how does a delta hedged portfolio earn the risk free rate?

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cgrady40

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I get the construction of the portfolio, but I do not see how it earns the RFR.
 
if you are hedged with short calls you’re short a option with time value premium. This premium is the amount you would earn on cash until expiration of the coption.
Think of it differently, if you sold the stock 3-months from now (short calls), the minimum return you could theortiically earn on your stock sale is the Rf rate of return over those 3-months. If you’re perfectly hedged you should only earn this amount.
Hope this is right, I feel rusty lately.
 
i’m not so convinced by this one. it seems to me that the RFR earned on premium of short calls is not enough to contemplate for the RFR for the entire portfolio as the intial question proposed. Does it make sense?
 
nechets wrote:
i’m not so convinced by this one. it seems to me that the RFR earned on premium of short calls is not enough to contemplate for the RFR for the entire portfolio as the intial question proposed. Does it make sense?
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Pretty sure the theory holds true if you’re holding 1 stock versus a basket of stocks.
 
Even I have the same confusion. Been not able to negotiate this.
 
ABAL wrote:
Even I have the same confusion. Been not able to negotiate this.
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Think of the trade as a time-value of money problem. Let’s say you want to purchase XYZ stock today but you have capital locked up in an offshore account that takes 30 days to clear. Since you want the stock today, you purchase an option to buy the stock in 30 days. Since you do not have to pay the full amount of the position today, you’re able to earn interest on the cash you have in your offshore account for the duration of the 30-days AND still get the benefit of stock ownership, which is appreciation of the asset.
The option seller is smart and knows you’re a greedy SOB and are earning interest on the cash you’re paying him in 30-days. He charges you a little bit more to account for the lost interest he never received since he already sold his position to you via the option on T=0.
In this case with the hedge, you’re the seller (from above) and want to be compensated for the time period in which the buyer is earning interest on the remaining balance of the sale of the underlying (stock).
There’s more to this with how the delta moves as the option expiration month and you have to scale down the amount of options you’re hedging with but the above is the gist of it.
 
Since you got the consturction of portfolio, I will not get into the details of calcualtion.
If you buy stocks and perfectly delta hedge the position, then you do not gain anything. Because the change in spot will exactly offset the loss in option (and vica-versa).
Leaving you with same amount of money on maturity. Which means opportunity loss of RFR. Hence delta hedging ensures that you atleast earn this RFR.
 
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