Are there opportunities when it may be advantageous to add capital to a trading/investment account based on the recent performance of the account? For example, after a string of losses there may be higher probability that a recovery in the account’s performance may take place, providing an opportunity to add additional capital for short period of time in order to take advantage of a recovery in the performance.
Since I trade based on systematic rules that I am able to code and test against historical data to see how they would have performed, I decided to see if coding rules based on my account’s performance could yield extra returns on cash that may otherwise be sitting idle. Below is a chart of the Net Asset Value of my trading account which I used in my test to decide whether or not adding capital to the account after a string of losses may generate additional returns on idle cash. The account was opened during 4th quarter of 2003, and my initial testing and optimization of the trading rules were run on data from 10/1/2003 through 1/1/2007. Out of sample testing was run for the period of 1/1/2007 – 4/15/2011.
The trading rules were pretty simple. Add additional capital to the account when the account’s value drops 1.5 standard deviations below its average value of the last X days (ie. the value of the account drops below the Lower Bollinger Band). Withdrawal the additional capital Y days after the capital was added. Both X and Y were optimized over the initial test period. A 3D plot of the optimization is shown below.
On the chart’s axis, StopTime is the amount of time to keep the additional capital in the account. bBandPeriod is the lookback period for the calculation of the account’s average/std. deviation. CAR/MDD is the Compound Annual Return divided by the Maximum Drawdown, which is basically a measure of the return relative to the risk taken. Based on the chart, there is a pretty solid range of optimal values where the time is between 28-35 days. I decided to use a value of 30 days for the time to hold the additional capital in the account, and 5 days for the calculation of the average price and its standard deviation.
The in-sample testing period from 10/1/2003-1/1/2007 produced the following results starting with $10,000 of initial capital.
Initial Capital: $10,000
Ending Capital: $37,881
Net Profit: 278.81%
Annual Return: 50.72%
# of Trades: 19
Average Profit per trade: $1,467.44
Average Profit per trade: +7.98%
# of winning Trades: 15 (78.95%)
Max drawdown: -21.93%
Sharpe ratio: 1.73
The optimized results over the in-sample test period look promising. The next step is to test over the out-of-sample test period, over which the results were not optimized, from 1/1/2007 to 4/15/2011. The results over this period are below:
Initial Capital: $10,000
Ending Capital: $81,521
Net Profit: 715.22%
Annual Return: 63.23%
# of Trades: 27
Average Profit per trade: $2,646
Average Profit per trade: +11.65%
# of winning Trades: 16(59.26%)
Max drawdown: -44.44%
Sharpe ratio: 1.09
The results here look good as well, although the Maximum drawdown of -44% could be rather hard to stomach. The increased volatility in the out-of-sample vs. the in-sample testing periods is due to the increased volatility in the trading account itself. The volatility in the account’s returns increased for a number of reasons towards the end of the 2007, including increased market volatility in general during and after the financial meltdown. I also brought a commodity trading system online at the end of 2007 which has increased the account’s volatility due the commodities that the strategy trades, as well as the length of time it holds those commodities for.
This test shows that idle cash could be used to help generate extra returns on an account if added (and removed) at an appropriate time. The next step in exploring this idea further would be to see if removing capital after the account has had a good run of winning days would help to protect profits from a potential string of losing days.