Question

A trader short sells a share currently worth $17 and invests the payoff in a bank. In the Cox-Ross-Rubenstein notation this share has up factor u= 1.08 and down factor d = 1/uand the return on an investment over one time-step is R = 1.02.

After one time-step the trader returns the short sold share to the original owner and also withdraws the bank invětement plus interest. Say the trader makes a profit on this investment. What is the trader's profit?

Answer 1

If the trader makes a profit, it means that the stock price must have gone down as that is when the profit happens in short trades.

 

So we calculate the down price:

d = 1/u 

    = 1/1.08

 

So down price = 17*(1/1.08)

                          = $15.74

 

Moreover, the trader gets 17*1.02 = 17.34 from his investment.

 

So trader's net profit = 17.34 - 15.74

                                       = $1.6

 

So trader's net profit = $1.6