Hi, In Chapter 14: The Binomial Model , there is a section in Replicating Portfolio about Hedging and Replicating strategies but the explanation is quite ambiguous. Would appreciate if someone could share the difference between the strategies and the conditions for a replicating strategy to be a hedging strategy. Thanks!
Hi It depends what you're hedging. If you want to hedge a liability, then you need to find a hedging portfolio of assets which replicates the behaviour of the liability. Then, the liability plus the replicating portfolio of assets results in a risk-free combination. So the hedging strategy is the one which replicates the liability. If you want to hedge an asset then you need to find a hedging portfolio whose performance is the opposite to that of your initial asset. Then the combination of the two results in a risk-free position. So here the hedging portfolio is the opposite of the replicating portfolio. Sometimes exam questions use these two terms synonymously relying on the context to make it clear what is meant. Hope that helps.
It's probably already clear to you from Steve's explanation above, but for clarity's sake: the hedging and replicating approaches to valuation of a derivative are the same. It's like solving the quadratic equation 'by completing the square' or 'by the quadratic formula' - these are exactly the same thing 'under the hood'. Under the hedging approach, you say "I'm going to hold the derivative, and hedge it by holding D of the underlying. My total portfolio is risk-free, and I can solve some equations to work out D and the value of my derivative." Under the replicating portfolio approach, you say "I'm going to hold a portfolio of D shares and the risk-free asset that replicates the value of the derivative. I can solve some equations to work out D and the value of my derivative." D in the above is just the 'delta' of the derivative.
