Expected value of a premium-selling trade

Expected value is the average outcome across every path, weighted by how likely each one is. On a short option priced by the market, that average is zero once you account for interest on the credit. The high win rate is not an edge. It is exactly paid for by the size of the loss on the paths where you lose.

People sell options because they win most of the time. That part is true and it is also not the point.

The tree

Short one CSCO April 17 $64 call for $0.62, stock at $58.40, 45 days, 28 percent implied volatility. Two branches.

Minus 87 cents. Carry the $62 credit at 4.2 percent for the 45 days you hold it and the residual disappears entirely: the expected value is zero, to the last decimal the model has.

The number in the second row

That $356 deserves a paragraph of its own, because almost nobody who sells a 0.20 delta call has looked at it.

Given that CSCO does finish above $64, where does it finish? The average is $67.56. Not $64.10. You are already conditioning on a move that cleared a 1σ threshold, and the distribution of moves past a threshold has a long right side, so the typical assignment is not a squeaker. It is a 15.7 percent rally in six weeks that takes $356 of upside off you and hands back $62.

The trade is about five small wins against one loss just under six times the size of a win. That is the shape of every premium-selling position ever opened, and it is the shape the market intends.

Why zero is the answer

Because $0.62 is what the option costs, and what it costs is what it is worth.

Black and Scholes (1973), Journal of Political Economy 81(3), 637 to 654 is the machinery, but the result needs none of it. If the expected value of selling this call were positive, buying it would have negative expected value, and the people buying it are not doing so as a favour. The price moves until neither side has an edge. That is what a price is.

So every published calculation showing that selling premium has positive expected value has smuggled in an assumption somewhere, and the assumption is almost always a view on the stock. "Assume CSCO drifts up 6 percent a year" turns a covered call into a positive-EV trade. It also turns holding the shares into a positive-EV trade, by more, and the covered call now caps it. The edge belonged to the stock, and the option gave some of it back.

Where an edge could actually come from

One place, and it is smaller than the marketing suggests: implied volatility runs a little above what stocks go on to do. Sellers get paid for carrying a risk buyers want to shed, the same way an insurer does.

Price it. The market wants 28 percent for this call. Suppose CSCO actually realises 26 over the 45 days, which is about the size of the gap this site measured on a different chain.

Eleven dollars a contract. Roll it eight times a year and the whole theoretical edge on this position is $86, against $5,840 of stock. One and a half percent a year.

Then subtract the costs

The market on that call is $0.58 bid at $0.66 ask. Sell it at the bid instead of the mid and you have handed back $4 of the $11 before the trade starts. Do that eight times a year and the spread costs $32 of the $86. Close early rather than letting it expire and you cross twice, which is $64 of the $86. The full arithmetic on spreads is a page of its own, and it is the least glamorous page on this site.

What is left, on a good name, executed at the mid, held to expiry, is something like $50 a year on $5,840. Call it 0.9 percent.

That is the honest size of the edge in selling covered calls, and it is why the execution pages in this cluster matter more than the probability ones. There is not enough margin here to give any of it away.

What EV is good for anyway

Not for choosing between two strikes. They all have the same expected value, which is zero, so EV cannot rank them and anybody using it to do so has made an arithmetic error.

It is good for three things. It kills the "I win 82 percent of the time" argument, which is the most common bad reason to sell options. It sizes the loss branch, which is the number that should set your position size. And it tells you that everything you actually control lives in the costs and the selection, not in the payoff.

OptionsKing scores every candidate strike on a deterministic 0 to 100 scale, blends that score with the return on the capital the trade ties up, and shows you the highest-ranked handful. There is no minimum score. How it works covers what the ranking does and does not tell you.

Questions people actually ask

Sources

• Black and Scholes (1973), Journal of Political Economy 81(3), 637 to 654
• Merton (1973), Bell Journal of Economics 4(1), 141 to 183
• OCC, Characteristics and Risks of Standardized Options

Rules and thresholds above were checked against these documents on August 4, 2026. Exchange and broker rules change. Confirm anything you are about to act on with your own broker.

Keep reading

• What the spread takes out of the edge
• Where the edge comes from in the first place
• What to check instead of EV

Do the math on your own trade

• Covered call calculator premium, break-even, static and if-called return, annualized.
• Black-Scholes calculator price and Greeks from five inputs.
• Annualized return calculator turn any credit and any holding period into a yearly rate.

Every price in this article is an illustrative worked example, not a quote. Read Screening and probability for the rest of the series, and the disclaimer before you act on any of it. Selling options carries real risk of loss, and the loss can be far larger than the premium you collected.