TRADING THE ODDS

Miscellaneous

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Due to their conceptual scope – if not explicitely stated otherwise -, all models/setups/strategies, statistics, key performance indicators, percentage-wise magnitudes of changes (on the open, intraday high, intraday low, close, close vs. open, …), returns, ratios (e.g. Sharpe Ratio) and others …

• refer to regular day sessions only (including shortened sessions like the one on December 24), starting at 9:30 AM EST and ending 4:00 PM EST (but 4:15 PM EST if the ES E-mini S&P 500 is utilized). Exchange holidays and/or GLOBEX sessions (e.g. shortened GLOBEX sessions on exchange holidays or GLOBEX on Sunday evening) are completely ignored,
• do not account for slippage, fees and transaction costs,
• do not account for return on cash,
• do not use position sizing (e.g. Kelly, optimal f) – they’re always ‘all in‘ -,
• do not use leverage (e.g. leveraged ETFs) – but a marginable account is mandatory -,
• do not utilize any kind of abnormal market filter (e.g. during market phases with extremely elevated volatility),
• do not use intraday buy/sell stops (end-of-day prices only), and
• models/setups/strategies are not ‘adaptive‘ (do not adjust to the ongoing changes in market conditions like bull and bear markets).

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How to Read the Stats

Example

Investment Strategy :
The basic strategy (like buy and hold, market timing, pairs trading, …).

Time frame:
Statistics cover all occurrences between start date and end date.

Investment Period:

Performance stats are based on the underlying’s performance over the course of the then following x sessions (regularly 1 session, means the underlying’ performance from close to close after a setup had been triggered).

Benchmark :
The utilized benchmark index (buy and hold), regularly the SPY (S&P 500 ETF).

PERFORMANCE METRICS
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Compound Return:
The total rate of return assumed one would’ve always invested the then current net asset value (cumulative effect, assumed that all gains are reinvested).

Commissions / Fees:
Assumes a fixed fee of USD 0.005 per share (including commissions, exchange and regulatory fees).

CAGR:
Compound annual growth rate: year-over-year growth rate (cumulative effect, assumed that all gains are reinvested).

Geom. Growth p. Trade:
Geometric growth rate per trade: trade-by-trade growth rate (cumulative effect, assumed that all gains are reinvested).

Profit Factor:
The sum of all percentage-wise profits (positive changes) divided by the sum of all percentage-wise losses (negative changes). The equivalent of the amount of dollar won for every dollar lost. Obviously, the larger the number is, the better.

w/ Long Trades:
Profit Factor concerning long trades only.

w/ Short Trades:
Profit Factor concerning short trades only.

R-squared:
Linear regression diagnostic (or the coefficient of determination): R-squared provides an indication of the level to which a series (i.e. an equity curve) is predicted by another (e.g. a straight line), or in other words: R-squared is an indication of the goodness of fit of two (real or hypothetical) equity curves, and computing a linear regression diagnostic between the strategy’s equity curve and a straight line or a geometric growth curve provides an indication of the smoothness of the strategy’s returns (are there heavy ups and downs – beside the maximum drawdown -, is the equity curve zigging and zagging or does it look more like a straight line).

Maximum Drawdown:
The percentage loss that incurred from the peak net asset value to the lowest value (states the largest percentage “Peak to Valley” decline experienced by the strategy during the time frame defined).

Maximum Sessions in Drawdown:
The maximum number of sessions being in a drawdown until the net asset value achieved a new peak (may not necessarily coincidence with start and end date of the maximum drawdown).

Maximum Consecutive Losses:
The equivalent of the maximum number of consecutive sessions with a loss (negative outcome).

Maximum Consecutive Gains:
The equivalent of the maximum number of consecutive sessions with a gain (positive outcome).

Tracking Error:
The tracking error ratio is a measure for the divergence between the return of a portfolio (setup/strategy) and the return of a benchmark index, reported as a “standard deviation percentage” difference.
(see http://en.wikipedia.org/wiki/Tracking_error )

Information Ratio:
The information ratio is equivalen to the risk-adjusted return of a portfolio, defined as the difference between the return of a security (setup/strategy) and the return of a benchmark index (Alpha) divided by the tracking error.
(see http://en.wikipedia.org/wiki/Information_ratio )

Sharpe Ratio (annual.):
(see http://en.wikipedia.org/wiki/Sharpe_ratio )

Sortino Ratio (annual.):
( see http://en.wikipedia.org/wiki/Sharpe_ratio )

Calmar Ratio:
Compounded annual return divided by the maximum drawdown. Provides an indication of returns on a downside risk-adjusted basis.

PERIODIC RETURNS
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Winning Trades (in %):
The equivalent of the percentage-wise ratio of trades with a positive return divided by the total number of trades.

Number of Winning Trades:
The equivalent of the number of trades with a positive return.

Number of Losing Trades:
The equivalent of the number of trades with a negative return.

Unchanged :
The equivalent of the regularly very low number of trades where the return equals zero.

Neutral (no position):
The equivalent of the number of sessions with no position at all (no setup triggered).

Month Positive :
The percentage number of month with positive returns.

Avg. Monthly Return:
The percentage number of average monthly returns.

w/ 1 Std. Dev.:
One standard deviation of average monthly returns.

w/ Maximum Drawdown:
The percentage loss that incurred from the peak net asset value (on close of the last session of a month) to the lowest value (on close of the last session of a month). States the largest percentage “Peak to Valley” decline – taking into account month-end values only – experienced by the strategy during the time frame defined.

Month Index Outperf.:
The percentage number of month where the strategy out-performed the benchmark index.

Distr. of Returns:
The equivalent of the percentage rank of the strategy’s median return in comparison to the – sorted in descending order – median benchmark return. Example: A percentage rank of 75% means that 50% (median indicates that one half of the group is higher and one half lower) of the strategy’s returns fall in the top quartile (top 25%) of the benchmark’s returns. Obviously, the larger the number is, the better.

Top 10% Winner:
The equivalent of the percentage of occurrences (strategy’s returns) which fall in the top 10% of the maximum positive benchmark’s returns. Provides an indication of the strategy’s efficency, means not only doing the right thing (the strategy’s effectiviness like a high percentage of winning trades), but it’s ability to do the things ‘right’. Obviously, the larger the number is, the better.

Top 10% Loser:
The equivalent of the percentage of occurrences (strategy’s returns) which fall in the bottom 10% of the worst (negative) benchmark’s returns. Provides an indication of the strategy’s efficency, means not only doing the right thing (the strategy’s effectiviness like a high percentage of winning trades), but it’s ability to do the things ‘right’ (in this event avoiding being on the wrong side of the market). Obviously, the lower the number is, the better.

Median Trade (in %):
The equivalent of the strategy’s median return (comprises all occurrences).

Median Winnig Trade:
The equivalent of the strategy’s median positive return (occurrences with negative and zero returns are left out).

Median Losing Trade:
The equivalent of the strategy’s median negative return (occurrences with negative and zero returns are left out).

Maximum Winnig Trade:
The equivalent of the strategy’s highest positive return (regularly a positive percentage).

Maximum Losing Trade:
The equivalent of the strategy’s lowest negative return (regularly a negative percentage).

Total Number of Sessions :
The equivalent of the total number of sessions with a position during the time frame defined.

Time in Market:
The equivalent of the percentage time one would’ve been invested in the market (total number of sessions, divided by the total number of trading days within the time frame defined).

t-score:
Student’s t-test for the statistical significance of the difference between two sample means in order to test whether there are differences between two groups on the same variable, means does the strategy perform better or worse when a specific setup had been triggered on close of the previous trading day in comparison to the benchmark’s performance over the course of x sessions. Estimates the probability that the strategy’s returns in comparison to benchmark returns occurred by chance only, or there is a statistically significant probability that the strategy show a statistically significant deviation from benchmark returns. With p = 0.05 (the calculated t-score falls into the extreme 5% of the distribution) and a sample size (the degrees of freedom) greater than 30 (adding up the number of observations for each group, and then subtracting the number two, means number of observations of the strategy and the benchmark minus 2), the calculated t-score must equal or exceed +/- 1.645 to indicate statistical significance (’+’ if the strategy indicates statistically significant positive returns, and ‘-’ for statistically significant negative returns).

t-score (vs. chance):
Estimates the probability that the strategy’s returns occurred by chance only. This number is different from the t-score (vs. market) – and regularly higher – due to the fact that the market shows a long-term positive performance (buy-and-hold approach), and even in the event the respective setup would show a long-term positive performance as well, but would under-perform a buy-and-hold approach, it would be a positive number while the t-score (vs. market) would show a negative number (due to it’s under-performance in comparison to the benchmark).

t-score (vs. market):
Estimates the probability that the strategy’s returns in comparison to the benchmark’s returns occurred by chance only, or there is a statistically significant probability that the strategy show a statistically significant deviation from benchmark returns (means a statistically significant out- or under-performance).