Single-Symbol Thinking versus Portfolio Reality

There is a specific and very common experience: a system tests beautifully symbol by symbol, and then the portfolio backtest of the identical rules produces something much less interesting. The temptation is to assume something is broken.

Nothing is broken. The two tests answer different questions, and the second one is the question you actually care about.

What an individual backtest is really simulating

AmiBroker’s Analysis window offers an Individual backtest alongside the ordinary portfolio backtest. It runs each symbol in its own account.

Read that again, because the consequence is larger than it sounds: the initial equity figure is applied per symbol. Run an individual backtest over 200 symbols with £100,000 of initial equity and you have simulated an account with £20,000,000 in it — one that never has to choose between two signals, never runs out of cash, and never holds two correlated positions in the same account, because there is no single account.

That is a legitimate thing to compute. It is a good way to ask “do these rules behave sensibly on this instrument?” It is not a simulation of trading.

!Important

An individual backtest cannot tell you whether your selection rule is any good, because it never has to select. PositionScore is inert. Every signal is taken. The entire second half of your system — the half that decides what to do when three good candidates appear and you have one slot — is untested and invisible.

The four things that change

1. The capital constraint

At portfolio level there is one cash balance. Signals beyond your slots or your cash are refused, and the refusal is not random — it is decided by PositionScore, which means the trades you actually get are a selected subset, not a sample.

The selection is often systematically different from the whole. Rank by liquidity and you get the biggest names. Rank by lowest RSI and you get the most beaten-down candidates. Whatever your score prefers, that preference is now baked into every performance figure you read.

2. Signal collisions

Systems built on market-wide conditions fire on many symbols at once, because the condition is market-wide. A breakout system generates a cluster of breakouts on the day the market surges.

So the bar where your rules produce twenty candidates is exactly the bar where you can take five. And the bars where you have plenty of free slots are the quiet bars where the rules produce two candidates you are not excited about. The constraint binds hardest precisely when the opportunity set is largest.

∴Research note

This is why a portfolio backtest can be worse than an individual one even when the selection rule is good. The individual test takes all twenty. The portfolio test takes the five best by your score, which is better per trade — but it takes fifteen fewer trades, and if the edge was real those fifteen were worth having. Which effect dominates is an empirical question with no general answer, and the only way to find out is to run both and look.

3. Correlation between positions

Ten positions is ten positions. Ten positions in the same sector, on the same signal, on the same day, is closer to one position ten times the size.

An individual backtest cannot see this at all, because each symbol has its own account and its own drawdown. At portfolio level the drawdowns add up on the days they coincide — and they coincide much more often than an average correlation figure suggests, because correlations rise in exactly the conditions that produce large moves.

The practical symptom: the portfolio’s maximum drawdown is far larger than the average of the individual symbols’ drawdowns, and the equity curve has fewer, deeper valleys rather than many shallow independent ones. Part 34’s concentration lesson is where this is measured.

4. Exposure

This is the one that most often produces a wrong conclusion, and it is purely arithmetic.

Exposure % in the backtest report is the fraction of the period during which capital was actually at work. An individual backtest of a selective system typically shows low exposure per symbol, and the portfolio run shows something quite different depending on whether signals were spread out or clustered.

Two systems with different exposure cannot be compared on return alone. A system that is in the market 30% of the time and returns 8% a year is doing something quite different from one that is in the market 90% of the time and returns 10%. The report’s Risk Adjusted Return % exists precisely to normalise for this — it is the annual return divided by exposure — and it is the figure to compare when exposures differ.

✕Common mistake

Reading Annual Return % before Exposure % is the most common misreading of an AmiBroker report. Read exposure first, every time. It tells you what kind of thing you are looking at, and it frequently explains an apparent difference entirely.

The comparison, run properly

Complete runnable AFL

same-rules-two-ways.afl

// same-rules-two-ways.afl
// Part 28 - Single-Symbol Thinking versus Portfolio Reality
//
// One rule set, two ways of paying for it. Nothing about the signals changes
// between the two runs; everything about the money does.
//
// HOW TO RUN IT
//   Run A - unconstrained. Set TestStyle = 1. In the Analysis window use the
//           Backtest button's INDIVIDUAL backtest. Each symbol is simulated in
//           its own account, with its own copy of the initial equity, and no
//           symbol ever competes with another for cash or for a slot.
//   Run B - portfolio. Set TestStyle = 2. Use the ordinary (portfolio)
//           Backtest. One account, one cash balance, PosQty slots, and a rank
//           deciding who gets them.
//   Run C - the signal count. Run the formula as a SCAN over the same universe
//           and the same range. That gives the number of entry signals the
//           rules produced, independent of whether any of them was affordable.
//
// Then compare three numbers across the three runs: signals generated, trades
// taken, and Exposure %. The gap between run A and run B is not an error in
// either one. It is the cost of having a finite account.
//
// ASSUMPTIONS
//   Fill price   Next bar's open, no slippage or spread modelled here.
//   Delays       One bar on every signal.
//   Costs        Whatever is in Settings. Keep them IDENTICAL across runs, or
//                the comparison measures your settings instead of the effect.
//   Equity       In an Individual backtest the initial equity figure is applied
//                PER SYMBOL. Ten symbols therefore start with ten times the
//                capital of the portfolio run, which is exactly the unrealistic
//                thing this comparison exists to expose.

TestStyle = 2;    // 1 = unconstrained single-symbol, 2 = portfolio
PosQty    = 10;   // portfolio slots, used by TestStyle 2 only

// ---------------------------------------------------------- 1. the account
SetOption( "InitialEquity",          100000 );
SetOption( "AllowPositionShrinking",   True );
SetOption( "MinPosValue",              1000 );
RoundLotSize = 1;

if( TestStyle == 1 )
{
    // Every symbol gets the whole of its own account. There is no competition
    // to model, so there is nothing for a rank to do.
    SetOption( "MaxOpenPositions", 1 );
    SetPositionSize( 100, spsPercentOfEquity );
}
else
{
    // One account, PosQty equal slots. Signals beyond the free slots are
    // refused, and the refusal is decided by PositionScore.
    SetOption( "MaxOpenPositions", PosQty );
    SetPositionSize( 100 / PosQty, spsPercentOfEquity );
}

SetTradeDelays( 1, 1, 1, 1 );

BuyPrice   = Open;
SellPrice  = Open;
ShortPrice = Open;
CoverPrice = Open;

// ------------------------------------------------------------ 2. the rules
// Identical in both runs. If you change anything here, change it once.
MinTurnover = 2000000;

Tradeable = MA( Close * Volume, 50 ) >= MinTurnover AND Close >= 2;
Regime    = Close > MA( Close, 200 );

Setup   = Regime AND Tradeable;
Trigger = Cross( Close, Ref( HHV( High, 50 ), -1 ) );

Buy  = Setup AND Trigger;
Sell = Cross( Ref( LLV( Low, 25 ), -1 ), Close );

// ------------------------------------------------------------- 3. the rank
// Ignored entirely in run A, because nothing is ever refused there. That is the
// point: a single-symbol test cannot tell you whether your selection rule is
// any good, because it never has to select.
PositionScore = MA( Close * Volume, 50 );

// -------------------------------------------------------- 4. what to record
// For each run write down: number of trades, Exposure %, Annual Return %,
// Risk Adjusted Return %, Max. system % drawdown, and Avg. Bars Held. Compare
// Annual Return % only after you have compared Exposure %, because a system
// that is in the market half as often is not comparable on return alone.

Download same-rules-two-ways.afl87 lines

One rule set. Nothing about the signals changes between the runs; everything about the money does.

The three runs

Run A — unconstrained. TestStyle = 1. Use the Individual backtest. One position at a time per symbol, 100% of that symbol’s own account, no competition, no rank.

Run B — portfolio. TestStyle = 2. The ordinary portfolio backtest. One account, PosQty slots, PositionScore deciding who gets them.

Run C — the signal count. Run the same formula as a Scan over the same universe and range. That gives you the number of entry signals the rules produced, independent of whether any of them was affordable.

Keep costs, delays and the date range identical across all three, or the comparison measures your settings rather than the effect.

What to record

	Run A (individual)	Run B (portfolio)	Run C (scan)
Entry signals generated
Trades taken			—
Exposure %			—
Annual Return %			—
Risk Adjusted Return %			—
Max. system % drawdown			—
Avg. Bars Held			—

=Expected result

The pattern you should see, and the reason each part of it happens:

• Run C ≥ Run A ≥ Run B in trades taken. The scan counts every signal; the individual test takes all of them that a one-position-per-symbol rule allows; the portfolio test takes the subset it could afford.
• Run B’s maximum drawdown is not simply the average of Run A’s per-symbol drawdowns. It is driven by what happened on the days when many positions moved together.
• Run A’s return figures are not achievable, because they rest on having a separate full account for every symbol.

If Run A and Run B are close in trade count, your constraint never bound — which means either your universe is small, your rules are very selective, or PosQty is generous. In that case the portfolio run has not tested your selection rule either, and you should say so rather than claiming it has.

Reading the gap honestly

The difference between Run A and Run B is not an error in either. It is the cost of having a finite account, and it decomposes into things you can name:

1. Signals you could not afford. Compare trades taken in A and B. This is the raw size of the constraint.
2. Whether your score picked well. Is Run B’s average profit per trade better than Run A’s? If yes, the selection rule earned something. If no, your score is picking the worse candidates and is worth replacing.
3. The skipped-signal cascade. In backtestRegular, a signal skipped for affordability silences that symbol until an exit. Some of the gap is this mechanism rather than the constraint itself — re-run in backtestRegularRaw to separate the two.
4. Correlation. Compare drawdowns. If Run B’s drawdown is much worse than Run A’s typical symbol drawdown, your positions are not independent.

Only the first is inevitable. The other three are design feedback.

▷Exercise

Run all three. Then change only PosQty, from 10 to 5 and then to 20, and re-run the portfolio test.

You are looking for the shape of the relationship. More slots means more signals taken and more diversification, but each position is smaller and the marginal candidate is lower-ranked. Fewer slots means concentration in your best-ranked ideas — and much more dependence on the score being right.

There is no correct answer, and finding out that the result is very sensitive to PosQty is itself important: it means the number you eventually publish depends on a parameter you chose, and it belongs in the stated assumptions.

When a single-symbol test is the right tool

Individual backtests are not a beginner’s mistake to be outgrown. They are the right tool for a specific job:

• Debugging. One symbol, one trade list, checked by hand against the chart. This is how you confirm your delays, fills and stops do what you think.
• Asking whether rules behave sensibly on an instrument before committing to a universe test.
• Testing something that genuinely trades one instrument — a single futures contract, one index ETF. Here the individual backtest is not an approximation; it is the correct model.

What they cannot do is produce a performance figure you should ever quote for a multi-symbol system.

Recap

An individual backtest gives every symbol its own copy of your capital, so it never chooses, never runs out of cash and never holds correlated positions in one account. A portfolio backtest adds the constraint, and with it a selected — not sampled — subset of your signals, chosen by PositionScore; collisions that bind hardest on exactly the bars with most opportunity; correlated drawdowns that add up; and an exposure figure that must be read before any return figure. Run both, plus a scan for the raw signal count, with everything else identical, and the gap between them decomposes into a constraint you cannot avoid and three pieces of design feedback you can act on.

Check your understanding

Question 1. You run an Individual backtest over 200 symbols with an initial equity of 100,000. What has actually been simulated?

• A 100,000 account trading 200 symbols
• 200 separate accounts of 100,000 each — 20,000,000 of capital in total, with no competition between symbols
• A 100,000 account that can hold at most one position
• The same thing as a portfolio backtest, reported per symbol

Show the answer and why

Answer: 200 separate accounts of 100,000 each — 20,000,000 of capital in total, with no competition between symbols

The initial equity figure is applied per symbol in an individual backtest. That is why its return figures are not achievable and why it cannot test a selection rule: nothing is ever refused.

Question 2. Why does the capital constraint tend to bind hardest exactly when a system finds the most opportunities?

• Because AmiBroker limits signals per bar
• Because systems built on market-wide conditions fire on many symbols simultaneously, so candidates cluster on the same bars
• Because PositionScore is recalculated less often on busy bars
• Because commissions increase with the number of signals

Show the answer and why

Answer: Because systems built on market-wide conditions fire on many symbols simultaneously, so candidates cluster on the same bars

The condition is market-wide, so the signals are correlated in time. The bar with twenty candidates is the bar where you can take five; the bars with free slots are the quiet ones. That is a structural property of the design, not a defect in the engine.

Question 3. System A: Exposure 30%, Annual Return 8%. System B: Exposure 90%, Annual Return 10%. Which statements are sound? Select all that apply.

• B is straightforwardly better because its annual return is higher
• Risk Adjusted Return % — annual return divided by exposure — is the figure designed for comparing these two
• A had capital idle for most of the period, which is itself a fact worth knowing about the design
• Exposure should be read before the return figures

Show the answer and why

Answer: Risk Adjusted Return % — annual return divided by exposure — is the figure designed for comparing these two, A had capital idle for most of the period, which is itself a fact worth knowing about the design, Exposure should be read before the return figures

They are not comparable on return alone: A produced 8% while working less than a third of the time. Whether that is better depends on what the idle capital could do — but the comparison has to start from Risk Adjusted Return, not from the headline.

Question 4. The portfolio run takes far fewer trades than the individual run. Which of these contribute? Select all that apply.

• Signals refused because slots or cash ran out
• The skipped-signal cascade in backtestRegular, where a skipped entry silences that symbol until an exit arrives
• MinPosValue or MinShares rejecting positions that were too small
• The scan and the backtest using different rules

Show the answer and why

Answer: Signals refused because slots or cash ran out, The skipped-signal cascade in backtestRegular, where a skipped entry silences that symbol until an exit arrives, MinPosValue or MinShares rejecting positions that were too small

The first three are all real mechanisms and can be separated: re-run in backtestRegularRaw to isolate the cascade, and check the Detailed log for MinPosValue rejections. The rules are identical by construction in this comparison — that is the whole design of the exercise.

Question 5. Run B's average profit per trade is lower than Run A's. What does that suggest?

• The portfolio backtester is less accurate
• The selection rule is preferring worse candidates than a random subset would, and is worth replacing
• Costs are higher in portfolio mode
• The universe is too large

Show the answer and why

Answer: The selection rule is preferring worse candidates than a random subset would, and is worth replacing

Run B takes a subset chosen by PositionScore. If choosing produced worse trades on average than taking everything, the score is actively harmful — which is exactly the kind of feedback an individual backtest can never give you, because it never selects.

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