Equity function, Individual and Portfolio Equity Charts

Introduction

The equity line is probably the best diagnostic tool for trading system developers. In one graph it shows the sum total of the success or failure of the system being tested, and the resulting effect on your equity.

Numbers from the Report telling of a drawdown are nice, but with a graph, one can see how things were going before, during, and after a drawdown.

The line produced by the equity function tracks the amount of equity in your account. So, for example, if you backtest a system over the last year, you should see that, at the beginning of that year, the line starts at the amount of your initial equity, and then rises and falls because, as each trade makes or loses money, the equity in your account will rise and fall. It shows how much money is in your account throughout the backtest period, so you can visually see how your system performed.

So, clearly you don't want to see the line go down - that means you lost money. It is generally accepted that you want to revise your system test parameters in order to get as close as possible to a smooth, straight, rising line. This means that your system has performed consistently over time, and presumably over different market conditions. A line that goes up and down frequently means that your system works well only under certain conditions, and poorly under other conditions.

Individual (single-security) Equity chart

To display a single-security Equity chart, it is enough to click on the drop-down arrow on the "Equity" button and choose "Individual Equity" from the menu in the Automatic Analysis window AFTER running a backtest.

This will plot the equity for the currently active symbol and the recently backtested system. If you want to see the Equity curve for another symbol, just switch to this symbol and the Equity line will be recalculated automatically.

You can also choose a symbol that was not included in the original backtest set and AmiBroker will calculate the correct equity curve as it would look if a real backtest was performed on it.

IMPORTANT: an individual equity chart is a single-security equity representation that does not show portfolio-level effects like skipping some trades due to reaching the maximum open position limit or funds being allocated to other securities. It also does not use some advanced functionality offered only by the portfolio-level backtester. For more information, see this.

Portfolio-level Equity chart

To display a portfolio-level equity chart, it is enough to double click on the "Equity" button in the Automatic Analysis window or click on the drop-down arrow on the "Equity" button and choose "Portfolio Equity" from the menu AFTER running a backtest.

Portfolio-level equity represents the equity of your entire portfolio and reflects all real-world effects like skipping trades due to insufficient funds or reaching the maximum number of open positions. It also reflects all scaling in/out, the HoldMinBars effect, early exit fees and any other feature that you may have been using in your formula. Portfolio-level equity also by default shows the remaining cash in the portfolio. Using the Parameters window (click with right mouse button over equity chart and select "Parameters" from the menu) you can turn on the display of drawdown (underwater equity curve), number of bars since last equity high and linear regression of the equity.

Equity function

The Equity() function is a single-security backtester-in-a-box. It has many interesting applications that will be outlined here. Let's look at the definition of the Equity function:

Using the Equity function, we can build an Equity "indicator" that will work without the need to run the backtester. Just type the following formula in the Formula Editor and press Apply:

buy = ... your buy rule ...
sell = .... your sell rule ...

graph0 = Equity();

Equity() function uses the buy/sell/short/cover rules that are defined BEFORE this function is called. The whole backtesting procedure is done inside the Equity function that generates the equity line.

Notes:

1. The Equity line is dependent on the parameters in the Automatic Analysis settings.
2. Equity traces interest earnings when you are out of the market.
   If you don't want this, just enter 0 into "Annual interest rate" field in the settings.
3. Equity also traces commissions. If commissions are not zero, entry commission is taken using the position size of the entry and exit commission is taken for each point to simulate how much money would you have if you closed position at a given bar.
4. AmiBroker uses SellPrice array for long trades and CoverPrice array for short trades to calculate the current equity value.
5. Equity() function is single-security and does not reflect portfolio-level effects like skipping trades. It does not handle some advanced functionality offered only by the portfolio-backtester. For more information, see this table.

Portfolio Equity special symbol

After running a portfolio-level backtest, AmiBroker writes the values of the portfolio equity to a special symbol "~~~EQUITY". This allows you to access portfolio-level equity of the last backtest inside your formula. To do so, use Foreign function:

PortEquity = Foreign("~~~EQUITY", "C" );

This is exactly what, for example, the built-in portfolio equity chart formula is doing.

Can I calculate system statistics using Equity function?

Yes, you can. Here are a couple of example calculations kindly provided by Herman van den Bergen:

E = Equity();

//How rich you were :-)
Plot(Highest(E,"I should have sold",1,3);

//Your Current Drawdown:
Plot(Highest(E) - E,"Current DrawDown",4,1);

//Trade profits:
LongProfit = IIf(Sell,E - ValueWhen(Buy,E),0);
ShortProfit = IIf(Cover,ValueWhen(Short,E)-E,0);
Plot(IIf(Sell,LongProfit,0),"LProfit",8,2+4);
Plot(IIf(Cover,ShortProfit,0),"SProfit",4,2+4);

//Current Trade Profit:
Lastbar = Cum(1) == LastValue( Cum(1) );
Plot(IIf(LastBar AND pos,E-ValueWhen(Buy,E),ValueWhen(Short,E) - E),"Current Profit",9,2+4);

//DailyProfits:
Plot(IIf(pos,E-Ref(E,-1),Ref(E,-1)-E),"Daily Profits",7,2);

How do you plot a composite Equity Curve? I don't want the whole database, but would like to see the curve based on the watchlist I use for the backtesting.

Just use the Portfolio-Level equity chart (see above). It represents the actual portfolio backtest equity, so if you run your backtest on the watchlist it will represent what you need. You can also write your own formula that does the same thing:

Plot( Foreign("~~~EQUITY", "C" ), "PL Equity", colorRed );