# How do we know that the instantaneous rate of return on this option, $\gamma$ is negative?

I am self-studying models for financial economics and encountered the following problem:

I don't see how the author can conclude that $\gamma = -0.62$. Let's rearrange the second to last equation: $$\gamma - r = -4(0.19 - r)$$ as

$$r = \frac{\gamma + 0.76}{5}.$$

If $\gamma = 0.62$, then $r = 0.276.$

If $\gamma = -0.62$, then $r = 0.028$, as the author states.

So I don't see how the author can conclude $\gamma = -0.62$ when letting $\gamma = 0.62$ does not contradict that $r \geq 0$.

• $4*0.19 = 0.76 \neq 0.71$, and what is $\gamma$ ? – MJ73550 Nov 16 '16 at 9:36
• You're correct. I edited the original post to reflect that. However, it still allows for $\gamma$ to be positive or negative. $\gamma$ is the instantaneous rate of return on the put option. – user2521987 Nov 16 '16 at 14:21
• It is very odd. I would have thought the condition should have been $r<\alpha$ i.e. $r<0.19$ not $r\ge 0$. In words: "the expected excess return on the stock is positive". – noob2 Nov 16 '16 at 14:32
• Can you provide the source of this problem? – muffin1974 Nov 25 '16 at 10:55
• Sure, it's from "Financial Economics" by Abraham Weishaus (It's a study manual for the actuarial exam "Models for Financial Economics") – user2521987 Nov 25 '16 at 16:16