based on this article create an option trading strategy:Finally, we take a closer look at some specific periods between January 2010 and August 2020 in which the S&P500
exhibited different characteristics.
– S1 (2010-2017): The performance of the S&P500 in these 8 years is best described as steadily growing, without
much volatility. Even though losses did not occur often, the options’ prices were rather low, which is not
positive for the strategy per se.
– S2 (2018): This year consisted of big and sudden losses in the S&P500’s value at the start and the end of the
year, and a steady growth in between. In terms of the put-write strategy, many sudden losses, such as the ones
that occurred in this period, are the worst possible scenario.
– S3 (January 2020 - June 2020): Early 2020 was a really special year, with a huge loss for the S&P500 in March
and a fast recovery by June, amid very high volatility in the markets. Option prices were enormously high in
this period.
Since these three periods are so fundamentally different, our interest now lies in finding strategies which worked
well in each of these periods. We aim to find tendencies as to which strategies work well in a wide range of scenarios.
The minimum-premium approaches seem to have very balanced outcomes throughout the different scenarios, while
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the other variants mostly have one scenario that leads to clearly negative results. Examples of such strategies are
shown in Table 9.
Table 6. Strategies which worked relatively well in periods of different characteristics
Short strike Long strike Exit Period S1 Return (p.a.) S2 return (p.a.) S3 return (p.a.)
MP 3% 0.92*k 5.00% 7d 52.81% 29.92% 34.45%
MP 5% 0.92*k 5.00% 7d 66.55% -0,76% 164.68%
(1-0.3*v) *s 0.92*k 5.00% 30d 28.89% 11.89% -12.02%
1.02*s 0.9k 5.00% 14d 114.56% -9.81% 4488.55%
0.94*s 0.9*k 10.00% 30d 36.74% 12.09% -14.56%
Especially interesting is the first strategy, not only since it is the best strategy overall in terms of Sharpe ratio, but
also since it worked well in all of the three different periods. Because of this remarkable performance we provide
some additional insights into this specific strategy and its performance in Figure 13. For better visibility we also
added the performance of that strategy on a logarithmic scale in Figure 14. Between 2010 and August 2020 this
strategy had 324 periods with positive results and 109 periods with negative results. For more in-depth details we
refer to our analysis software on app.lsqf.org.
The second notable result is the S3 return of the “1.02·s” strategy in Table 9. At first glance the 4488.55% return
(p.a.) might seem like an error, however, the very high volatility in this specific time span led to this enormously high
profit (486.80% from January to June). Calculating the per-annum return thus gives us 4488.55%.
Figure 13. Profit of the 3% MP strategy with 0.92 · K1, exit at 5% and 7d period from 2010 to August 2020 (lin. scale)
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Figure 14. Profit of the 3% MP strategy with 0.92 · K1, exit at 5% and 7d period from 2010 to August 2020 (log scale)
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Table 7. Best strategies between January 2010 and August 2020 in terms of Sharpe ratio
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Table 8. Best strategies between January 2010 and August 2020 in terms of return per anno
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Real-data backtests for the Lambda strategies
As was already pointed out earlier, variants as well as combinations of such Lambda strategies in real trades since
summer 2012 have yielded exceptionally good results. In the following we are going to start a first comprehensive
study of this type of strategies.
Just like we did for the put-write strategy in the previous section, we are now going to describe the detailed settings
and execution of the Lambda strategy, and of the backtesting program on our website. The basic control parameters
to be set by the user are
• the available investment capital I at the beginning of each period
• the duration of each period
• the period to be checked (start and end date)
• the type of hedging with long options. Available variants are
– “Put” – hedging against underlying price drops with a single long put option
– “Call” – hedging against underlying price increases with a single long call option
– “Both – left side” – hedging against strong fluctuations of the underlying in any direction, while the
maximum-loss parameter described below applies only to underlying price drops
– “Both – right side” – the same principle is applied, but the "max loss" only applies to underlying price
increases
– “None” – no long options will be used
– “Dynamic” – the type of long options chosen is decided for each trading period individually according to
a formula described below
• the maximum loss as a percentage of the current investment capital, but applied only to the side specified in
the type of hedging chosen
• the intensity of the strategy, with a parameter to specify how many option combinations are to be traded,
depending on the currently available capital at the beginning of each period, as described in the relevant section
below.
In addition to the basic parameters described above, users can provide additional parameters like bid-ask spreads
or transaction costs to consider real-market frictions.
Basic parameter settings and execution of the strategy
The following steps are repeated in a loop starting at the given start date until the end date is reached.