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Unformatted text preview: 1. Math 373 Final December 13, 2010 (5 points) The current spot price (So) of the stock of Sajali Corporation is 50. You sell a put short on Sajali stock with an expiration date of one year. The strike price of the put is 45. The premium for the put is 4.00 The annual effective risk free interest rate is 5%. Complete the following table. (Show your work!) Spot Price at Expiry Payoff __l_ 35 Future Value of Cost Profit 40 45 50 55 60 2. 3. (1 point) A purchased straddle is a bet on volatility.
True or False (1 point) A purchased strangle is a bet against volatility. True or False 4. (8 points) Ren Realty Company has a three year loan with a variable loan interest rate. The
amount of the loan is 0.5 million in the first year, 1.0 million in the second year and 2.0 million in the third year. Ren enters into an interest rate swap so it can lock in a fixed interest rate. The following is the spot interest rate curve: Spot Interest Rate Calculate the fixed interest rate that Ren will lock in during the next three years. 5. (7 points) Andrea purchases ten S&P 500 futures contracts. The S&P 500 futures price is 400 at
the date of purchase. The margin requirement is 8%. The maintenance margin is 90%. The margin account earns
5.2% compounded continuously. The futures contracts are marked to market weekly. At the end ofone Week, the S&P 500
futures price is X and the amount in the margin account is exactly equal to the maintenance
margin amount. Determine X. 6. Anne enters into a synthetic forward on the stock of Guerra Industries. The synthetic forward
has a strike price of 55 and expires in one year. The current spot price of the Guerra Industries is 55 and the annual effective risk free interest
rate is 8%. ‘ The premium for a 55 strike one year call is 6.00. (4 points) Find the premium for a 55 strike one year put. (4 points) Calculate the profit on the synthetic forward if the spot price of the stock of Guerra
Industries is 50in one year. 7. 8. (2 points) Which of the following is the graph of a short call? Profit Profit ﬁg: _ Stock Price Stock Price Profit E Stock Price Proﬁt a . Stock Price (1 point) The profit on a loan is equal to the premium on a forward. True or False 9. (4 points) Jennifer sells 200 shares of Pace LTD for 500 per share. Jennifer pays a commission of
1%. Dan purchases 200 shares of Pace LTD a the exact same time. Dan pays a commission 300. The total transaction costs involved in this transaction is 1550. Calculate the price that Dan paid for his stock. 10. (1 point) The Bid price is always higher than the ask price. True or False Profit Stock Price 11. (2 points) The profit graph at the top ofthe page could represent which of the following? Circle all correct answers. More than one answer could be correct. A long forward A short forward A collar A short stock 12. (3 points) Hayan enters into a six month long forward contact on the stock of Barker Company.
At the exact same time, Robin enters a six month short forward contract on the stock of Barker
Industries. The current spot price of Barker Company is 200. Barker does not pay a dividend.
The annual effective risk free interest rate is 10.25%.
In six months, the spot price for Barker Company is 505. At the expiry date, the Hayqal’s profit is equal to Robin’s payoff. Determine 50.5. 13. (6 points) George intends to buy soybeans in the future to be used in biological research. He will
buy 100 bushels of soybeans at the end of one year and another 100 bushels of soybeans at the
end of two years. George wants to lock in the price of soybeans today. Therefore, he enters a swap with a swap
rate of 8.48. The one year forward price of soybeans is 8.00 and the two year forward price is 9.00.
The spot rate yield curve is as follows: Time Period Spot Rate
1 year 5% 2 years Calculate r2. 14. (5 points) Qian owns a swap that gives her the right to purchase 100 carats of diamond in one
year and 200 carats of diamonds in two years. Qian’s swap rate is 8000 per carat. The current forward prices of diamonds and the spot rate yield curve is given below: Time Period Forward Price of Diamonds Spot Rate
1 Year 7900 6.0%
2 Years 8200 8.0% Determine the market value of Qian’s swap. 15. (6 points) The current spot price of the stock of Kiba’s Kreations is 100. Kiba’s Kreations pays a
quarterly dividend of3. The next dividend will be paid in one month. The risk free interest rate compounded continuously is 6%. Calculate the forward price for a one year forward contract. 16. The S&P 500 Index has a current spot price of 1200. The dividend rate on the S&P 500 is 3%
payable continuously. The risk free interest rate compounded continuously is 5%. (4 points) Yiyan buys a prepaid forward on the S&P 500 index. How much does she pay today
to get the Index in 2 years. (2 points) Iinyan had entered into a long forward to buy the Index, what would her forward
price have been? 17. (1 point) The price of a prepaid forward on a stock is equal to the current spot price of the
stock. True or False 18. (3 points) List the three conditions that must be present for there to be arbitrage. 19. (4 points) List four of the five ways that Futures Contracts differ from Forward Contracts. 20. (7 points) The bidask prices for the stock of TuCo are 39.50 and 40.00. TuCo does not pay a
dividend. Transaction costs associated with buying or selling TuCo are 0.40.
The lending interest rate is 4% and the borrowing interest rate is 5%. Calculate the range of one year forward prices for TuCo for which there would be arbitrage. 21. (1 point) The rule for taking advantage of arbitrage is "Buy low and sell high.”
True or False 22. (1 point) You can create a synthetic forward by buying a stock using borrowed funds.
True or False 23. (1 point) You can create a synthetic forward by purchasing a call and selling a put with the same
strike price and same expiration date. True or False 24. (8 points) Stock for Sun Corporation has a current spot price of 50. The price of a 50 strike one
year call is 7.00 and the price of a 50 strike one year put is 2.45. The annual effective risk free interest rate is 10%.
You enter into a Cap on Sun Corporation. Determine the maximum profit that can realized on the Cap. 25. (7 points) Candace purchases a one year collar. In other words, she buys a one year put with a
strike price of 30 and sells a one year call with a strike price of 40. The annual effective risk free interest rate is 10%. The premiums for puts and calls are: Ca" Premium W
m Calculate the spot price ofthe underlying asset in one year is Candace’s profit at the end of one
year is 20. ; 26. (3 points) Circle the following position if the profit is maximized when the spot price of the
underlying asset is zero at the expiration date. Put an X through the position if the profit is
maximized at any other spot price. Collar
Cap Long Stock Bull Spread Straddle Short forward ...
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