ED - Back Testing Results

Below are given back testing results of the ED strategy, generated by the software. These results should be considered as extrapolation into the past of the ED quantitative US equity trading strategy, which was live trading from July 2009 to July 2011. Returns are net of commissions and bid/ask spreads, but performance fees (20% of new net profit above high water mark) were not deducted from back testing returns. To see actual trading results, please go to the ED - Real Trading page.

I. HYPOTHETICAL RATES OF RETURN (ROR) FROM STRATEGY BACK TESTING

Below are given back testing rates of return of the ED daily trading strategy (read the hypothetical disclaimer first). Commissions, spreads and slippage of 0.06% of the trade size were taken into account, but performance fee was not. It was assumed that all the 100 stocks could be traded at all times. This is a reasonable assumption since the strategy only opens long positions (60-70 positions out of 100 stocks) and holds a single short position in the S&P 500 SPDR ETF (SPY) only. Most stocks in the trading portfolio have at least 20 years of trading history and market capitalization of more than $10 billion.

There is no survivorship bias in the results. The sharp drawdown in July 2008 was due to the collapse of Fannie Mae (FNM) and Freddie Mac (FRE). These stocks were intentionally held  in the backtesting portfolio to stress-test the strategy against individual company bankruptcy. The strategy is extremely robust, i.e. it is insensitive to stock selection. It has no parameters to optimize except the long/short ratio (1.0), maximum single stock exposure (3%) and the strategy leverage (long leverage = short leverage =1.0), which were selected according to the preferred risk tolerance level.

  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YTD VAMI
1987               2.49% 2.50% (1.23%) 5.53% 0.75% 10.32% 1,103.2
1988 1.48% 3.68% 6.51% 4.10% 1.22% 1.99% 0.84% 3.68% 1.40% 1.54% (1.34%) 2.47% 31.08% 1,446.1
1989 0.49% 5.01% (0.81%) 2.11% 2.80% 3.12% 0.27% 3.23% 2.10% 5.07% (1.17%) (1.03%) 23.04% 1,779.3
1990 5.95% 2.32% 1.95% 1.42% 0.77% 2.76% (1.39%) 5.94% (0.03%) 4.27% 6.73% 4.46% 40.90% 2,507.0
1991 4.27% 3.93% 4.84% 6.15% 2.10% 3.20% 1.71% 3.18% 1.86% 4.47% 1.80% (4.81%) 37.50% 3,447.1
1992 8.99% 1.49% 1.57% 2.45% 3.84% 0.13% 3.13% 1.04% 2.14% 2.45% 2.62% 2.53% 37.28% 4,732.3
1993 (0.38%) 0.25% 3.90% 4.38% 2.98% 1.17% 2.25% 2.98% 2.00% 1.64% 3.35% 0.45% 27.90% 6,052.6
1994 0.76% 3.16% 4.24% 1.52% 4.65% 2.14% (0.90%) 1.38% 2.25% 2.82% 5.49% 1.45% 32.92% 8,045.0
1995 (0.83%) 0.70% 2.10% 2.79% 3.15% 4.33% 2.20% 2.79% 0.84% (1.09%) (0.09%) 1.11% 19.38% 9,604.2
1996 0.98% 5.34% 4.37% 0.46% 3.28% 0.41% 1.13% 3.96% 1.59% (0.26%) (0.60%) 3.89% 27.23% 12,219.2
1997 2.10% 2.49% 6.04% 0.24% 3.44% 2.88% 0.42% 4.73% 3.01% 4.34% 2.45% 0.38% 37.60% 16,813.8
1998 5.66% 1.78% 2.20% 3.83% 1.56% (0.33%) 1.63% 1.99% 2.95% 3.12% 4.83% (0.22%) 32.94% 22,351.9
1999 (0.77%) 6.90% 1.49% 7.63% 4.13% 3.29% 3.95% 3.45% 0.99% (3.01%) 3.27% (5.43%) 28.22% 28,660.5
2000 7.40% (1.35%) 7.64% 10.56% 9.48% (1.53%) 1.59% (0.17%) 6.10% 5.48% 7.61% 6.51% 76.86% 50,688.1
2001 1.86% 5.23% 6.21% 5.01% 3.85% (0.03%) 3.84% 2.19% (3.93%) 5.36% 0.81% 1.09% 35.84% 68,855.6
2002 4.06% 2.40% 0.63% 3.08% 1.46% 0.02% 4.84% 0.92% (0.60%) 0.23% 2.23% 2.55% 23.94% 85,337.4
2003 1.10% 0.83% (0.27%) 2.55% 2.39% (0.06%) (1.29%) 0.72% 0.16% 0.77% (0.02%) 0.92% 8.00% 92,166.7
2004 (0.67%) 0.90% 0.80% 0.40% (0.26%) 0.75% 1.21% 0.18% 1.40% 1.74% (0.65%) 1.59% 7.61% 99,183.1
2005 0.36% (0.46%) 2.01% 0.05% 0.28% 0.12% 0.83% (0.08%) (0.73%) 0.12% 0.31% 0.83% 3.67% 102,823.5
2006 0.28% 0.64% 2.18% (0.38%) 1.72% (0.01%) 0.07% 0.70% (1.14%) 1.45% 0.41% (0.53%) 5.48% 108,460.5
2007 (0.50%) 0.79% (0.60%) 0.48% 0.22% 0.40% (0.16%) 1.68% 0.34% (0.14%) 1.73% (0.66%) 3.59% 112,355.1
2008 (1.00%) 0.66% (0.47%) 2.58% (0.40%) (5.10%) 4.93% (0.25%) 8.46% 0.84% 5.66% 0.26% 16.62% 131,029.4
2009 (6.21%) 1.11% 13.01% 2.39% 4.14% 3.58%   Start of live trading - see the Real Performance page 18.36% 155,091.1

Monthly rates of return (ROR) have been calculated by dividing the monthly hypothetical net performance by the previous month account equity. The VAMI (Value Added Monthly Index) charts below shows the hypothetical growth of $1,000, by compounding monthly.

The above tables and charts document ED's historical hypothetical performance based on strategy back testing. Commissions and bid/ask spread were factored into calculations (0.06% of trade size). Price slippage can also affect performance, but slippage (as a random variable, and as proven in real trading) cancel each other in long term. Smaller accounts would have relatively larger commission costs, which negatively impact the strategy performance.

II. PERFORMANCE ANALYTICS

(net of commissions/spreads, but before performance fees)

Strategy Return Statistics (Before Performance Fees)

Testing period (August/1987-June/2009)

263 months/ 22 years

Net profit on fixed capital with / without monthly profit reinvesting

15,409.1% / 517.5%

Sum of positive/ negative monthly rates of return - ROR (gross gain / gross loss)

572.9% / (55.4%)

Compound average annualized ROR

25.88%

VAMI - Growth of $1,000, compounded monthly (fees not deducted)

$155,091

Monthly Profit Factor (Profit to Loss Ratio); (sum of positive RORs) to (sum of negative RORs)

10.34

# Profitable months / average positive ROR

212 / 2.70%

# Losing months / average negative ROR

51 / (1.09%)

Kurtosis of monthly RORs

2.05

Skewness of monthly RORs

0.57

% Profitable months

80.61%

Ratio avg. positive / avg. negative monthly ROR (Gain to Loss Ratio)

2.49

Max. # of consecutive profitable / losing months

17 / 2

Maximum / minimum monthly ROR

13.01% / (6.21%)

Maximum / minimum daily ROR

5.99% / (4.83%)

Maximum / minimum 5-day rolling ROR

17.81% / (9.52%)

Risk Measures

Annualized standard deviation of monthly RORs

8.80%

Annualized downside deviation (MAR = RF return of 3% per annum)

3.00%

Sharpe Ratio, annualized (RF rate of return 3.0%)

2.60

Sortino Ratio, annualized (below RF ret. 3%)

7.62

Calmar Ratio (ratio compound average annual ROR to worst intra month drawdown)

1.88

Omega Ratios

Download

Tracking error, relative to the S&P 500 Index, annualized

18.56%

Historic 5-day Value at Risk (VaR); (for 95% and 99% confidence levels)

 (1.41%) / (2.92%)

Alpha relative to the S&P 500 Index, annualized

26.76%

Beta and correlation coefficient, relative to the S&P 500 Index

(0.055) / (0.098)

Jensen's Alpha relative to the S&P 500 Index, annualized

22.99%

Active premium, relative to the S&P 500 Index, annualized

20.93%

Information Ratio, relative to the S&P 500 Index

0.945

Worst month-to-month drawdown depth / duration

(6.21%) / Jan-Mar 2009

Worst peak-to-valley (intra month) drawdown ; (see graph below)

(13.77%) / July 15, 2008

Longest recovery period; see also the Drawdown Histogram chart below

7 months

 

Basic Strategy Characteristics
Strategy name

EQ-100DL

Type of trading Equity statistical arbitrage
Portfolio composition

100% US stocks

Long to short ratio 1.0
Long/short leverage (long/short positions value relative to Net Asset Value - NAV) 1.0 / 1.0
How generated

Back testing - hypothetical

Maximum single stock exposure 3% of portfolio NAV

Turnover / Cost Parameters

Average positions value, relative to NAV

 100% long  100% short

Average daily portfolio turnover (daily traded positions value as a percentage of NAV)

13%

Annual turnover ratio

33.8

Average holding period

7.7 days

Average annual transaction costs

1.7% of NAV per annum

Commissions + bid/ask spread cost, as a fraction of the transaction value

0.06%

Minimum recommended portfolio size

$2,500,000

 

III. DRAWDOWN ANALYSIS

The Drawdown Histogram above shows:

1.) how many days the system was in drawdown of given magnitude (blue colored bars). Backtesting period is 5515 days;

2.) what time (as percentage of the total backtesting time) the system spent below a given drawdown level (the red colored line). For example, the system spent only 5% of time (276 out of 5515 days) in drawdown worse than 3%, and only 1% (55 out of 5515 days) in drawdown worse than 6.7%. These figures also give some idea on the recovery time.

 

The most important facts to remember from the Drawdown Histogram are that:

1.) large drawdowns are rare (the larger the drawdown - the less the probability, although it still exists - see the 13.8% drawdown far left in the histogram above);

2.) the system quickly recovers from extremely large drawdowns. There is no answer, however, how deep the drawdown can go; statistics only show it should not last for too long. This chart also shows how important it is to be patient and not to quit trading during drawdown (which is the worst possible moment to do so).

 

Hypothetical Performance Disclaimer:

HYPOTHETICAL AND SIMULATED PERFORMANCE RESULTS HAVE CERTAIN INHERENT LIMITATIONS. UNLIKE AN ACTUAL PERFORMANCE RECORD, HYPOTHETICAL RESULTS DO NOT REPRESENT ACTUAL TRADING. ALSO, SINCE THE TRADES HAVE NOT ACTUALLY BEEN EXECUTED, THE RESULTS MAY HAVE UNDER-OR-OVERCOMPENSATED FOR THE IMPACT, IF ANY, OF CERTAIN MARKET FACTORS, SUCH AS LACK OF LIQUIDITY. SIMULATED TRADING PLATFORMS IN GENERAL ARE ALSO SUBJECT TO THE FACT THAT THEY ARE DESIGNED WITH THE BENEFIT OF HINDSIGHT. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN.

Risk Disclaimer

PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS. THE PERFORMANCE QUOTED REPRESENTS PAST HYPOTHETICAL PERFORMANCE AND CURRENT PERFORMANCE MAY BE LOWER OR HIGHER. THIS IS NOT A SOLICITATION TO INVEST AND YOU SHOULD CAREFULLY CONSIDER YOUR FINANCIAL SITUATION PRIOR TO MAKING ANY INVESTMENT OR ENTERING INTO ANY TRANSACTION.

free counter statistics