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1) I agree that IF the risk premium (i.e. spread) is constant, then  dk ~ d(rfr), but in reality the risk premium is very volatile, so is that a reasonable assumption to make?
2) OK, maybe I am alittle rusty on my math (although I have taken upper division calculus courses at UCLA), but isn’t  dp/dk already the price change rate? So then, why would you divide it by the price to get the % change? Isn’t dP/dK already the limit of [(change in P)/(change in k)]? And in general, can you divide a rate by an absolute value, i.e. wouldn’t you divide change in price (in dollars) by the price to get the % change in price? Again, my apologies if I am missing anything that’s obvious.

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