Page\ 2\ of 3\ 1\ Options, Futures and Other Derivative Securities\ FINE 4800A, Fall 2023\ Individual Assignment #2\ Due on Dec. 8 at 11:59pm (EST/Toronto local time)\ Important:\ Your assignment can be either typed or hand-written. Make sure your handwriting is legible\ if you submit a hand-written assignment.\ You must explain your answers in detail and show all calculations. As for how much detail to\ provide, the rule of thumb is that someone else must be able to replicate your numbers by\ following your explanation. For repeated calculations (such as risk-neutral valuation using a\ binomial tree), it is acceptable to show detailed calculations for a few cases (at some nodes)\ and omit the detailed calculations for the rest if they are similar. For a good example of what\ you should include in your solution, take a look at the solution to the recommended Hull\ textbook questions posted on Canvas. A counter example of what not to do is to work out the\ problem entirely in a spreadsheet and then simply cutting and pasting it to your submitted\ assignment without any explanation. Although there is nothing wrong with using\ spreadsheets, you must fully explain your calculations in words and/or formulas.\ You must submit your completed assignment online by uploading it, in either a pdf or a word\ file, on Canvas via the Assignments tab. You may submit your assignment on Canvas at\ any time prior to the deadline on the due date of the assignment. If you did not finish your\ assignment by the deadline, you should submit the part you already completed via Canvas\ prior to the deadline. This part of the assignment will be accepted without penalty. You may\ submit the remainder of your assignment later, subject to penalty, as described below.\ After the submission deadline, you will not be able to submit your assignment online via\ Canvas. In that case, your submission is considered overdue and late submission penalty\ applies. You must then email your completed assignment to my email address\ (ytian@schulich.yorku.ca) as file attachments. I will use the time stamp of your email to\ determine the exact penalty. Penalty for late submission is a 20% loss of the total possible\ marks for each day past the deadline. Homework submitted one minute to 24 hours after the\ due date (stated above) is considered one day overdue. Late penalty will be waived if there\ are extenuating circumstances (e.g., illness with documented proof) at the instructors\ discretion.\ Question 1 (20%)\ A portfolio manager runs a $500 million equity fund and wishes to hedge her stock portfolio\ over the final 2 months of the year. The beta of her stock portfolio is 1.45. Her portfolio has\ performed quite well relative to comparable funds over the first 10 months of the year and she\ now wants to hedge against a possible market-wide crash during the final 2 months of the year.\ Rather than liquidating her stock portfolio or purchasing put options, she wants to use stock\ index futures with a three-month maturity to hedge her portfolio. Each futures contract is for\ delivery of $250 times the index. The stock index currently stands at 10,000 and its dividend\ yield is 2.5%. The risk-free rate is 5%. The manager wishes to lower the beta of her portfolio to\ 0.5 (from its current level of 1.45). All rates are compounded continuously unless stated\ otherwise.\ 2\ a) (5%)\ What position in the three-month futures contract should she take?\ b) (15%)\ If the stock index drops to 9,200 by yearend, how does the hedge work out? Assume there is no\ change in either the risk-free rate or the dividend yield on the stock index.\ Question 2 (20%)\ A stock is expected to pay a dividend of $0.90 per share in two months and again in five months.\ The stock price is $100, and the risk-free rate of interest is 5% per annum with semi-annual\ compounding for all maturities. An investor has just taken a short position in a six-month\ forward contract on the stock.\ a) (10%)\ What are the forward price and the initial value of the forward contract?\ b) (10%)\ Three months later, the price of the stock is $110 and the risk-free rate of interest is still 5% per\ annum. What are the forward price and the value of the short position in the forward contract?\ Question 3 (20%)\ The 2-month silver futures contract is currently trading at the price of $20.50 per ounce. The price\ of a 2-month European call with a $20 strike price on this silver futures contract is selling for $1.05\ per ounce. The risk-free interest rate is 5% per annum (compounded continuously). If the price of a\ European put option on the same silver futures contract with identical strike price and maturity is\ selling for $0.35 per ounce, are there any arbitrage opportunities? If there are, show how an\ arbitrager can take advantage of the opportunities. If there arent any, explain why not.\ Question 4 (20%)\ A fund manager has a well-diversified portfolio that has a beta of 1.5 (measured against the\ S&P/TSX 60 index) and is worth $250 million. The S&P/TSX 60