Adding Spot, Call, and Put Deltas in a Portfolio

Summary

The document explains how to combine the deltas of a position containing one underlying share, one call, and one put. It gives the share delta as 1, the call delta as 0.45, and the put delta as −0.14. The key calculation is to add the component deltas, assuming each position has one share of underlying exposure as its notional: the portfolio delta is 1.31.

The questioner initially multiplies the option deltas, which does not represent the portfolio’s total sensitivity to a move in the underlying. Delta is an additive exposure across positions, with each instrument’s delta adjusted for its quantity and contract or notional size. The answer depends on the stated assumption that the call and put each correspond to one underlying unit; different contract multipliers or position quantities would change the result. The example gives a simple calculation, not a broader treatment of option Greeks or nonlinear risk.

Key ideas

• A share has delta 1 under the convention used in the example.
• Portfolio delta is found by adding the delta exposures of its positions.
• Multiplying the call and put deltas does not give the combined portfolio delta.
• The example’s total assumes that each option represents one underlying unit.

Tags

# Confused in regards to calculation of delta of one share including one call and one put


# Confused in regards to calculation of delta of one share including one call and one put












Q:My investment portfolio has one share of one call and one put, what would be the delta of my portfolio ?

delta of call:0.45

delta of put: -0.14

My thought process:

To begin with since im dealing with a single share this automatically means that the delta of this share is 1 [ according to what i found in the book of hull] therefore would my portfolio delta be : share number x call delta x put delta = portfolio delta

1 x 0.45 x -0.14 = 0.31

It feels as if im missing something very important and ive been over the same chapter for hours now.

## Answer by AKdemy (score 1)

https://quant.stackexchange.com/a/63849

I am not sure what you mean with share of one call and put. Based on the later formula I assume you have on underlying unit, plus a call and put which also has one share as notional value. Spot has delta 1 Call 0.45 Put -0.14 Overall is sum of all deltas, here 1.31.

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