strategies are chosen in part to simulate different rates of parameter responsiveness to new information. The first of the alternative strategies is an expanding sample beta estimation in which unconditional model parameters are estimated by OLS at each time t based on the full sample up to time t beginning at t = 250 and continuing through the end of the sample. For the second strategy, estimates of unconditional model parameters are re-estimated every 50 periods using the full sample. The final two additional strategies are rolling beta specifications, the first using a sample from t-249 to t at each time t and the second using a shorter sample of t-49 to t at each time t. For each case, predicted returns for each portfolio at each time t are generated by
Ei ,t [ ri ,t 1
t t i t f | , ]
where i,t|t is the latest vector of portfolio factor loadings conditional only on information
through time t.
Geometric returns and Sharpe ratios for the five strategies are presented in Table 7. For each of the strategies, with the exception of the TVPFM generated positions, there is at least one negative year. The discrete rolling OLS strategy has the poorest yearly return and Sharpe ratio while the Kalman filter estimated TVPFM has the highest return and Sharpe ratio. The TVPFM outperforms the other strategies most dramatically in the last three years of the sample, following the March 2000 market peak. A comparative look at the cumulative returns for each strategy is presented in Figure 3.
(Insert Table 7 here)
A crucial issue that needs to be addressed in the evaluation of model profitability is the drag of transaction costs. Given the specific set of portfolios we are trading, a reasonable estimate of these costs can be addressed and is done so here. From the simulation discussed earlier in this section, the average portfolio holding period was 1.48 weeks resulting in approximately 35 annual liquidations and initiations for the long and short strategies. To quantify approximate costs, we propose a strategy of simulating the sector index by buying constituents comprising