Nestor Sulikowski

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:

1. 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.
2. 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.
3. 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:

1. 2 Moving averages (MA100 and MA350)
2. Signal = Sign( MA100 – MA350)
3. Start with Capital=10MM on 1999-06-01, trade for 10 years until 2009-03-30.
4. 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:

1. 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:

1. 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:

1. Trades less contracts than TY because US is more volatile, and we are keeping intraday risk at 1%.

• Abs(Returns):

NOTES:

1. The Mean = 43.1 bps, less than 1% because of intraday volatility.
2. 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:

1. The Mean = 40.9 bps, less than 1% because of intraday volatility.

• Performance:

Summary: Individual Strategies

NOTES:

1. TY and SP performed better
2. The cumulative returns are 54.4% and 57.7% for TY and SP respectively.
3. 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