2007 GARP Practice Exam Question 15

[intuit2k2]

Assuming the stock price and all other variables remain the same, what will be the impact of an increase in the risk-free interest rate on the price of an american put option?

Answer B} negative

As interest rates increase, investors require higher expected returns from stock and the present value of future payoffs decreases. These two effects decrease the value of a put option.

My analysis: as rates go up, PV of futures cash flows goes down which implies stock price goes down, which means the put option gains in value. I know that expression for rho for a put is negative which implies the inverse correlation, but could you provide some intuition as to why puts are inverse relationship to interest rates while calls are positvely related to interest rates.

 

[David Harper CFA FRM]

Hi intuit2k2,

That explain does not work for me. (I think is actually not helpful for the way it might promote a false belief that option value cares about expected return; BSM has no expected return. It is a riskfree rate per risk neutral, no arbitrage idea).

I lean on my favorite BSM building block, minimum value:
MV (call option, non div) = stock - discounted strike = S0 - K*exp(-rT)
MV (put option, non div) = discounted strike - stock = K*exp(-rT) - S0

So, here you can see, higher riskfree rate lowers the discounted strike price term [K*exp(-rT)].

I was curious how my favorite BSM text handles the intuition (Neil Chriss, BS & Beyond). He simply writes: "Rho is always positive for Euro calls and always negative for Euro puts. So, at interest rates increase, the values of Euro call options rise, and the values of Euro put options fall. This makes intuitive sense since as interest rates rise, the forward value of a stock increases."
… similar to first part of GARP's answer, but I frankly am more comfortable with my mathy approach

Good luck on the exam!! Please let us know how it goes

David