Nishant1

Thanks BChadwick, I found Hussman’s piece (an excerpt from it is pasted below, and the full article can be found here: http://www.hussman.net/wmc/wmc040223.htm).
[Geek’s note: to see this, consider the dividend discount model P = D/(k-g). Differentiate with respect to k to get dP/dk = -D/(k-g)^2. Divide through by price, which is D/(k-g), and then substitute P/D for 1/(k-g). Notice that this result is independent of g. For stocks that don’t pay a predictable stream of dividends, you have to calculate duration explicitly from the stream of expected free cash flows, but for blue-chip indices, the price/dividend ratio is an excellent proxy for modified duration.]
I have 2 questions - one conceptual and one technical:
1) Can the duration be approximated by taking a partial derivative with respect to the discount rate, which includes the risk premium? Isn’t this more like an equivalent of the spread duration vs. interest rate duration? I think it is intuitive that the price of the stock will have much higher spread duration (i.e. ~ sensitivity to a change in the risk premium) than to interest rates. Would you agree?
2) This may be a naive question, but I do not see how the partial differential of price (dP/dk) divided by price reprsents the sensitivity of price to interest rates (or even to the discount rate for that matter).
Thanks!