# FIN312: Draw the payoff diagrams of portfolios 1 and 2 on the same figure, ignoring any transaction costs: Mathematics and Programming for FinTech Assignment, SUSS, Singapore

 University Singapore University of Social Science (SUSS) Subject FIN312: Mathematics and Programming for FinTech

Question 1

An investment analyst has formulated two investment portfolios consisting of options, based on his market outlook in the coming month. The options are held to expiry.

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

(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.

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

• Method 1: Calculating the probability, assuming the returns follow a Normal distribution with a mean of µ and standard deviation of σ. The values of µ and σ are obtained from the historical returns.
• 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.

Question 2

A company is offered an investment where the following cash flows are being observed: The investment provides a cash flow every 6 months and the interest rate environment is as stipulated in Table 1.

(a) Given the following cash flows, make use of discrete compounding to evaluate the present values of the cash flows from the investment, corrected to two (2) decimal points.

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