How Contract Size Scales a Bull Put Spread’s Profit and Loss

Summary

The document explains what happens to a bull put spread when the position size increases. The example sells a higher-strike put and buys a lower-strike put, with stated premiums for both options. Increasing both legs from one contract to ten leaves the strategy’s shape and break-even structure unchanged while multiplying its profit and loss at each underlying price by ten.

The premium received and the maximum loss both scale with the number of spreads. Between the two strikes, the profit-and-loss line becomes steeper because each unit of underlying movement affects ten times as many option positions. Above the short strike, the profit is the premium difference multiplied by the position size; below the long strike, the loss is bounded by the strike gap less the net premium, also multiplied by the size. This is a simple payoff-scaling explanation based on a particular example; it does not cover transaction costs, margin, contract multipliers, or changes in market conditions.

Key ideas

• A bull put spread sells a higher-strike put and buys a lower-strike put.
• Increasing both legs by the same factor multiplies the spread’s profit and loss by that factor.
• The strategy’s price regions and payoff shape remain the same as position size scales.
• The maximum gain and bounded maximum loss both grow in proportion to the number of spreads.
• A larger position makes the profit-and-loss slope between the strikes steeper.

Tags

# Differences in bull put spread option strategy


# Differences in bull put spread option strategy












I am supposed to construct a profit and loss diagram for a bullish spread strategy: −1put($X_{1}$) + 1put($X_{2}$) and compare it to the profit and loss diagram for the strategy: −10put ($X_{1}$)+ 10put ($X_{2}$).

So I have made the strategy for the first one which looks similiar like this:

But I do not know undesrtand what will be the difference when I made the strategy for −10put ($X_{1}$)+ 10put ($X_{2}$).

Would it be higher and wider or is there something else?

## Answer by Magic is in the chain (score 2, accepted)

https://quant.stackexchange.com/a/50412

Assume the put option with strike 45 is worth 8 and the put option with 40 is trading at 5. For the bull spread, you sell the 45 strike option and buy the 40 strike option. So your payoff and profit will look as follows (profit=payoff+net premium):

Instead if you sell 10 options of strike 45 and buy 10 options of the other strike, profit graph will just scale by 10:

So you collect the premium difference 10 times and hence your profit in the upper region (stock price above 45) shifts by 10 times, and in the lower region you pay 10 times the difference between the two strikes less premium , i.e., 10 *(5-3); and in the region between the two strikes, the P&L becomes steeper to reflect the leverage.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.