Return Per Dollar-Day of Capital
Two trades with the same credit are not equal if one holds twice the cash twice as long.
Course contents73 lessons · 28 questions
Two trades both collect $200. One ties up $9,500 for 45 days; the other ties up $4,000 for 14 days. They are not comparable, and comparing them by credit — which is what most people do — gets the ranking exactly backwards.
The unit that makes them comparable is the dollar-day: one dollar of capital committed for one day.
The same trade at different durations
Watch how profit accumulates against days held. The annualised figures at the bottom are dollar-day comparisons in disguise — return normalised for both capital and time.
- Profit captured, stock held still
Closing early gives back some premium and frees the capital sooner. Whether that trade is worth making is an arithmetic question, and the two annualised figures above answer it — assuming, importantly, that you actually have somewhere good to redeploy the capital.
Dollar-days
Dollar-days = capital committed × days heldA single number capturing both how much capital a trade used and for how long.
A $9,500 put held 45 days consumes 427,500 dollar-days. A $4,000 position held 14 days consumes 56,000. The second uses about an eighth of the resource for the same $200 credit.
Return per dollar-day = net profit ÷ (capital × days)Return per unit of the resource actually consumed.
| Trade | Capital | Days | Return per $1,000 of capital per month |
|---|---|---|---|
| 45-day CSP | $9,500 | 45 | $14.04 |
| 30-day CSP | $9,500 | 30 | $21.05 |
| 14-day CSP | $4,000 | 14 | $107.14 |
| 30-day spread | $386 | 30 | $518.13 |
Four trades, all collecting $200. Ranked by credit they look identical.
By credit, all four are the same trade. By capital efficiency they differ by a factor of thirty-seven.
The half nobody counts
Dollar-days are consumed by capital that is committed — but capital that is idle earns nothing and still occupies your account.
A trader with $50,000 who averages $30,000 deployed is achieving 60% utilisation. Their headline return on deployed capital could be excellent while their account return is mediocre.
Account return = return on deployed capital × utilisationWhy closing early only helps if the capital goes back to work.
This is the missing premise in the close-early argument: freeing capital is only an improvement if there is somewhere comparable for it to go. Freed capital sitting idle for two weeks has simply reduced your utilisation.
Rolled chains need this treatment
A chain that ran through three legs over four months, holding $9,500 the whole time, cannot be annualised from its final leg's thirty days. That would ignore the three months of capital commitment that preceded it.
Capital-time weighting is the correct approach — sum capital × days across every leg, then scale — and it is why roll linkage matters for performance measurement and not only for P&L. Without the chain, the duration is unknown.
Using it in practice
Compare candidate trades on it. Two setups with similar risk and different capital requirements are not equivalent, and the credit alone will not tell you which is better.
Track utilisation. If it is persistently below 60%, your constraint is finding trades rather than capital, and the fix is different.
Never optimise it alone. The most capital-efficient position available is always the most leveraged one. Constrain by maximum loss first, then optimise efficiency within that.
What can go wrong
Ranking trades by credit. Ignores both capital and duration.
Optimising efficiency alone. Leads straight to maximum leverage.
Forgetting idle capital. Deployed-capital returns are not account returns.
Annualising a rolled chain from its last leg. Ignores the months already spent.
Key takeaways
- A dollar-day is one dollar of capital committed for one day — the unit that makes different trades comparable.
- Trades with identical credits can differ thirty-fold in capital efficiency.
- Efficiency is a resource measure, not a risk measure: the most efficient position is always the most leveraged.
- Account return is return on deployed capital multiplied by utilisation, and idle capital is invisible in the first figure.
- Rolled chains must be weighted across every leg's capital and duration, not annualised from the final one.
Check your understanding
1. Trade A: $200 on $9,500 for 45 days. Trade B: $200 on $4,000 for 14 days. Which used capital better?
2. Why is optimising purely for capital efficiency dangerous?
3. You return 20% on deployed capital but average 60% utilisation. What is the account return?