You Can Be Right 70% of the Time and Still Go Broke

The seven pieces of mathematics that decide whether a trading edge survives

Most traders want to know how often a strategy wins.

Quants ask a different question:

What happens to the capital after thousands of imperfect bets?

That difference sounds small. It separates a prediction from a trading system.

A strategy can win 70% of its trades and lose money. Another can lose more often than it wins and compound for years. A real edge can disappear under bad sizing. A diversified portfolio can secretly be one giant bet. A beautiful backtest can be nothing more than the luckiest result from thousands of failed experiments.

The market does not pay you for being right.

It pays you for combining probability, payoff, size, correlation, cost, and survival better than the person on the other side.

Below is the mathematics that controls that machine.

01 — WIN RATE IS NOT AN EDGE

Start with two imaginary strategies.

Strategy A wins 70% of the time.

• Winning trade: +1 unit

• Losing trade: −3 units

Across ten average trades, it earns seven units and loses nine.

It is right most of the time and still has a negative expectancy:

EV = 0.70 × 1 − 0.30 × 3 = −0.20

Now take Strategy B.

It wins only 40% of the time.

• Winning trade: +2 units

• Losing trade: −1 unit

Its expectancy is positive:

EV = 0.40 × 2 − 0.60 × 1 = +0.20

Strategy B feels worse. It produces more losing trades, longer red streaks, and fewer screenshots worth posting.

It is also the only one making money.

This is the first equation every trading system has to survive:

Expected value = P(win) × average win − P(loss) × average loss

Accuracy is psychologically satisfying because every trade gives immediate feedback.

Expected value is economically important because it tells you what repeated exposure should do to the capital.

The market does not care how often you get the direction right. It cares about the full distribution of what happens when you do.

02 — A POSITIVE EDGE CAN STILL LOOK BROKEN

Expected value is an average across many repetitions.

Your account lives through the sequence.

Those are not the same thing.

Suppose a strategy has a genuine positive expectancy but loses 40% of its trades. Six consecutive losses in one specific block have probability:

0.40⁶ = 0.004096

That is roughly four blocks in a thousand. Across many trades, many strategies, and many traders, streaks that feel impossible become ordinary.

The edge did not necessarily disappear.

Variance temporarily became louder than the edge.

This is why a short live result cannot confirm or destroy a strategy. A small sample is dominated by path noise. The same system can produce a smooth curve in one sequence and a brutal early drawdown in another.

The correct question is not:

Did the strategy make money this month?

It is:

Was this outcome plausible under the distribution the strategy was built for?

That requires more than an average return. You need the variance, drawdown distribution, tail behavior, trade dependence, and enough observations to know whether the result is unusual.

A backtest that shows only the final return hides the most important part:

the path required to reach it.

03 — SURVIVAL COMES BEFORE OPTIMIZATION

A strategy with positive expected value is useless if normal variance can bankrupt you before the edge appears.

This is the logic behind gambler’s ruin.

When capital reaches zero, the game ends. Future expected value no longer matters because you have lost the ability to place the next bet.

The arithmetic becomes especially brutal after a drawdown:

LOSS — GAIN REQUIRED TO RECOVER

10% — 11.1%

25% — 33.3%

50% — 100%

75% — 300%

A 50% loss does not require a 50% recovery.

It requires doubling what remains.

This asymmetry is why professional risk systems obsess over maximum exposure, concentration, leverage, and drawdown limits. They are not trying to remove all losses. They are trying to prevent one sequence from ending the game.

The first objective of a quant system is not maximum return.

It is continued participation.

Because every compounding strategy has one hidden prerequisite:

you must still have capital when the next opportunity arrives.

04 — KELLY TELLS YOU WHEN A GOOD BET BECOMES A BAD POSITION

In 1956, Bell Labs scientist John Kelly connected information theory to the problem of repeated betting.

For a simple bet, the Kelly fraction can be written as:

f* = (b × p − q) / b

Where:

• p is the probability of winning;

• q is the probability of losing;

• b is the net payoff per unit risked;

• f* is the fraction of capital allocated.

The insight is deeper than the formula.

Betting too little wastes some growth. Betting too much does not merely increase volatility. Beyond the growth-optimal point, long-run compound growth falls. Aggressive sizing can turn a favorable game into a destructive capital path.

But there is a trap.

Kelly assumes your estimate of the edge is meaningful. Markets do not hand you the true probability and payoff. You estimate them from noisy, changing data.

If the estimated edge is too optimistic, full Kelly becomes full exposure to your own estimation error.

That is why practitioners often think in fractions of Kelly rather than treating the output as a command. Half-Kelly or another conservative fraction sacrifices some theoretical growth in exchange for lower drawdowns and greater protection against a misspecified edge.

The lesson is not “always use Kelly.”

It is this:

Position size should shrink when uncertainty about the edge grows.

Confidence is not a sizing model.

05 — TEN TRADES CAN BE ONE BET WEARING TEN NAMES

Diversification is not the number of positions on the screen.

It is the number of independent risks underneath them.

Harry Markowitz formalized the importance of covariance in portfolio construction in 1952. Portfolio risk depends not only on the variance of each position, but also on how those positions move together.

For a two-asset portfolio:

σ²p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂

The final term is where fake diversification hides.

You can own a technology stock, a semiconductor stock, a crypto asset, a growth ETF, and an options position — and still be making one underlying bet on liquidity, risk appetite, or interest rates.

During calm periods, correlations can look low enough to make the portfolio appear diversified. During stress, different positions may suddenly respond to the same force.

The labels remain different.

The risk converges.

This is why exposure should be mapped by common drivers, not tickers. Ask what makes each position win, what makes it lose, and which scenario damages several positions at once.

The real portfolio is not the list of trades.

It is the correlation structure between their failure modes.

06 — THE BEST BACKTEST MAY BE THE LUCKIEST EXPERIMENT

Imagine testing one random strategy.

It will probably look random.

Now test ten thousand variations across different assets, time periods, indicators, entry rules, exits, and parameters. One of them will look extraordinary even if none contains a persistent edge.

You did not necessarily discover a signal.

You may have conducted a search large enough to manufacture a winner.

This is the multiple-testing problem behind backtest overfitting. The more ideas you try, the less impressive the best result becomes. Standard performance statistics become misleading when they ignore the number of rejected strategies that existed before the winning chart was selected.

This is why honest research keeps a graveyard: every hypothesis, parameter family, market, period, failed result, and decision made after seeing the data.

Then demand evidence the optimizer never touched: a locked holdout, walk-forward testing, different market regimes, realistic costs, slippage, latency, parameter sensitivity, and a live period defined in advance.

A real edge should not depend on one exact parameter discovered after thousands of attempts.

It should survive small changes without collapsing.

The backtest is not evidence because the curve is beautiful.

It becomes evidence when the research process made beauty difficult to fake.

07 — EVERY PUBLISHED EDGE STARTS DYING

Suppose the signal is real.

The problem is not over.

Once other traders discover the same mispricing, their orders push against it. The opportunity becomes smaller, faster, more crowded, or more expensive to capture.

McLean and Pontiff studied 97 return predictors reported in academic research. In their sample, returns were 26% lower out of sample and 58% lower after publication. They attributed part of the decline to statistical bias and part to publication-informed trading.

The exact decay differs by strategy, but the mechanism is general:

An edge changes when the market learns that the edge exists.

Costs create a second attack.

A strategy can have positive gross expectancy and negative net expectancy after spreads, commissions, slippage, market impact, borrowing costs, funding, and taxes.

The faster the turnover and the smaller the predicted edge, the more those details determine the result.

This produces the final equation:

Net edge = gross edge − all implementation costs − decay

A strategy is not finished when it passes the backtest. It has entered a lifecycle:

Hypothesis → Research → Validation → Deployment → Monitoring → Capacity saturation → Decay or retirement

The model can stay unchanged while the market around it moves.

Monitoring is not maintenance after the work.

Monitoring is part of the strategy.

THE QUANT SURVIVAL CHECKLIST

Before risking capital, answer these questions:

EDGE — Is expected value positive after realistic costs, and is there a plausible mechanism behind it?

EVIDENCE — How many strategies were tested, was the holdout genuinely untouched, and does the result survive nearby parameters and different regimes?

RISK — Which losing streaks and drawdowns are plausible, and what position size survives estimation error?

PORTFOLIO — Which positions share the same driver, and what happens to their correlation during stress?

EXECUTION — What remains after spreads, slippage, latency, impact, and financing?

DECAY — Which live metrics reduce size, pause trading, or retire the strategy?

If those questions are unanswered, the strategy is not ready.

It is a hypothesis with a chart.

THE PART THAT ACTUALLY MATTERS

Most people search for a prediction that is right more often.

Quants build a system that can survive being wrong.

That system knows how much each outcome pays, how noisy the path can become, how much capital to risk, which positions are secretly the same bet, how many experiments created the backtest, what execution removes from the theoretical return, and when the original edge no longer exists.

The goal is not to eliminate uncertainty.

The goal is to price it, size it, diversify it, test it, and survive it.

You can be right 70% of the time and still go broke.

You can be wrong 60% of the time and still build a profitable system.

The difference is not confidence.

It is mathematics applied with enough discipline to stay in the game.

SOURCES & FURTHER READING

• J. L. Kelly Jr. — A New Interpretation of Information Rate (1956) — https://www.princeton.edu/~wbialek/rome/refs/kelly_56.pdf

• Harry Markowitz — Portfolio Selection (1952) — https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

• Bailey, Borwein, López de Prado and Zhu — The Effects of Backtest Overfitting on Out-of-Sample Performance — https://obj.portfolioconstructionforum.edu.au/articles_perspectives/Pseudo-mathematics-and-financial-charlatanism.pdf

• McLean and Pontiff — Does Academic Research Destroy Stock Return Predictability? — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2156623