# Delta of a Vertical Spread | Slower than delta of long option?

People often prefer to trade options spreads rather than buying options, since those reduce your cost and have a defined profit and loss but what is the probability of success of a spread? For example if I buy a Call with 0.5 delta and sell a strike further with delta of 0.25, doesn't that make net delta for the position 0.25(+0.5-0.25), If so that would mean this spread would move slower than a long option. What that means is that if the underlying had moved 100 delta I would have made 50 delta on long option but only 25 delta on the spread.

I understand that there is lower capital requirement and defined risk/reward but is it correct understanding that it will also reduce delta of position and hence reducing the probability of success?

Edit: Updated(wording changed from point to delta) as suggested in answers below.

Per your original question, some old timers used to describe owning options as being long a naked option. That can make a discussion confusing. Today, as noted by gamma, the phrase "naked option" is used for "unprotected short option position".

If so that would mean this spread would move slower than a long option. What that means is that if the underlying had moved 100 point I would have made 50 point on naked option but only 25 point on the spread.

If the underlying moves up 1 point then long call would increase by 50 delta and the short call would increase by 25 delta. So change the word point to delta (for 100 point, 50 point and 25 point) and it makes sense and your conclusion is correct. The vertical spread lags the long call.

If instead you meant that the underlying rose 100 points then both options would go to parity with deltas of 100 and you would make 25 delta times the move from current price to the upper strike, offset by time decay. This is far too convoluted a way to assess the spread. The simple answer would be that your profit would be the strike width less the premium paid (debit spread).

• Thanks @Bob, This is what got me curious, so if a spread has lower delta and the whole objective is to reduce the cost, won't it be same as going long in a slightly out of the money Call which has a similar delta and cost? – Vibhore Tanwer May 10 at 3:25
• Look at the risk graph of a bull call spread and at that of a long call. The two strategies have totally different P&L graphs so no, it wouldn't be the same. If that's not obvious, combine the two strategies into one position (one long, one short) and look at the resultant risk graph. Where it's a horizontal line, they're equal. Where the line has slope, they're not. A simple example is graph of long covered call and its equivalent short put. The output graph is a horizontal line, hence they are equal. – Bob Baerker May 10 at 10:40
• Hey @Bob Thanks, that was helpful. So I figured that a spread would move slower compared to a long option but also it requires little movement to be profitable and that's what makes probability of profitability higher. Break even point for a spread turned out to be much much better than a long option. I will accept your answer. – Vibhore Tanwer May 11 at 10:44

The phrase "naked option" is used for "unprotected short option position". That's not the case in the example you are given (you have a long option position).

In your case, buy an (approximately) ATM call then sell an OTM call vs. only buy the ATM call, the spread one actually has a higher chance to profit, but the max profit is limited by the width of the spread. The stock needs to close at strike of long call+premium for you to be profitable at expiration. The less you pay the more likely you end up in profit.

On the other hand if you are comparing selling a naked option vs. selling a spread (buying a further out of money option to protect). It's the naked option that has higher chance of success, but the max loss is undefined.

• you are correct, I meant long position I will update the question as well. My confusion is around lower delta, is my understanding correct that it will have lower delta? I get your point but trying to understand how does lower delta impact this trade? – Vibhore Tanwer May 6 at 5:54
• Delta is d(profit of option position)/d(stock price), since derivative is a linear operator, delta is also additive. If your position combines a positive delta position (long ATM call) with a negative delta position (short OTM call) the overall delta will be lower compare to the "long option only" position – user67084 May 6 at 6:02
• Prior to expiration, a long call and a bullish vertical with the same long call will have different results and that result is determined by the amount of theta decay and price movement. IOW, as a generalization, the spread will lag the performance of the long call by the negative delta performance of the short call. Per the OP's suggestion of an up move, the long call has the higher probability of profit in his set up. This also holds true for comparing a naked option versus selling the spread. – Bob Baerker May 6 at 8:57