Subject: Scatter of Dartboard Screen Results
A Dartboard screen picks at random from the S&P 1500. The average CAGR of a group of Dartboard screens will be about the same as the S&P 1500 equal weight, but there will be variation depending on the depth, backtest length, and start date. The scatter of Dartboard screen CAGRs should roughly scale with the square root of depth and square root of time. Average CAGR and GSD will be similar for Dartboard screens with depths of 20 or 80, but the scatter will be about double for 20 depth compared to 80 depth.
SDcg is the standard deviation of CAGR of 253 portfolios with different start dates.
define SDpop == SDcg * sqrt(yrs * Depth)
Screen CAGR SAWR GSD Sharpe AT From To yrs Depth SDcg SDpop
Dartboard2023b20 10.0 8.0 23 0.55 0.25 20130308 20230310 10.0 20 2.35 33
Dartboard2023c80 10.3 8.4 21 0.58 0.25 20130308 20230310 10.0 80 1.14 32
Dartboard2023d320 10.3 8.4 21 0.58 0.24 20130308 20230310 10.0 320 0.55 31
Dartboard2023b20 11.7 7.9 24 0.58 0.26 20030310 20230310 20.0 20 1.75 35
Dartboard2023c80 12.0 8.2 23 0.61 0.26 20030310 20230310 20.0 80 0.86 35
Dartboard2023d320 12.0 8.3 22 0.62 0.25 20030310 20230310 20.0 320 0.46 37
Dartboard2023b20 12.2 7.7 21 0.48 0.25 19570301 20230310 66.0 20 1.00 36
Dartboard2023c80 12.4 8.4 20 0.51 0.25 19570301 20230310 66.0 80 0.46 33
Dartboard2023d320 12.4 8.5 19 0.52 0.23 19570301 20230310 66.0 320 0.21 31
SDpop is roughly constant for the different depths and backtest lengths, and so can be used to estimate the depth needed for a given CAGR scatter. For example, to get a SDcg of 1.5 over 10 years, a depth of about 54 is needed.
Depth = ((SDpop / SDcg)^2) / yrs
Depth = ((35 / 1.5)^2) / 10 = 54
Rebalance and holding time of 5 years was used in the previous screens. Rebalancing every 1 year or never doesn't change results much (r1 is 1 year rebalancing, r5 is 5 year, r0 is never):
Screen CAGR SAWR GSD Sharpe AT From To yrs Depth SDcg SDpop
Dartboard2023c80r1 12.6 8.5 20 0.52 0.30 19570301 20230310 66.0 80 0.51 37
Dartboard2023c80r5 12.4 8.4 20 0.51 0.25 19570301 20230310 66.0 80 0.46 33
Dartboard2023c80r0 12.4 8.3 20 0.52 0.23 19570301 20230310 66.0 80 0.48 35
SP1500EqualWeight 12.1 8.4 20 0.49 0.32 19570301 20230310 66.0 1500 0.09 27
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