Exam 1 Notes

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School

Iowa State University *

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424

Subject

Finance

Date

Apr 3, 2024

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Uploaded by BarristerTitaniumStingray41

1. A company takes a short position in a six-month forward contract on one million euros; the delivery price (forward price) in the contract is $1.13 per euro. Six months later, the spot exchange rate is $1.32 per euro. What is the company’s profit (in total dollars) on the forward contract? Short on a 6-month forward contract for 1 million euros Delivery price = $1.13/euro, Spot Exchange Rate = $1.32/euro Profit = 1.13-1.32 = -0.19, -0.19*1,000,000 = -$190,000 2. George, who is not involved in the biodiesel business as a producer or user, thinks biodiesel prices will rise soon. George decides to trade a biodiesel futures contract, creating a long position to try to earn a profit based on this price expectation. Is George acting as a hedger or speculator? George takes a long position and thinks biodiesel prices will rise. George is acting as a speculator . If an investor has exposure to the price of an asset, he or she can hedge with futures contracts. If the investor has no exposure to the price of the underlying asset, entering a futures contract is speculation. 3. True or False? As soon as two parties create a futures contract by trading, the clearinghouse splits the contract in two and becomes the counterparty to each of the original parties. True – Remember AI Photo 4. True or False? If someone who holds a futures contract position receives a margin call, they only need to deposit enough cash in their margin account to bring the balance back up to the maintenance margin to prevent the position from being liquidated. Futures contract receives margin call – can they deposit cash in margin account to prevent position liquidation? - False – If a futures trader receives a margin call, they must immediately – Transfer cash into the account, only cash will do, and bring the balance at least back to the initial margin requirement, otherwise their position will be closed. - This does not apply to stock market margin calls. 5. When two parties create a new futures contract by trading, the value of the contract to each party immediately upon completion of the trade is: A. Zero – Nothing needs to be exchanged, net value for each side is 0 upon creation. B. The futures price times the number of units of the underlying included in the contract C. The initial margin 14. Zero rates per year compounded semiannually are given below. Find the two-year par yield (of a bond with semiannual coupons). t Zero rate per year 6 months 0.028, 12 months 0.032, 18 months 0.037, 24 months 0.040 a. Months Given R Solutions Formula (CC R) 6 2.80% 2.78% 2*LN(1+B2/2) 12 3.20% 3.17% 2*LN(1+B3/2) 18 3.70% 3.67% 2*LN(1+B4/2) 24 4.00% 3.96% 2*LN(1+B5/2) b. Months CC R from (a) Solutions PV of $1 (2 year par yield) 6 2.78% 0.9862 EXP(-B9*A9/12) 12 3.17% 0.9688 EXP(-B10*A10/12) 18 3.67% 0.9465 EXP(-B11*A11/12) 24 3.96% 0.9238 EXP(-B12*A12/12) 3.8253 SUM(C9:C12) c= 3.98% ((1-C12)*2)/C13 Formula used is ((1-d)*m)/A 15. Zero rates per year compounded semiannually are given below. Find the value of an FRA where the holder pays 0.074 (per year semiannually compounded) and receives SOFR for a six-month period beginning in 18 months. The current (forward) SOFR rate for this period is 0.067 (per year semiannually compounded). The principal is $15 million. B Months C Zero Rate D Answers: 48 6 5.60% $ 52,500.00 =0.5*(7.4%- 6.7%)*15000000 49 12 6.90% $ 46,827.16 =D48/((1+C51/2)^(2* 2)) 50 18 6.40% 51 24 5.80% 16. Geri's margin balance after the Thursday settlement is $5900. The maintenance margin is $4500. The Thursday settlement price is $3.7695. There is 25,000 pounds in a contract and Geri is long one contract. What is the lowest Friday settlement price at which Geri would not receive a margin call?

D. The maintenance margin 6. One wheat futures contract is on 5000 bushels. Suppose that in September 2022, a company buys a March 2023 wheat futures contract for $3.90 per bushel. In December 2022, the futures price is $3.65 per bushel. In March 2023, the final futures price is $4.50. The company is classified as a speculator for tax purposes. What is its taxable income in dollars from this futures contract for 2022 and 2023? One contract = 5000 bushels In Sept 22’, buys Mar. 23’ futures for $3.90, In Dec. 22’ futures price is $3.65, In Mar. 23’ final futures price is $4.50 Company classified as a speculator 22’ Tax Return = (P1-P0) * contract multiplier (3.65-3.90) = 0.25, 0.25*5000 bushels = -$1250 (Loss of $1250) 23’ Tax Return = (4.50-3.65) = 0.85, 0.85*5000 bushels = $4250 (Gain of $4250) Hedging gains/losses are recognized when the transaction being hedged takes place, other positions are speculative for tax purposes, which are done year by year. 7. A company uses 20 futures contracts to hedge exposure to the price of wheat. Each wheat futures contract is on 5000 bushels. At the time the hedge is closed out, the basis is $0.77 cents per bushel. Find the effect of the basis on the hedger's (company's) financial position if the company is hedging the purchase of wheat. (The effect of the basis can also be thought of as their gain or loss if their prior expectation were that the basis would be zero.) 20 futures contracts to hedge exposure to wheat, Contract = 5000 bushels When hedge is closed = $0.77 per bushel -S+ (New F - Original F) = - (Original F + Basis) 20*-5000*0.77 = -77,000 = Buying 77,000 in futures Delta Hedge, not a perfect hedge example 8. A company decides to hedge its exposure to Grain X, a crop that does not have traded futures. The price changes of Grain X have a 0.33 correlation with wheat futures price changes. The company is planning to buy Grain X and will lose $12 million for each 1 cent increase in the Grain X price per bushel over the next six months. The Grain X price change has a standard deviation that is 45% greater than wheat futures price changes. If wheat futures are used to hedge the exposure, how many wheat futures contracts should be traded? Each futures contract is on 5000 bushels. Settlement Price is $3.7695, Margin Balance after Settlement is $5900, Maintenance Margin is $4500 Contract Size is 25,000 pounds =Settlement Price - (MB after Settlement – MM)/Contract Size = 3.7695 - (5900-4500)/25000 =3.7695 - 0.056 = 3.7135 17. Given these rates, find the zero rate for T=1.5 years. T Zero Rate Par Yield 0.5 6.00%, 1 6.30%, 1.5 6.15% c/2= 3.075 =100*6.15%/2 S= 5.871371197 =C66*(EXP(-6%*0.5)+EXP(-6.3%*1)) R= 0.06052976 =LN((100-C67)/(C66+100))/-1.5 6.0530% Percentage 18. On Wednesday, George buys one aluminum futures contract at $2149 per metric ton. The initial margin requirement is $2750. The contract size is 25 metric tons. Later Wednesday, the settlement price turns out to be $2156 per metric ton. What does George's margin balance become? IM Requirement = 2750, Settlement Price = 2156/ton, Orig. Contract = 2149/ton, Contract Size = 25 tons 2750+(2156-2149)*25 = $2925 19. On Wednesday, Harriet sells one aluminum futures contract at $2149 per metric ton. The initial margin requirement is $2750. The contract size is 25 metric tons. The first two daily settlement prices after her trade are (per metric ton): Wednesday $2156, Thursday 2162 What is Harriet's margin balance after the daily settlement process on Thursday? Wed. Price = 2156, Thurs. Price = 2162 IM Requirement = 2750, Contract Size = 25

.33 correlation/ 45% sd / 5000 bu. Per contract Lose $12,000,000 per 1 cent increase in Grain X price per bushel Cross hedging, like delta hedging – commodity mismatch instead of price (same formula) .33*1.45 = 0.4785 --> (.4785 *1,200,000,000)/5,000 = 114,840 contracts - NOTE: 1 .45 SD b/c grain x price change sd is 45% GREATER THAN wheat futures - NOTE: 12,000,000*100 TO CHANGE TO $ INCREASE 9. Today is April 2. A company has a portfolio of stocks worth $450 million. The beta of the portfolio is 1.54. The company wants to use the September futures contract on a stock index to change the portfolio's beta to 0.90 from today to July 31. The index futures price is 4812, and each contract is on $250 times the index. What position should the company take? Date is 4/2, Portfolio is worth $450,000,000 Portfolio Beta = 1.54, Future Beta = 0.90 on July 31 st , using a September futures contract Index Futures price = $4812, each contract is 250x the index. Sell (beta current – beta desired) Va/Vf, Va = Portfolio Value, Vf = Index Future * Multiplier Sell (1.54 - 0.90) * 450,000,000/ (4812*250) 4812*250 = 1,203,000 Sell (0.64) * 450,000,000/1,203,000 450,000,000/1,203,000 = 374.0648 Sell (.64* 374.0648) = 239.4015, Round to Short 239 contracts, round to NEAREST whole number 10. The following continuously compounded zero rates are given: t Zero Rate (CC) 0.5 year 1.8%, 1 year 2.1%, 1.5 years 2.6%, 2 years 3.0% Find the forward rate for the six-month period beginning in 1.5 years. Use Forward Rate Formula – 1.5 years = (3%*2-2.6%*1.5) *2 = 4.20% 11. A bond pays the following cash flows: a coupon of $3.81 every six months (0.5 year, 1 year, and 1.5 years from now), and a face value of $100 at maturity 1.5 years from now. Margin Balance post Thursday Settlement: 2750-(2162-2149)*25 = $2425 Option buyer duty (not in a slide deck) Under what circumstances is the buyer of an option required to exercise it? A. When it is a put option B. Never C. When the option seller calls the option Who buys at bid (Futures Hedging) Who routinely buys at the bid and sells at the ask? A. Anyone trading futures B. Futures commission merchants C. Market Makers D. Trader who receives margin calls Perfect hedge basis (Futures Hedging) A perfect hedge has a basis of zero at its ending date. A. True B. False Perfect or delta (Futures Hedging) Alset Corp. is hedging a planned August 2024 purchase of copper using September 2024 copper futures. Is this a perfect hedge or a delta hedge? A. Perfect B. Delta Know the basis or not (Futures Hedging) With a futures delta hedge, the hedger knows when they set up the hedge what the basis will be when they close out the position. A. True B. False

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The continuously compounded zero rates are the same as in the preceding problem. Find the bond's theoretical price. t zero rate coupon pv (formula) pv price 0.5 1.80% $ 3.81 =D30*EXP(-C30*B30) 3.7758638 4 1 2.10% $ 3.81 =D31*EXP(-C31*B31) 3.7308242 6 1.5 2.60% $ 103.81 =D32*EXP(-C32*B32) 99.839341 1 =SUM(F30:F32) 107.34603 12. The table below gives cash flows on a Treasury bond. The bond's price is $990.8144. Find the bond's yield as a decimal (not percent) annual rate (compounded semiannually). t (Years) Coupon $ Face Value (Principal) $ 0.5 27, 1.0 27, 1.5 27, 2.0 27, 2.5 27 1000 Make sure to make the bonds redemption 100 for the yield formula 13. Zero rates per year in continuously compounded form are given below. Find the forward rate for the six-month period beginning in 18 months. B Months C Zero Rate D Fwd Rate E Formula 38 6 2.90% 39 12 3.20% 40 18 3.70% 41 24 4.30% 6.10% =(C41*2-C40*1.5)*2 NOTES SECTION - Forward Contracts – two agree on the term, the buyer has the long position, the seller has the short position. Binding to both. Each party has zero net value at contract creation. Future Contracts – typically done on exchange, everyone must put up liquid collateral (margin). Clearinghouse is central medium. Can close position by trading. Options – One party has right to buy (call) or sell (put) underlying at fixed price Deriv. Trading Motivations – Hedging, Arbitrage (mkt. observation), Specul. (predictions) Futures Margin Call – Trader must transfer cash or bring bal. back to initial margin req. Tax (Q2/6) – Hedge G/L recognized when transac. being hedged takes place, spec. is YtY Daily Settlement – daily ending price set by exchange rules. Long pos. has gain when settlement price is higher // short pos. has gain when settlement price is lower SOFR – secured overnight fin. rate // int. rate on overnight loans using T-bills as collateral Zero/spot Rate – as in zero coupon bond, but not necessarily a literal bond involved Perfect Hedge – Underlying/delivery or maturity date match exactly (basis will be 0) Delta Hedge – Closing a future before maturity, will be a basis Cross Hedge – Uses futures with a different underlying Optimal Hedge Ratio - - h* is optimal ratio, std dev S is the std dev of Delta S, the change in the spot price during the hedging period. Std dev F is std dev of Delta F, the change in the futures price during hedging per. P is coefficient of correlation bet. Delta S and Delta F. Portfolio Hedging using Index (Q9) --> ( β ̂ _current- β ̂ _desired) V_A/V_F PV / FV formulas? Which is negative? pv Coupon Bond Yield (Q12) – Remember to make redemption 100 in excel formula