Question

1b) You have $100 to invest and are wondering where to put it. You are considering whether to buy your favorite stock (B) or put it in your couch (C), either decision occurring today. You know the stock price today, conveniently enough $100 per share, but you don’t know the stock price tomorrow. For simplicity, it could either be double ($200) or nothing ($0), with the probability of double being ?, and the probability of nothing being 1−?. If you invest in your couch you get your $100 back tomorrow. Your discount factor is ?, and you are risk neutral (i.e. your payoffs only depend on time discounting and money.)

At what level of ? should you buy your favorite stock?

Answer 1

The payoff from the stock investment either $200 or $0 with probabilities p and (1-p) respectively.

Assuming that the discount factor is compounded on a daily basis, the expected present value of the return is :

When invested in the couch the payoff is exactly $100 the next day. Hence the present value is:

Given that the investor is risk neutral he will only invest in the stock if the present value of the stock is greater than the present value of the investment in the couch i.e.

PV1 = PV2

Solving both sides of the equation to get the value of p we get:

p = 1/2 or the value of p should be greater than 0.5