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Interest Rates Futures

Interest Rates Futures. Fin 288 Futures Options and Swaps. Interest Rate Future Contracts. Traded on the CBOT 30 Year Treasury Bond &30 Yr Mini 10, 5, & 2 year Treasury note futures 30 Day Fed Funds 5 & 10 year Swap German Debt Traded on CME Eurodollar Futures.

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Interest Rates Futures

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  1. Interest Rates Futures Fin 288 Futures Options and Swaps

  2. Interest Rate Future Contracts • Traded on the CBOT • 30 Year Treasury Bond &30 Yr Mini • 10, 5, & 2 year Treasury note futures • 30 Day Fed Funds • 5 & 10 year Swap • German Debt • Traded on CME • Eurodollar Futures

  3. A quick look at contract Specifications • Treasury Bonds and Notes- • Range of delivery dates • Fed Funds Futures • Price • Swaps • Delivery • Muni • Underlying Asset

  4. Treasury Securities • Since a majority of the interest rate instruments we will use are related to treasury securities, we need to discuss some basics relating to the pricing of Treasury securities.

  5. Some Pricing Issues • Day Count Conventions • Used to determine the interest earned between two points in time • Useful in calculating accrued interest • Specified as X/Y • X = the number of days between the two dates • Y = The total number of days in the reference period

  6. Day Count Conventions

  7. Price Quotes for Treasury Bills • Let Yd = annualized yield, D = Dollar Discount F= Face Value, t = number of days until maturity • Price = F -D

  8. Price Quotes on T- Bills • Note: Return was based on face value invested, not the actual amount invested. • 360 day convention makes it difficult to compare to notes and bonds. • CD equivalent yield makes the measure comparable to other money market instruments

  9. Accrued Interest • When purchasing a bond between coupon payments the purchaser must compensate the owner for for interest earned, but not received, since the last coupon payment

  10. Price Quotations • QuotationsThe quoted and cash price are not the same due to interest that accrues on the bond. In general:

  11. Example • Assume that today is March 5, 2002 and that the bond matures on July 10, 2004 • Assume we have an 11% coupon bond with a face value of $100. The quoted price is 90-05 (or 90 5/32 or 90.15625) • Bonds with a total face value of $100,000 would sell for $90,156.25.

  12. Example continued • Coupons on treasuries are semiannual. Assume that the next coupon date would be July 10, 2000 or 54 days from March 5. • The number of days between interest payments is 181 so using the actual/actual method we have accrued interest of (54/181)(5.50) = $1.64 The cash price is then $91.79625 = $90.15625 + $1.64

  13. Conversion Factors • Since there are a range of bonds that can be delivered, the quoted futures price is adjusted by a conversion factor.

  14. Price based upon 6% YTM • The conversion factor is based off an assumption of a flat yield curve of 6% (that interest rates for all maturities equals 6%). • By comparing the value of the bond to the face value, the CBOT produces a table of conversion factors.

  15. Conversion Factor Continued • The maturity of the bond is rounded down to the nearest three months. • If the bond lasts for a period divisible by 6 months the first coupon payment is assumed to be paid in six months. (A bond with 10 years and 2 months would be assumed to have 10 years left to maturity)

  16. Conversion Factor continued • If the bond does not round to an exact six months the first coupon is assumed to be paid in three months and accrued interest is subtracted. • A bond with 14 years and 4 months to maturity would be treated as if it had 14 years and three months left to maturity

  17. Example 1 • 14% coupon bond with 20 years and two months to maturity • Assuming a 100 face value the value of the bond would equal the price valued at 6%: The conversion factor is then 1.92459/100 = 1.92459

  18. Example 2 • What if the bond had 18 years and four months left to maturity? The bond would be considered to have 18 years and three months left to maturity with the first payment due in three months.Finding the value of the bond three months from today

  19. Example 2 continued Assume the rate for three months is (1+r)2 = 1.03 r = .014889 Using this rate it is easy to find the PV of the bond 187.329/1.014889 = 184.581 There is one half of a coupon in accrued interest so we need to subtract 7/2=3.50 184.581 - 3.50 = 181.081 resulting in a conversion factor of 181.081/100 = 1.81081

  20. Price Quote on T-Bills • Quotes on T- Bills utilize the actual /360 day count convention. • The quoted price of the treasury bill is an annualized rate of return expressed as a percentage of the face value.

  21. T- Bills continued The quote price is given by (360/n)(100-Y) where Y is the cash price of the bill with n days until maturity 90 day T- Bill Y = 98 (360/90)(100-98) =8.00

  22. Rate of Return • The quote is not the same as the rate of return earned by the treasury bill. • The rate of interest needs to be converted to a quarterly compounding annual rate. 2/98(365/90) = .0828

  23. Quoted Price • The price quote on a Treasury bill is then given by 100 - Corresponding Treasury bill price quote (quoted price = 8 so futures quote =92) Given Z = the quoted futures priceY = the corresponding price paid for delivery of $100 of 90 day treasury bills thenZ = 100-4(100-Y) or Y = 100-0.25(100-Z)Z = 100-4(100-98) = 92

  24. Cheapest to Deliver Bond • There are a large number of bonds that could be delivered on the CBOT for a given futures contract. • The party holding a short position gets to decide which bond to deliver and therefore has incentive to deliver the cheapest.

  25. Cheapest to Deliver • Upon delivery the short position receives The cost of purchasing a bond is Quoted bond price + accrued interestBy minimizing the difference between the cost and the amount received, the party effectively delivers the cheapest bond:

  26. Cheapest to deliver The bond for which is minimized is the one that is cheapest to deliver.

  27. Example: Cheapest to Deliver Consider 3 bonds all of which could be delivered Quoted Conversion Bond Price Factor 1 99.5 1.0382 99.5-(93.25(1.0382)) =2.69 2 143.5 1.5188 143.5-(93.25(1.5188))=1.87 3 119.75 1.2615 119.75-(93.25(1.2615))=2.12

  28. Impact of yield changes on CTD • As yield increases bonds with a low coupons and longer maturities become relatively cheaper to deliver. As rates increase all bond prices decrease, but the price decrease for the longer maturity bonds is greater • As yields decrease high coupon, short maturity bonds become relatively cheaper to deliver.

  29. Wild Card Play • Trading at the CBOT closes at 2p.m. however treasury bonds continue to trade until 4:00pm and a party with a short position has until 8pm to file a notice of intention to deliver. • Since the price is calculated on the closing price in the CBOT the party with a short position sometimes has the opportunity to profit from price movements after the closing of the CBOT. • If the Bond Prices decrease after 2 pm it improves the short position.

  30. Eurodollar Futures • Eurodollar – dollar deposited in a foreign bank outside of the US. Eurodollar interest rate is the interest earned on Eurodollars deposited by one bank with another bank. • London Interbank Offer Rate (LIBOR) – Rate at which banks loan to each other in the London Interbank Market.

  31. Simple Hedge Example • Assume you know that you will owe at rate equal to the LIBOR + 100 basis points in three months on a notional amount of $100 Million. The interest expenses will be set at the LIBOR rate in three months. • Current three month LIBOR is 7%, Eurodollar futures contract is selling at 92.90.

  32. Simple Hedge Example 100 - 92.90 = 7.10 The futures contract is paying 7.10% Assume the interest rate may either increase to 8% or decrease to 6%

  33. A Short Hedge • Agree to sell 10 Eurodollar future contracts (each with an underlying value of $1 Million). • We want to look at two results the spot market and the futures market. Assume you close out the futures position and that the futures price will converge to the spot at the end of the three months.

  34. Rates increase to 8% Spot position: Need to pay 8% + 1% = 9% on $10 Million $10 Million(.09/4) = $225,000 Futures Position: Fut Price = $92 interest rates increased by .9% Close out futures position: profit = ($10 million)(.009/4) = $22,500

  35. Rates Increase to 8% Net interest paid $225,000 - $22,500 = $202,500 $10 million(.0810/4) = $202,500

  36. Rates decrease to 6% Spot position: Need to pay 6% + 1% = 7% on $10 Million $10 Million(.07/4) = $175,000 Futures Position: Fut Price = $94 interest rates decreased by 1.1% Close out futures position: loss = ($10 million)(.011/4) = $27,500

  37. Rates Decrease to 8% Net interest paid $175,000 + $27,500 = $202,500 $10 million(.0810/4) = $202,500

  38. Results of Hedge • Either way the final interest rate expense was equal to 8.10 % or 100 basis points above the initial futures rate of 7.10% • Should the position be hedged? • It locks in the interest rate, but if rates had declined you were better off without the hedge.

  39. Simple Example 2 • On January 2 the treasurer of Ajax Enterprises knows that the firm will need to borrow in June to cover seasonal variation in sales. She anticipates borrowing $1million. • The contractual rate on the loan will be the LIBOR rate plus 1% • The current 3 month LIBOR rate is 3.75% and the Eurodollar futures contract is 4.25%

  40. Simple Example 2 Continued • To hedge the position assume the treasurer sells one June futures contract. • Assume interest rates increase to 5.5% on June 13. • Assume that the expiration of the contract is June 13, the same day that the loan will be taken out. The futures price will be 100-5.50 = 94.50

  41. Rates increase to 5.5% Spot position: Need to pay 5.5%+1%= 6.5% on $1 Million $1 Million(.065/4) = $16,250 Futures Position: Fut Price = $94.50 interest rates increased by 1.25% Close out futures position: profit = ($1million)(.0125/4) = $3,125

  42. Rates Increase to 5.5% Net interest paid $16,250 - $3,125 = $13,125 $1 million(.0525/4) = $13,125 which is the interest rate implied by the Eurodollar futures contract 4.25% +1% = 5.25%

  43. Assumptions • The hedge worked because of three assumptions: • The underlying exposure is to the three month LIBOR which is the same as the loan • The end of the exposure matches the delivery date exactly • The margin account did not change since the rate changed on the last day of trading.

  44. Basis Risk revisited • The basis is a hedging situation is defined as the Spot price of the asset to be hedged minus the futures price of the contract used. When the asset that is being hedged is the same as the asset underlying the futures contract the basis should be zero at the expiration of the contract. Basis = Spot - Futures

  45. Basis Risk • On what types of contracts would you expect the basis to be negative? Positive? Why?(-) Low interest rates assets such as currencies or gold or silver (investment type assets with little or zero convenience yield. F = S(1+r)T(+) Commodities and investments with high interest rates (high convenience yield) F = S(1+r+u)T Implies it is more likely that F < S(1+r+u)T

  46. Mismatch of Maturities 1 • Assume that the maturity of the contract does not match the timing of the underlying commitment. • Assume that the loan is anticipated to be needed on June 1 instead of June 13.

  47. Simple Example Redone • On January 2 the treasurer of Ajax Enterprises knows that the firm will need to borrow in June to cover seasonal variation in sales. She anticipates borrowing $1million. • The contractual rate on the loan will be the LIBOR rate plus 1% • The current 3 month LIBOR rate is 3.75% and the Eurodollar futures contract is 4.25%

  48. Simple Example 2 Continued • To hedge the position assume the treasurer sells one June futures contract. • Assume interest rates increase to 5.5% on June 1. • Assume that the futures price has decreased to 94.75 (before it had decreased to 94.50) implying a 5.25% rate (a 25 bp basis)

  49. Rates increase to 5.5% Spot position: Need to pay 5.5%+1%= 6.5% on $1 Million $1 Million(.065/4) = $16,250 Futures Position: Fut Price = $94.75 interest rates increased by 1.00% Close out futures position: profit = ($1million)(.0100/4) = $2,500

  50. Rates Increase to 5.5% Net interest paid $16,250 - $2,500 = $13,750 $1 million(.055/4) = $13,750 which is more than the interest rate implied by the Eurodollar futures contract 4.25% +1% = 5.25%

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