Replication/Perfect Hedge/Risk Free Rate of Return

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archived_user

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Hi
In relation to the following equation:
risky asset + derivative = risk-free asset
If the long and short position on a perfect hedge offset exactly, can someone please explain why it is assumed that a return at the risk free rate is generated? i.e. why is the return not 0 as opposed to the risk free rate?
Many thanks
 
Derivatives – here, likely a forward contract – are priced to earn the risk-free rate; if they were priced otherwise, there would be an arbitrage opportunity (either cash and carry or reverse cash and carry).
 
To add to that - the key to derivatives is the assumption of “No Arbtrage Pricing.” If you could buy the underlying asset and hedge it with a forward/futures contract then your payment in the future is known. Theoretically the only asset with a known payoff in the future would be a risk free asset. Thus this “hedged” position could only earn the risk free rate of return - otherwise arbitrage would exist.
 
Many thanks for the reply. I’m still not 100% sure however. When you say they are priced to earn the risk free rate, do you mean they are priced such that the price at a point in time in the future (e.g. the price in the forward contract) is equal to the the present value of the underlying if you were to discount that forward price back to the present using the risk free rate as the discount rate?
 
Ok, I get it now. Safe to say my post above is a bit of a convoluted way of saying what s2000 stated in a few words. Thanks again for the replies.
 
stevoDE wrote: Many thanks for the reply. I’m still not 100% sure however. When you say they are priced to earn the risk free rate, do you mean they are priced such that the price at a point in time in the future (e.g. the price in the forward contract) is equal to the the present value of the underlying if you were to discount that forward price back to the present using the risk free rate as the discount rate?
Click to expand...
Yes.
 
stevoDE wrote: Ok, I get it now. Safe to say my post above is a bit of a convoluted way of saying what s2000 stated in a few words. Thanks again for the replies.
Click to expand...
My internet provider charges me by the word; therefore, I’m terse.
(Punctuation’s free, however.)
 
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