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

https://gtr1.net/2013/?~Dartboard2023b20:h253n5r5f...
https://gtr1.net/2013/?~Dartboard2023c80:h253n5r5f...
https://gtr1.net/2013/?~Dartboard2023d320:h253n5r5...
https://gtr1.net/2013/?~SP1500EqualWeight:h63f0.4:...

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