An investment analyst has formulated two investment portfolios consisting of options,

based on his market outlook in the coming one month. The options are held to expiry.

x Portfolio 1 is a portfolio holding 10 stock A call options struck at K.

x Portfolio 2 is a portfolio holding 10 of stock A call options struck at K

and shorting 10 units of stock A call options struck at K + 'K.

(a) Draw the payoff diagrams of portfolios 1 and 2 on the same figure, ignoring any

transaction costs. Hence, determine and clearly explain the investment outlook -

-- bullish or bearish, of the analyst.

(10 marks)

(b) If K = $100, 'K = $10 and the final price of A is $110, which one of the portfolios

will have a higher return? Explain your answer clearly.

(10 marks)

The investment analyst wishes to know the probability that the return of Portfolio 1 is

greater than 12%. He can obtain the probability figure by

x Method 1: Calculating the probability, assuming the returns follows a

Normal distribution with a mean of P and standard deviation of V. The

values of P and V are obtained from the historical returns.

x Method 2: Counting the number of incidents where historical returns are

greater than 12%, i.e.

Probability=

Count of return data points > 12%

Total count of return data points

(c) Which one of the methods will you recommend? Explain your answer carefully.

(5 marks)