In this blog I analyze the different aspects of Risk and Money Management when combining strategies into a single portfolio.
Single strategy: Risk in terms of Units (Turtles risk)
One possible method of risk management is the Turtles system, i.e. volatility adjusted position sizing.
Definitions:
- TR: True Range = Max(H-L, H-C[t-1], C[t-1]-L). That is, the maximum price swing from close to close including intraday prices.
- N: 20-day exponential moving average of the True Range. More commonly known as ATR (Average True Range). N is the average maximum intraday price swing from close to close.
- QInUnit: quantity that reflects a risk of 1% of total capital from close to close (including intraday movements). That is, if I buy QInUnit at the close and hold the position until the next close, I expect the P&L to swing on average a maximum 1% of total capital intra-daily. IMPORTANT: since volatility from close to close including intraday prices is higher than the volatility from close to close excluding intraday prices, the returns resulting from daily mark-to-market will in general be smaller than 1%!
Strategy I: TY – Dual MA
For illustration purposes we’ll simulate the following single strategy:
- 2 Moving averages (MA100 and MA350)
- Signal = Sign( MA100 – MA350)
- Start with Capital=10MM on 1999-06-01, trade for 10 years until 2009-03-30.
- Rebalance positions daily in order to stay invested (QInUnit_1 * Signal) all the time
- Daily events:
- Strategy Definition (in JScript):
function event_OpenBook() {
context.AddCapital(10000000,"Initial Capital");
}
function event_OpenDay() {
context.AddMark( "TY", vars.Close );
var targetQ = SMath.Sign( vars.MAShort - vars.MALong ) * vars.QInUnit_1;
context.AddTrade(null,"TY", targetQ-book.accQ("TY"), vars.Close, "Rebalance");
}
function event_CloseBook() {
context.Liquidate("End of Trading");
}
- The cumulative position generated by this strategy is:
NOTES:
- This is almost a step function, except that we rebalance the longs and shorts according to the prevailing volatility, so maintain the 1% risk from close to close, including intraday movements.
- The daily mark-to-market produces the following Abs(returns) in basis points:
NOTES:
- The Mean of the daily Abs(returns) is 38bps, smaller than 1% due to the higher intraday volatility.
- Performance:
Strategy II: US – Dual MA
This is the same strategy described above applied to US.
- Cumulative position:
NOTE:
- Trades less contracts than TY because US is more volatile, and we are keeping intraday risk at 1%.
- Abs(Returns):
NOTES:
- The Mean = 43.1 bps, less than 1% because of intraday volatility.
- Also 43.1 bps ~ 38.3
- Performance:
Strategy III: SP – Dual MA
This is the same strategy described above applied to S&P futures (SP).
- Cumulative position:
- Abs(Returns):
NOTES:
- The Mean = 40.9 bps, less than 1% because of intraday volatility.
- Performance:
Summary: Individual Strategies
NOTES:
- TY and SP performed better
- The cumulative returns are 54.4% and 57.7% for TY and SP respectively.
- Maximum Draw Down Length “Max(DDLen)” is quite long: 29 months and 20 months for TY and SP respectively.
Correlations
The correlation of monthly returns are:
US is not only a bad strategy (Sharpe=0.15), but also it’s quite correlated to TY (0.8), so it doesn’t add much.
However, SP is very uncorrelated to TY (0.07), thus I expect the Shape of the combined [TY, SP] portfolio to be better than the individual strategies.
Math: Portfolio return and standard deviation
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