This section reviews some of the calculations involved to measure the Bankers Dozen performance. Daily log returns are calculated for 20 different stocks. The same 20 stocks are included for all years in the historical results and the same 20 stocks are used to calculate the recent daily measurements. These stocks are listed below. Then, 250 different portfolios are simulated for different portfolio sizes. Each simulated portfolio draws from the same 20 stocks. Two measurements of portfolio volatility are then calculated for each portfolio; one that assumes correlation benefits, and one that does not. The volatility is measured using the daily log returns over the past calendar month. Then, risk aversion is calculated for both the traditional portfolio and the Bankers Dozen. Finally, the security weights of the Bankers Dozen are calculated so the risk aversion delta versus the traditional portfolio is minimized. This is done in R using Steven G. Johnson’s NLopt nonlinear-optimization package (nloptr). Each security weighting is constrained by upper and lower bounds of 100 and -100 per cent, and the total portfolio weights are constrained to sum 100 per cent. The security weights are held constant over the next calendar month, and then performance versus the traditional portfolio is compared. This result is averaged for 250 simulated portfolios for each portfolio size to depict the risk function. Regarding the daily measurements, log returns are calculated using 30 intervals over a preceding day and the performance is measured over the following day.
AAPL, BA, CAT, CVX, DD, GE, HD, IBM, JNJ, JPM, KO, MCD, MMM, MRK, MSFT, PFE, PG, UTX, WMT, XOM