# Synthetic Covered Call: Cash-Secured Put Equivalence vs. PMCC

Use put-call parity to show when a cash-secured short Put matches a covered Call at expiration, then distinguish that exact payoff relation from a Poor Man's Covered Call diagonal.

Canonical: https://wiki.fcontext.com/options/synthetic-covered-call/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## Direct answer

“**Synthetic covered call**” is used for two different ideas that should not be merged:

1. Under put-call parity, a covered Call's expiration payoff can be replicated by a **cash-secured short Put** with the same strike and expiration, plus cash that grows to the strike.
2. A **Poor Man's Covered Call (PMCC)** buys a longer-dated, usually deep-in-the-money Call and sells a nearer-dated Call. It is a Call diagonal that uses the long Call as a stock substitute, not an exact covered-Call replication.

The cash-secured Put has the same idealized terminal payoff as stock plus a short Call after financing and dividends are treated consistently. The PMCC has different expirations, less than one-for-one Delta, long-option extrinsic value, term-structure exposure, and assignment mechanics. Calling both “synthetic” does not make their path, capital, tax, or operational outcomes identical.

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## Exact expiration equivalence

For one share, same strike `K`, same expiration `T`, and European-style exercise for the clean identity:

`Covered Call terminal wealth = S_T − max(S_T−K,0) = min(S_T,K)`

If risk-free cash invested today grows to `K` at expiration:

`Cash-secured Put terminal wealth = K − max(K−S_T,0) = min(S_T,K)`

For a non-dividend-paying stock, put-call parity gives:

`C − P = S₀ − PV(K)`

or equivalently:

`S₀ − C = PV(K) − P`

The left side is the net cost of stock minus the Call premium; the right side is strike cash minus the Put premium. Dividends, stock borrow, rates, and exercise features must be incorporated consistently. Equal terminal payoff does not mean identical interim cash flow: the stock owner receives dividends while held and can face early Call assignment; the Put writer earns cash yield and can face early Put assignment.

### Why a PMCC is different

A PMCC consists of a long Call expiring later and a short Call expiring sooner, often with a higher strike. At the short expiration, the long Call still has time value and its Delta is generally below `1`. If the short Call is assigned, the account owes shares; owning a different Call does not automatically deliver them. Exercising the long Call can sacrifice remaining extrinsic value, and its strike, multiplier, or deliverable may not match.

Because the expirations differ, no single `min(S_T,K)` formula gives the entire strategy's maximum profit or loss through all roll decisions. The result depends on the long Call's value when the short leg expires or is closed, implied-volatility term structure, skew, dividends, and the next action.

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## Example: parity at zero rates

Assume for a controlled expiration comparison:

- Stock `S₀ = $100`
- Strike `K = $105`
- Same-expiration Call premium `C = $4`
- Same-expiration Put premium `P = $9`
- Interest and dividends are `0`; multiplier is `100`

The premiums satisfy parity: `$4 − $9 = $100 − $105 = −$5`.

Covered Call net cost:

`$100 − $4 = $96 per share`

Cash-secured short Put net committed cost:

`$105 − $9 = $96 per share`

| `S_T` | Terminal wealth `min(S_T,$105)` | Profit per share | Profit per 100 |
| ---: | ---: | ---: | ---: |
| `$70` | `$70` | `−$26` | `−$2,600` |
| `$100` | `$100` | `$4` | `$400` |
| `$120` | `$105` | `$9` | `$900` |

Both have a `$96` breakeven, maximum expiration profit of `$9` per share, and maximum loss of `$96` if the stock becomes worthless, before fees and taxes. The short Put premium is not free income; it accompanies an obligation economically similar to owning capped-upside stock.

Real quoted premiums need not match this zero-rate example. Use executable prices, present-value strike cash, dividends, exercise value, and transaction costs before interpreting a discrepancy.

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## Comparison and control checklist

- Write the actual legs, quantities, strikes, expirations, style, multiplier, and deliverable before naming the strategy.
- For parity, use the same strike and expiration and value strike cash at the correct discount factor.
- Include expected dividends and the possibility that an American Call or Put is exercised early.
- Reserve the full assignment cash for a cash-secured Put; displayed buying power is not the same as economic funding.
- Compare executable package Bid/Ask, commissions, cash yield, stock financing, and tax treatment.
- Treat downside as stock-like: premium provides only a limited buffer against a collapse.
- For a PMCC, measure the long Call's Delta, extrinsic value, expiry, and loss if IV falls.
- Stress the short Call being assigned before a dividend or after a gap; plan how shares will be delivered.
- Do not exercise a long Call automatically without comparing its remaining extrinsic value with alternatives.
- Keep the long leg until the short obligation is closed or otherwise covered; selling it can create an uncovered Call.
- Model separate moves in near- and far-term IV, skew, and time; a diagonal is exposed to their relative change.
- Recalculate after rolls. Closing the old short Call and opening another is a new trade, not recovery of prior loss.
- Verify broker option level, margin, exercise cutoff, liquidation, and handling of assignment across expirations.

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## Common misconceptions

- **“A cash-secured Put is safer because no stock is owned.”** Its downside payoff can match a covered Call and remains substantial.
- **“Covered Call premium protects the whole stock loss.”** Protection is limited to the premium and upside is capped.
- **“PMCC is the same position with less capital.”** It adds long-option time value, less-than-one Delta, expiry mismatch, and IV risk.
- **“A long Call automatically covers assignment.”** Assignment creates a share-delivery obligation; operational action is still required.
- **“Parity guarantees a retail arbitrage.”** Bid-Ask, dividends, early exercise, rates, fees, taxes, borrow, and execution can consume differences.
- **“Rolling preserves the original equivalence.”** A roll closes one contract and opens another with new terms and risks.
- **“Limited maximum loss means low risk.”** Losing most of `$96` per share is limited but economically large.

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## Related topics

- [Covered Call](/options/covered-call/)
- [Cash-secured Put](/options/cash-secured-put/)
- [Put-call parity](/options/put-call-parity/)
- [Poor Man's Covered Call](/options/poor-mans-covered-call/)

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## Authoritative sources

- [Options Industry Council: Put/Call Parity](https://www.optionseducation.org/advancedconcepts/put-call-parity)
- [Options Industry Council: Covered Call](https://www.optionseducation.org/strategies/all-strategies/covered-call-buy-write)
- [Options Industry Council: Cash-Secured Put](https://www.optionseducation.org/strategies/all-strategies/cash-secured-put)
- [Options Industry Council: Covered Calls, PMCC, and Cash-Secured Puts](https://www.optionseducation.org/news/june-webinar-takeaways)
- [OCC: Characteristics and Risks of Standardized Options](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document)