75% of the value weighted portfolio. The average weighted constituent price per sector for January 1, 2002 is presented in Table 8.
(Insert Table 8 here)
Assuming an average price of $45 per share, (slightly lower than that for the average portfolio), broker commissions of 3 cents per share and one cent of slippage per transaction, we arrive at an average transaction cost per week of 0.104%. The annual drag is approximately 5% per year. Once transaction costs are accounted for, the simulated strategy using the Kalman filter estimated TVPFM still has a final cumulative return of 177.34% and an annualized Sharpe ratio of 0.92. The next best strategy, using 250 period rolling OLS betas, posted a total cumulative return of 69.73% and a Sharpe ratio of 0.44 after accounting for transaction costs. The poorest performing strategy after accounting for transaction costs, with a final arithmetic return of –
%, is the discrete rolling beta strategy.
Monte Carlo Simulations
To investigate the possibility that the results of our simulation were the result of fortuitous random sampling, we conduct a simple Monte Carlo experiment. Following Lander, Orphanides, and Douvogiannis (1997), we implement parametric bootstrapping techniques in order to obtain a distribution of random returns, which in turn could be compared with the ones from our econometric specifications. In our original trading rules design, we allowed the possibility to invest in long-short, long only, and short only positions. Most often, when the portfolio was not invested in a neutral fashion, it would assume a long only position. For example, in the Kalman strategy, out of the 155 weeks that the portfolio was invested in only one leg of the long-short strategy, in 153 cases, the portfolio was long only. The results are very similar for the other specifications as well. Since we need to get comparable returns from the random portfolios, we specify a number of weeks, which are randomly selected, when we form long only portfolios. The rest of the time we assume a balanced long-short position.
The solid line in Figure 4 graphs the annualized geometric average return from 5,000 random rule replications for each design. The dotted lines represent the 5th and 95th percentile of the