Equity Plot Titles
The Customize Titles for Equity Plots option offers the means to select the equity plot titles desired for the plot as well the performance metrics to be included in the titles.
There can be up to three titles containing performance metrics:
The Underlying Buy-Hold title contains the performance information for holding the entity for the duration of the analysis period. No trading occurs.
The Tradescape Signal (EM) title contains the performance information for the EM signal used in the tradescape for the time horizon and lag fraction of the point that was selected. If this is not a user-signal point, the trades shown in the equity plot represent those originating from this EM signal. If the equity plot derives from a point representing a user-defined signal, this will be the EM signal for the time horizon and lag fraction estimated from the user's trading signal. In this case, the tradescape results will be shown as a reference in the plot.
If the point is a user-defined trading signal, the Trading Signal (Signal) title contains the performance information for the user's entry-exit signals signaling. This will be the principal equity plot in the graph.
The Toggle Display of Reference data in the equity graph toolbar will toggle the references on and off. If the equity plot contains the underlying and the tradescape signal, the underlying will be present as a reference. If the equity plot also contains a user-defined signal, the underlying and the tradescape signal will be shown as references.
If you uncheck any title that corresponds with a reference, that particular reference will not be drawn in the plot.
The Annualized Return (ArRtn in titles) is the simple yearly return. If an entity's price increases from 10 to 40 across ten years, there is a +300% increase for 10 years, or +30% annualized return.
The CAGR (Cagr in titles) is the compound annual growth rate as a percent. This is the standard CAGR formula compounded each trading day (the formula adjusts for the actual average count of trading days in a year). This formula uses the value at the starting and ending dates for the computation. The value can be highly sensitive to the specific dates chosen.
The Robust CAGR (Trend) (Trnd in titles) is the CAGR fitted to all data points in the analysis period using a linear regression procedure. Compound growth is assumed, which means the ln of the prices is assumed to be linear. By using this approach, the impact of the specific starting and ending dates is much lessened. One achieves a better picture of the overall trending during the period. This is also expressed as an annual growth rate in percent.
The Trend r² ( in titles) is the coefficient of determination from the regression used to compute the robust trend. An r² of 1 is a perfect fit, a 0 is what one would expect from fitting random noise. The closer the r² is to 1, the better an equity curve is shown to be continuously trending.
The Total Round Trips (RndTrps in titles) is the total count of complete trade cycles (an entry and an exit counts as 1 round trip) for the analysis period.
The Average Trade Length (TradeLen in titles) is the average bar count for all of the trade cycles in the analysis period.
The Win Percentage (Win in titles) is the percent of trades executed for a net increase in equity.
The Percentage Invested (InMkt in titles) is the percent of bars where one was in a position.
The Volatility (Vlty in titles) is the standard SD definition of bar-to-bar volatility annualized to a % using the sqrt(n) Gaussian assumption.
The Sharpe Ratio (Sharpe in titles) is a robust modified Sharpe. The risk-free return rate in the Sharpe is set to 0. The return for the period is set using the robust trend instead of a simple equity difference on the starting and ending dates. The Sharpe ratio, as used in the Tradescape module, is the robust CAGR as a % divided by the annualized SD-based volatility.
The Sortino Ratio (Sortino in titles) is a robust modified Sortino. It is identical to the Sharpe ratio, as used in the Tradescape module, except that the denominator uses only the downside volatility instead of the volatility in both directions.
The Sterling Ratio (Sterling in titles) is also modified to use the robust trend. The denominator is the worst drawdown in the period, as a %.
The Robust Return-Pain (R³) (R³ in titles) uses the robust trend in the numerator and defines the denominator, the pain, as the magnitude * duration of the n-worst drawdowns in the analysis period, where n is 1 for each 2 years of data. A white paper is available that describes R³ and RRt in some detail.
The Robust Return-Retracement (RRt) (RRt in titles) similarly uses the robust trend in the numerator. The pain defined in the denominator is the average retracement from the all-time high across the analysis period. RRt is our preferred reward-pain metric since is uses fundamental properties of the time series and can be optimized by procedures requiring smooth partial derivatives of the function being minimized. For more information, please refer to the white paper that describes our preference for RRt.
The Average Drawdown Info (DrwDn in titles) displays the count of drawdowns and the average depth and duration as used in the R³ pain component.
The Average Retracement Info (Rtrc in titles) displays the average retracement across the analysis period, the pain used in the RRt metric.
The Backtest Engine
The equity curves and their performance metrics are generated using the Trading Sciences backtest engine. To have the curves as representative as possible of the fundamental times series and to standardize the backtest process, the following particulars we have locked into place are important if any effort is made to replicate the equity curve using other platforms:
1. The starting equity is 100K.
2. There is zero trading cost.
3. All monies are invested in subsequent trades up to an integer unit of shares. If the equity curve is growing, subsequent trades will be larger. If the equity curve is diminishing, subsequent trades will be smaller. There is no rounding to lots of a hundred.
4. The entry signal for the EM signaler occurs based on the closing price and any trades are assumed executed at that same close. This would be equivalent of taking the price just before close and using that price to execute a trade-the errors are assumed to balance out across time.
5. There are no stops, no pyramiding, and no partial booking. One is either fully in a position or fully out of market.