# Surfing the Equity Curve

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.

Net Asset Value of trading account

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.

Optimization

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 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%