An analyst kept track of the daily price quotation for a given stock. The frequency data led to the following probability distribution of daily stock price:
Price x in Dollars P(x)
17 ............ 0.05
17.125 .......... 0.05
17.25 .......... 0.10
17.375 .......... 0.15
17.5 .......... 0.20
17.625 .......... 0.15
17.75 .......... 0.10
17.875 .......... 0.05
18 ............ 0.05
18.125 .......... 0.05
18.25 .......... 0.05
Assume that the stock price is independent from day to day.
a. If 100 shares are bought today at 17 1/4 and must be sold tomorrow, by prearranged order, what is the expected profit, disregarding transaction costs?
b. What is the standard deviation of the stock price? How useful is this information?
c. What are the limitations of the analysis in part (a)? Explain.