoothing parameter. This paper proposes a model which allows this ratio to change over time, depending upon defined growth states in the observed series, using a threshold model with multiple regimes. A rent level index and initial yields are unsmoothed using this model and implied unsmoothed capital value growth rates are calculated. The implied unsmoothed capital value growth rates and unsmoothed yields are then used to construct a total returns series which is compared with the original smoothed total returns series, in terms of its mean and standard deviation, and in terms of its correlation and covariance with total returns on the FTSE. Some implications for two-way asset allocation between a portfolio of shares and property are drawn.