FX Quant 11 / S&P 500 Options Combined

Below is given optimal portfolio construction based on FX Quant 11 / Equity Quant 100 back testing data. To see actual performance of combined strategy trading, please go directly to section IV below.

Risk-adjusted returns (Sharpe Ratio) can be improved by strategy diversification, i.e. combining the EQ-100 - Equity Trading Program with FX Quant 11 - Currency Trading Program.

According to the Modern Portfolio Theory (MPT), by combining trading strategies in a multi-strategy portfolio, better returns can be achieved for the given risk (or, the same return can be achieved at lower risk). Open this Excel worksheet (6 MB) and click on the Sharpe Ratio (Monthly) and Sharpe Ratio (Daily) tabs to see optimal portfolio construction based on the Modern Portfolio Theory. Both monthly and daily ROR correlations are used for optimal portfolio construction.

We are currently trading a more complex, 7-strategy portfolio. For more details, please see this FX / VIX Multi Strategy (from the www.fx-quant.com web site).

The portfolio on the efficient frontier with the highest Sharpe Ratio is known as the Tangent (Market) Portfolio (see the dark blue colored square in above diagram), or sometimes the super-efficient portfolio; it is the tangency-portfolio in the above diagram. The optimal - market portfolio would have the following strategy allocation:

When the market portfolio is combined with the risk-free asset, the result is the Capital Market Line (CML). All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier. Just the special case of the market portfolio with zero cash weighting is on the efficient frontier. Additions of cash (risk-free asset) or leverage (cash lending) in combination with the market portfolio are on the Capital Market Line. All of these portfolios represent the highest possible Sharpe Ratio.

The Selected Portfolio (red colored square in diagram above) is over-levaraged by 20%. Despite the increased leverage, the standard deviation of returns is lower than standard deviations of returns of individual strategies (the light blue and orange square in diagram above) and the combined mean return is higher than individual mean returns of individual strategies. The end result id that combined portfolio has a higher Sharpe Ratio (better risk-adjusted return) than individual strategies have.

To learn more on MPT, read this excellent Introduction to Investment Theory by William N. Goetzmann of Yale School of Management.

II. RATES OF RETURN (ROR) AND VAMI OF DIVESRIFIED PORTFOLIO (BACK TESTING RESULTS)

Below are given the hypothetical composite equity (VAMI) curves and ROR distributions of the FX Quant 11 (9) and EQ-100DL programs combined. They are solely given as an illustration of trading program combined performance.

To take advantage of diversification and decreased drawdowns, the combined strategy trades 60% Fx Quant 9 and 40% EQ-100DL, but at 20% increased leverage. See the calculations by clicking the FXQ-EQ Monthly VAMI tab in this Excel table.

Optimal Combined Portfolio - Monthly VAMI (60% FX Quant 9, 40% EQ-100DL, 20% overleveraged)

Optimal Combined Portfolio - Daily VAMI (60% FX Quant 9, 40% EQ-100DL, 20% overleveraged)

Optimal Combined Portfolio - Monthly RORs (60% FX Quant 9, 40% EQ-100DL, 20% overleveraged)

Optimal Combined Portfolio - Monthly ROR Distribution (60% FX Quant 9, 40% EQ-100DL, 20% overleveraged)

Optimal Combined Portfolio - Annual ROR (60% FX Quant 9, 40% EQ-100DL, 20% overleveraged)

Strategy Returns (Before Performance Fees)
Testing period	Jan/1999 -Jun/2009
Net profit on fixed capital, with/ without monthly profit reinvesting	1616.33% / 290.53%
Sum of positive/ negative monthly rates of return - ROR (gross gain / gross loss)	305.67% / (15.14%)
Compounded average annual ROR	31.09%
Growth of $1,000, compounded monthly (fees not deducted!)	$17,163.3
# Positive months / average positive ROR	113 / 2.71%
# Negative months / average negative ROR	13 / (1.16%)
Kurtosis & skewness of monthly RORs	0.408 / 0.451
Percentage of positive months	89.68%
Ratio avg. positive / avg. negative monthly ROR	2.32
Max. # of consecutive positive/negative months	44 / 2
Profit-to-Loss Ratio; ratio gross profit to gross loss (Monthly Profit Factor)	20.19

Risk measures
Annualized standard deviation of monthly RORs	7.57%
Annualized downside deviation (MAR = RF ROR = 3% per annum)	1.91%
Sharpe Ratio, annualized (RF rate of return 3.0% per annum)	3.64
Sortino Ratio, annualized (below RF rate 3%)	14.69
Calmar Ratio, for life of trading, using EOM drawdown	11.69
Strategy Alpha relative to the S&P 500 Index, annualized	73.14%
Jensen's Alpha relative to the S&P 500 Index, annualized	28.09%
Active premium relative to the S&P 500 Index, annualized	27.25%
Worst drawdown depth / duration (month end to month end)	(3.20%) / 1 month
Worst peak-to-valley (intra-month) drawdown	(11.24%)
Longest recovery period	<3 months
Strategy Beta and correlation coefficient, rel. to the S&P 500 Index	0.00 / (0.172)

Conclusion. Although individual/component trading programs are excellent, combined trading further improves the risk-adjusted return and maximizes Sharpe Ratio.

THIS COMPOSITE PERFORMANCE REPORT IS HYPOTHETICAL AND THESE TRADING ADVISORS HAVE NOT TRADED TOGETHER IN THE MANNER SHOWN IN THE COMPOSITE. HYPOTHETICAL PERFORMANCE RESULTS HAVE MANY INHERENT LIMITATIONS, SOME OF WHICH ARE DESCRIBED BELOW. NO REPRESENTATION IS BEING MADE THAT ANY MULTI-ADVISOR MANAGED ACCOUNT OR POOL WILL OR IS LIKELY TO ACHIEVE A COMPOSITE PERFORMANCE RECORD SIMILAR TO THAT SHOWN. IN FACT, THERE ARE FREQUENTLY SHARP DIFFERENCES BETWEEN A HYPOTHETICAL COMPOSITE PERFORMANCE RECORD AND THE ACTUAL RECORD SUBSEQUENTLY ACHIEVED.

ONE OF THE LIMITATIONS OF A HYPOTHETICAL COMPOSITE PERFORMANCE RECORD IS THAT DECISIONS RELATING TO THE SELECTION OF TRADING ADVISORS AND THE ALLOCATION OF ASSETS AMONG THOSE TRADING ADVISORS WERE MADE WITH THE BENEFIT OF HINDSIGHT BASED UPON THE HISTORICAL RATES OF RETURN OF THE SELECTED TRADING ADVISORS. THEREFORE, COMPOSITE PERFORMANCE RECORDS INVARIABLY SHOW POSITIVE RATES OF RETURN. ANOTHER INHERENT LIMITATION ON THESE RESULTS IS THAT THE ALLOCATION DECISIONS REFLECTED IN THE PERFORMANCE RECORDS WERE NOT MADE UNDER ACTUAL MARKET CONDITIONS AND, THEREFORE, CANNOT COMPLETELY ACCOUNT FOR THE IMPACT OF FINANCIAL RISK IN ACTUAL TRADING. FURTHERMORE, THE COMPOSITE PERFORMANCE RECORD MAY BE DISTORTED BECAUSE THE ALLOCATION OF ASSETS CHANGES FROM TIME TO TIME AND THESE ADJUSTMENTS ARE NOT REFLECTED IN THE COMPOSITE.