Can anyone please explain the following two questions? I’ve looked up the solution but still could not understand the logic.
The question is on 2020 CFA Textbook L2V5 p 433 Example 18 Delta Hedging
Suppose we know S = 100, X = 100, r = 5%, T = 1.0, σ = 30%, and δ = 5%. We have a short position in put options on 10,000 shares of stock. Based on this information, we note Deltac = 0.532, and Deltap = –0.419. Assume each stock option contract is for one share of stock.
1 The appropriate delta hedge, assuming the hedging instrument is stock, is executed by which of the following transactions? Select the closest answer. A Buy 5,320 shares of stock. B Short sell 4,190 shares of stock. C Buy 4,190 shares of stock.
2 The appropriate delta hedge, assuming the hedging instrument is calls, is executed by which of the following transactions? Select the closest answer. A Sell 7,876 call options. B Sell 4,190 call options. C Buy 4,190 call options.
Once you understand the formula, the rest should come relatively simply.
where:
NH is the Number of units of the hedging instrument, and
DeltaH is the Delta of the hedging instrument.
Using a simple example without any options, let’s say we are long 100 shares of stock in our portfolio. By definition, our portfolio delta is +100.0. The delta of our hedging instrument (each share) is +1.0 (not -1.0, remember, the DeltaH is the actual Delta, not the ACTION of what we do with the instrument). We solve for NH and find that it is equal to -100.0, which is the number of units of the hedging instrument. We ONLY look at the sign of NH. If it’s positive, we go long on the chosen hedging instrument. If it’s negative, we go short the hedging instrument. Thus, we sell 100 units of stock to make our portfolio delta neutral.
Applying our understanding of that formula to the question:
Our portfolio delta is (Short DeltaP) * 10,000 shares = -(-0.419) * 10,000 = +4,190.
The question asks us to long or short stock based on the choices we have. Our DeltaH is +1.0, because the delta of one stock is +1.0.
We solve for NH. We will get NH = -4,190. That means we will sell 4,190 shares of stock.
You should be able to go through the same exercise with #2.
Go through the derivation of the formula by using only shares. That should help with your understanding.
