INTRODUCTION
The probability distribution of the SP500 daily return was calculated and posted in Part I. The calculations showed that the Efficient Market Hypothesis is a good approximation, i.e. most of the time the daily return of the SPX index is a variable with close to zero expectation. In Part II, it was shown that both for longs and shorts a positive expectation can be achieved using Stop Loss optimized with respect to Standard Deviation of the probability distribution of the daily return.
On an algorithmic level, this approach was formulated as follows:
1. Every trading day: if (no position) {open SPX position at the close of the trading session};
2. Next day: if (return < StopLoss) {close the position}.
When the only parameter in this algorithm (StopLoss) is optimized, the algorithm is expected to outperform the total return of SP500 (see Part II). Here we modified the algorithm by introducing the TakeProfit variable.
ALGORITHM
1. Every trading day: if (no position) {open SPX position at the close of the trading session};
2. Next day: if ( return < StopLoss ) { close the position}
else{
if ( return > TakeProfit ) {close the position}
};
Based on the results in Part II, the StopLoss variable was set as follows:
StopLoss = 1/4*Standard Deviation,
The TakeProfit variable was altered using the following formula:
TakeProfit = x*Standard Deviation.
The calculated return averaged over the years 2007 to 2017 is shown below.
The result means that taking profit before 1 Standard Deviation is expected to decrease the long-term return of the algorithm almost 4 times for shorts and 2 times for longs while taking profit before 0.5 SD makes trading negative. Note that taking profit before 3 SD significantly decreases the performance.
BLACK SWANS
The normal distribution with the calculated historical SD of SPX, 1.25%, predicts 24 days (since 1950) with a daily return of 3*SD or more. There were 102 days when SP500 printed 3.75% or more. For a 10x leverage day trader, a 3SD move against the position is a Black Swan by any means. This side of the distribution is taken care of by the Stop Loss part of the algorithm. At the same time, the "let your winners run" part accumulates Black Swan - x*SD price movement in your favor - providing that the Take Profit parameter is large enough.
CONCLUSIONS
In algorithmic day trading, the take profit parameter has to be x*SD, x >=3.
Taking profit early results in day trading with a negative expectation.
1. Every trading day: if (no position) {open SPX position at the close of the trading session};
2. Next day: if (return < StopLoss) {close the position}.
When the only parameter in this algorithm (StopLoss) is optimized, the algorithm is expected to outperform the total return of SP500 (see Part II). Here we modified the algorithm by introducing the TakeProfit variable.
ALGORITHM
1. Every trading day: if (no position) {open SPX position at the close of the trading session};
2. Next day: if ( return < StopLoss ) { close the position}
else{
if ( return > TakeProfit ) {close the position}
};
Based on the results in Part II, the StopLoss variable was set as follows:
StopLoss = 1/4*Standard Deviation,
The TakeProfit variable was altered using the following formula:
TakeProfit = x*Standard Deviation.
The calculated return averaged over the years 2007 to 2017 is shown below.
The result means that taking profit before 1 Standard Deviation is expected to decrease the long-term return of the algorithm almost 4 times for shorts and 2 times for longs while taking profit before 0.5 SD makes trading negative. Note that taking profit before 3 SD significantly decreases the performance.
BLACK SWANS
The normal distribution with the calculated historical SD of SPX, 1.25%, predicts 24 days (since 1950) with a daily return of 3*SD or more. There were 102 days when SP500 printed 3.75% or more. For a 10x leverage day trader, a 3SD move against the position is a Black Swan by any means. This side of the distribution is taken care of by the Stop Loss part of the algorithm. At the same time, the "let your winners run" part accumulates Black Swan - x*SD price movement in your favor - providing that the Take Profit parameter is large enough.
CONCLUSIONS
In algorithmic day trading, the take profit parameter has to be x*SD, x >=3.
Taking profit early results in day trading with a negative expectation.
No comments:
Post a Comment