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Call Replicating Portfolio

Can someone explain to me why this higher dividends would lower the number of bonds to sell short in a call replicating portfolio? 

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this is a tough one.  here’s my thinking but i’m not super confident on it: higher dividends –> larger drop in stock price on ex-dividend date –> lower delta (because numerator is smaller while denominator is unchanged) –> fewer long shares in call replicating portfolio –> fewer short bonds in call replicating portfolio

There is a carry benefit when owning a dividend paying stock (cash flow from dividend). However with derivative instruments, you would not receive the same cash flow benefit even though you are still long the stock through a call option. That value needs to be adjusted. Recall the carry benefit adjusted BSM Model to replicate a call: 

c = Se–γTN(d1) – e–rTXN(d2)

The continuous yield (γ) has a negative impact on the stock portion of the equation so an increase in the dividend yield would result in a lower call value, keeping the bond portion constant. So to maintain the call value, the bond portion would also have to decrease.

Hope this helps.

#HODL