*There is some improvement in pricing, but the leverage effect dominates. In down years you do better (less poorly) with in-the-money calls.*

*Here are the results for the last 14 January cycles:*

*Start 1st 1st 2nd*

*Date OTM ITM ITM*

*1/21 71% 83% 88%*

*1/20 262 217 193*

*1/19 425 342 300*

*1/18 -100 - 86 - 76*

*1/17 902 730 598*

*1/16 194 167 155*

*1/15 -100 -100 -100*

*1/14 - 17 21 35*

*1/13 598 432 363*

*1/12 - 22 - 1 16*

*1/11 42 55 61*

*1/10 - 59 - 7 16*

*1/09 38 70 65*

*1/08 - 69 - 58 - 36*

*.*

*Average 154% 133% 120%*

*DB2*

Thanks so much for sharing these results!

The averages you show *seem* to indicate that the 1st OTM Strike Price is the clear winner but this deserves some more thought.

As has been discussed here before, nobody invests their entire principal in such a strategy, but the actual allocation *does* make a difference.

As an example, let’s assume we begin 2008 with a principal of $100 and allocate 30% ($30) of it to the 1st_OTM strategy, leaving 70% ($70) as cash (earning 0%). In the first year, we lose 69% of the $30 and none of the cash, leaving us with $79.30 to start 2009. The 30% allocation resulted in an effective total return of -21.7%.

The next year, we put 30% of this $79.30 into the strategy ($23.79) and keep the rest in cash ($55.51). By January of 2010, we have a total of $88.34. Here’s a general description of the Total at the start of each year (t).

```
Total[t] <- Total[t - 1]*(alloc*(strategy_return[t - 1] + 1) + (1 - alloc))
```

Rebalancing each year to 30% in the strategy and 70% in cash, the effective returns for the table you provided would be:

```
Start OTM1st Total
2008-01 -69% $100.00000
2009-01 38 79.30000
2010-01 -59 88.34020
2011-01 42 72.70398
2012-01 -22 81.86469
2013-01 598 76.46162
2014-01 -17 213.63376
2015-01 -100 202.73844
2016-01 194 141.91691
2017-01 902 224.51255
2018-01 -100 832.04349
2019-01 425 582.43045
2020-01 262 1325.02926
2021-01 71 2366.50226
2022-01 NA 2870.56724
```

The Total CAGR of this strategy (OTM_1st with 30% allocation) is 27.1% ( i.e. (2870.57/100)^(1/14) - 1 ). One of the reasons many people think of things in terms of log-returns (the log-return is: ln(P1/P0) and the arithmetic return is: (P1 - P0)/P0 ) is that we can also arrive at this CAGR by taking the average of the log-returns and then converting it to arithmetic return using: arithmetic return = exp(log-return) - 1 ).

Rebalancing to different allocation fractions will result in different CAGRs. Here’s a table with various allocation fractions (0 to 100%) simulated on the 14 returns given for each of the three strategies tested and posted by DrBob2:

```
alloc OTM1st ITM1st ITM2nd
0% 0.00000% 0.00000% 0.00000%
10 12.45532 11.37782 10.62093
20 20.99829 20.18077 19.29307
30 27.11807 27.10045 26.47019
40 31.28839 32.71759 32.47637
50 33.54719 36.57261 37.29168
60 34.04351 39.33219 40.96422
70 32.16856 40.42181 43.13471
80 27.67465 38.79042 43.10850
90 17.38093 33.38359 39.74313
100 -100.00000 -100.00000 -100.00000
```

Notice that for an allocation of 0%, the return will be 0% (i.e. same as Cash) and for an allocation of 100%, the return will be -100% (i.e. at some point we would have lost everything).

These data simulate what would have happened if we had invested and rebalanced as described and the returns are as reported. If we can assume that the yearly returns will be distributed in the same way for any year in the future, then we can get a better idea of the distribution of possible CAGRs by using taking repeated samples (with replacement) for each case from these 14 years of data (this is bootstraping).

Using this technique (w/ 2,000,000 re-samples for each strategy), the optimal allocation for each strategy is:

OTM1st optimal alloc is: 57.31% with a CAGR of 33.98%

ITM1st optimal alloc is: 69.65% with a CAGR of 40.25%

ITM2nd optimal alloc is: 75.74% with a CAGR of 43.53%

To summarize, it’s not clear that the average of the arithmetic returns gives enough information about which strategy to use. The allocation/rebalancing strategy also needs to be considered.

heink