Max Reward on a Long Option Is a Convention, Not a Fact

Two positions, two very different kinds of number.

A vertical spread has a maximum gain that is a fact. Long the 100 call for $4.20, short the 110 call for $1.60: the net debit is $2.60, the strikes are $10 apart, and above 110 both legs are fully exercised. The most the structure can ever return is $10.00 − $2.60 = $7.40 per share, or $740 per contract. That figure is arithmetic. Nobody had to assume anything about where the underlying goes, how volatile it is, or how long it takes to get there. Every screener that computes it correctly will print the same number.

A long call has a maximum gain that is unbounded. There is no price above which the payoff stops growing. So when a screener prints "max reward: $559" next to a single long call, it has not measured anything. It has chosen a stopping point and reported the payoff there — and the number it prints depends entirely on which stopping point it chose.

That distinction is worth understanding, because the reward figure feeds the reward/risk ratio, and the reward/risk ratio is one of the most commonly sorted columns in any options tool. A column that is a fact for one structure and a convention for another cannot be read the same way in both rows.

The Three Conventions in Common Use

Take one contract and hold everything about it fixed. Underlying at $100. Thirty-five days to expiry. At-the-money implied volatility of 30%.

First, the premium. A one-standard-deviation move over 35 days is:

1 sigma = S x IV x sqrt(DTE / 365)
        = 100 x 0.30 x sqrt(35 / 365)
        = 100 x 0.30 x 0.3097
        = $9.29

An at-the-money call with no dividend and a negligible financing rate is worth about $3.70 at those inputs. That is the risk: $370 per contract, and it is a fact in the same sense the spread's $740 was. The premium paid is the most that can be lost.

Now the reward, under three different stopping points:

Same contract. Same premium. Same market. Three defensible conventions, and the ratio moves from 1.5 to 4.0 depending on which one the tool's author picked. None of the three is wrong. What would be wrong is comparing a 1.51 from one screener against a 4.02 from another and concluding the second position is better.

This is the first thing to establish about any reward number on an unbounded payoff: ask what the boundary is. If the documentation does not say, the number is not comparable to anything.

The Horizon Trap

There is a way to get this badly wrong, and it is common enough to be worth spelling out, because the symptom it produces looks like a data error rather than a methodology error.

An option premium grows with the square root of time. Double the days to expiry and the at-the-money premium rises by a factor of about 1.41, not 2. A one-standard-deviation move grows the same way, for the same reason — both are proportional to IV x sqrt(T).

So the boundary and the premium must be measured over the same horizon. If a tool has a convenient seven-day implied move already computed for its earnings screen, and reaches for that number when pricing the reward on a 35-day contract, the arithmetic breaks in a specific direction:

1 sigma over 7 days  = 100 x 0.30 x sqrt(7 / 365)  = $4.16
1 sigma over 35 days = 100 x 0.30 x sqrt(35 / 365) = $9.29

Understatement factor = sqrt(35 / 7) = 2.24x

The seven-day boundary is $4.16. The premium priced at the contract's real expiry is $3.70. Reward becomes $4.16 − $3.70 = $0.46, and the ratio prints 0.12 — a structure that looks nearly hopeless purely because the boundary was measured over a fifth of the contract's life.

Push the contract out to 45 days and it gets worse. The premium rises to about $4.20 while the seven-day boundary stays at $4.16. Reward is now negative. A tool that clamps negatives to zero will print a literal "0.0x" payoff ratio and a "$0" max reward for a perfectly ordinary at-the-money call, and every downstream figure computed from that zero — expected value most of all — inherits the error.

The diagnostic is easy once you know to look for it. If a screener shows a cluster of long options with exactly zero reward, and the zeros concentrate in the longer-dated rows rather than scattering at random, the boundary is almost certainly measured over the wrong horizon. It is a methodology bug wearing a data bug's clothes.

Two rules follow. First, the horizon of the boundary must match the horizon of the premium. Second, a boundary that cannot be measured at the right horizon should produce an empty field, never a zero — because a zero passes through null guards and renders as a number the reader will believe.

Why the Multiple Cannot Be the Same for Every Structure

Here is the part that is genuinely counterintuitive, and it is where most reward/risk columns quietly stop being comparable across rows.

Suppose a tool settles on "one standard deviation at the contract's expiry" as its boundary and applies it uniformly to every long-premium structure. Reasonable-sounding. Now watch what it does to a straddle.

At the same inputs — $100 underlying, 35 days, 30% IV — an at-the-money straddle costs the call plus the put. With no dividend and a negligible rate, put-call parity makes the at-the-money put worth the same as the at-the-money call, so the straddle costs about $7.40: exactly twice the single call.

Under a uniform one-sigma boundary the straddle's ratio collapses to 0.26 — not because the structure is six times worse, but because it paid for two legs and was credited for the move on one. The comparison is broken by the convention, not by the market.

The third row shows the fix, and the arithmetic behind it is exact rather than tuned. Write the one-sigma move as m and note that an at-the-money call is worth roughly 0.4m:

Long call at k sigma:      (k x m - 0.4m) / 0.4m
Long straddle at k' sigma: (k' x m - 0.8m) / 0.8m

Setting the two equal and solving:  k' = 2k

The factor of two is not a fudge. It falls directly out of the straddle costing twice the call, which itself falls out of put-call parity at the money. And because both the premium and the move scale with the same IV x sqrt(T), the relationship holds at every volatility and every expiry — it is not calibrated to one market.

The general principle: a reward boundary is only comparable across structures when it is scaled to the number of legs being paid for. One boundary unit per single long leg; two for a two-legged long-premium structure. Any tool that uses a single flat multiple for everything is publishing a column whose rows cannot be ranked against each other, no matter how precisely each individual cell is computed.

Breakeven Is a Fact. Reward Is Not.

There is one number on a long option that never depends on a convention, and it is the one most worth trusting.

A long call breaks even at strike + premium. A long put breaks even at strike − premium. A straddle breaks even at put strike − total premium on the downside and call strike + total premium on the upside. None of those expressions contains a volatility, a horizon assumption, or a boundary. They are definitional: they state the price at which the position's payoff at expiry equals what was paid for it.

That makes breakevens genuinely comparable across sources in a way that reward figures are not. If two tools disagree about a breakeven, one of them has the wrong premium or the wrong strike, and that is a bug worth chasing. If two tools disagree about max reward, they have probably just chosen different boundaries, and there may be nothing wrong with either.

A useful discipline follows from this. Read the breakevens first, because they tell you what the underlying has to do. Read the reward figure second, and only after you know its boundary — it is a scaling of the breakeven distance, not independent information.

One more caution on the same theme. A probability of profit reported next to a breakeven inherits a second assumption on top of the first: it requires a distribution for the terminal price. A log-normal model and an empirically fat-tailed model will disagree about the probability of the same breakeven being crossed, sometimes by ten percentage points or more, and neither is obviously the right one. So probability of profit is a convention layered on a fact, and it deserves the same question: which distribution, and measured over what horizon?

Four Questions for Any Reward Number

When a screener, broker platform, or options profit calculator shows a max reward for a structure with unbounded payoff, four questions settle whether the number means anything:

1. What is the boundary? A fixed percentage, a standard-deviation multiple, or something else. If it is not documented, the number cannot be compared to any other tool's.
2. Over what horizon is the boundary measured? It must be the contract's own expiry, not a convenient seven- or thirty-day figure borrowed from elsewhere.
3. Does the multiple scale with the structure? A two-legged long-premium position needs twice the boundary distance of a single leg before its ratio is comparable.
4. What happens when the boundary is unavailable? An empty field is honest. A zero is a fabricated number that will be read as real, and every figure derived from it is wrong too.

A tool that answers all four is not necessarily using the convention you would choose. But its numbers are at least internally consistent, which is the condition for ranking on them at all.

How This Shows Up in Equity Rank

Equity Rank's options view states its convention rather than leaving it implicit, because the reasoning above makes it clear that an undisclosed convention is an unusable number.

Defined-risk structures — verticals and four-legged range structures — are quoted from their realised strikes and quoted prices, so the maximum gain and maximum loss are the arithmetic facts of the structure and carry no boundary assumption at all.

Long-premium structures with unbounded payoff are quoted against a stated expected-move boundary measured at the contract's own expiry, one boundary unit for a single long leg and two for a two-legged long-premium structure, which is the scaling the section above derives. Where that boundary cannot be measured, the maximum-gain and payoff-ratio fields are left empty rather than written as zero, and the breakevens — which need no boundary — are shown regardless.

Related reading: option premium covers what makes up the price being paid, the Greeks cover how that price changes, implied volatility covers where the standard-deviation move comes from, and risk/reward ratio covers how the ratio behaves alongside a win rate once you have a defensible version of it.

Frequently Asked Questions

Why can't a screener just report the maximum gain as unlimited? It can, and some do. The difficulty is that "unlimited" cannot be sorted, cannot be compared between two long calls, and cannot feed a payoff ratio — so a tool that wants a rankable column has to pick a finite boundary. The honest version reports the boundary alongside the number.

Is a one-standard-deviation boundary better than a fixed percentage? It is more consistent across names, because it adapts to each underlying's own volatility and each contract's own time to expiry, whereas a flat 10% means something very different for a utility than for a biotech. Neither is more correct in principle; the standard-deviation version just keeps the column comparable across a mixed universe.

Does the factor of two apply to a strangle as well as a straddle? The reasoning applies — the boundary should scale with how many legs were paid for — but the exact factor does not carry over cleanly. A strangle's two legs are struck away from the money and cost less than two at-the-money legs, so the correct multiple sits somewhere between one and two and depends on how far out the strikes are.

Why does a zero reward matter so much if the position is genuinely poor? Because zero is not the same claim as "unknown". A zero says the payoff at the boundary exactly equals the premium, which is a measurement; an unavailable boundary is an absence of measurement. The two render identically to a reader, and the zero survives every null check a display layer applies, so it propagates into payoff ratios and expected-value figures that then look computed rather than missing.

If breakevens need no assumptions, why do tools disagree about them? Almost always because of the price used for the premium. A mid-price breakeven and an ask-price breakeven differ by half the spread on every leg, which on a wide market is a substantial distance. The formula is identical; the input is not.

Does this apply to a covered call or a cash-secured put? Less so, because both have a capped payoff at expiry and therefore a maximum gain that is a fact. The structures needing a convention are the ones whose payoff keeps growing with the underlying — long calls, long puts below zero aside, straddles, strangles and back-spreads.

This content is for educational and informational purposes only and does not constitute investment advice. Equity Rank is not a registered investment adviser. Every figure above is an arithmetic demonstration at stated inputs, not an estimate about any security, and the at-the-money approximations used (a call worth roughly 0.4 standard deviations, put-call parity at a negligible financing rate) are simplifications that hold near the money and drift away from it. Options involve risk and are not suitable for all investors; review the options disclosure document (ODD) and consult your own financial adviser before trading options.