55 lines
2.1 KiB
Markdown
55 lines
2.1 KiB
Markdown
# Indicators
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# Optimal Strategy
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The optimal strategy works by applying every possible buy/sell action to the
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current positions. A position is cash value, the current amount of shares, and
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previous transactions.
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The algorithm then starts with a single initial position with the initial cash
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amount, no shares, and no transactions. The algorithm first executes all
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possible trades (sell 2000, sell 1000, do nothing, buy 1000, buy 2000). Next, it
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filters the invalid holdings, i.e., the other ones where shares are not equal to
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-1000, 0, or 1000. Finally, the algorithm keeps the highest cash value for each
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amount of shares.
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That is the critical insight that makes the algorithm work. Since the same
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amount of shares has the same future potential for creating cash, the only
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differentiating factor is the current cash value. Accordingly, for each day, the
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algorithm ends up with three new positions. The algorithm could drop the
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position with zero shares because buying and selling 2000 shares leverages
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future price movements optimally.
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After each trading day, the positions have the same value. I did not expect
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that, but it makes sense because the algorithm only keeps the best position from
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the previous day. In other words, we can simplify the algorithm by selecting the
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best position and then compute the two different positions. Since we already
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established that holding zero shares does not make sense, the only two
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possibilities are buying or selling 2000 depending on the current amount of
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shares.
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```
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Date Range: 2008-01-02 00:00:00 to 2009-12-31 00:00:00
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Sharpe Ratio of Optimal Strategy: 13.322769848217233
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Sharpe Ratio of bench: 0.1569184064240322
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Cumulative Return of Optimal Strategy: 5.7861
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Cumulative Return of bench: 0.012299999999999978
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Standard Deviation of Optimal Strategy: 0.004547823197907996
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Standard Deviation of bench: 0.01700436627121376
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Average Daily Return of Optimal Strategy: 0.0038167861508578214
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Average Daily Return of bench: 0.00016808697819094233
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Final Portfolio Value Optimal: 678610.0
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Final Portfolio Value Bench: 101230.0
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```
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