Interest rate futures Treasury Bills Future

Interest rate futures Treasury Bills Future - Transcript

Derivatives Management Topic 6 Interest rate futures TB futures

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Objectives
Distinguish between discount yield and bond equivalent yield Know how to hedge and speculate with treasury bill futures Familiarise with arbitrage between treasury bill futures and repo

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A note on interest rate futures
Interest rates can be viewed as returns on fixed income securities so buying and selling returns is difficult However the prices of fixed income securities imply interest rates trading fixed income securities allows expressing one s view on the future movements of interest rates
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A note on interest rate futures
Prices of fixed income securities have an inverse relationship with interest rates so an expected rise in interest rate would lead to sale of fixed income securities Interest rate futures are not the only financial derivatives that allows buying and selling interest rates interest rate swaps interest rate floors caps etc
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Treasury bills TBs
Duration 3 or 6 month Sold at a discount of the par value and redeemed at par Proceeds are normally used for adjusting the government s foreign exchange reserves

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TBs discount yield calculation
Market practice quote discount yield on a 360 day basis Discount yield par market price par 360 days Bond equivalent yield par market price market price 365 days
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Example
The 26 week TB auctioned on February 9 was told at 96 775 per 100 face value The bill had 182 days to maturity What are the discount yield and the bond equivalent yield Discount yield 1 96 775 100 360 182 0 0638 6 38

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Bond equivalent yield
Bond equivalent yield 100 96 775 1 365 182 0 0668 6 68 Given discount yield calculate the market price The TB with a maturity of 180 days is quoted at 5 What is the market price P F F DY t 360 100 100 5 0 5 97 5
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FT quotation
18 Sep Open Sett Change High low Sterling 93 89 93 84 0 04 3m Dec 08 Sterling 94 33 94 21 0 11 3m Mar 08 Sterling 94 51 94 36 0 13 3m Jun 08 Sterling 94 57 94 42 0 12 3m Sep 08
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93 89 93 80 94 33 94 18 94 51 94 33 94 57 94 40

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TB futures price
N X N 360 D percentage quote Where N nominal price of the contract face value X actual price of the contract D days to mature X N 1 D 360

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Example from FT quotation
3 month Sterling deliverable in December 500000 X 500000 360 91 10093 84 X 492214 44 500000 X 500000 360 91 10093 845 X 492220 76
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TB futures price
3 month Sterling deliverable in March
500000 X 500000 360 91 10094 21 X 492682 08 Jun 492871 67 Sep 492947 5
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Speculating with TB futures
Example On September 2 Luma Al Badri predicted a drop in short term interest rate She bought one December 3 month short sterling futures contract at 93 95 face value 500 000 One week later the shortterm interest rate fell and the December contract was traded at 94 45 Calculate Luma s profit from such strategy

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Speculating with TB futures
Price of 3m short sterling futures on Sep 2

500000 X1 500000 360 91 10093 95 X1 492353 47 buy One week later 500000 X2 500000 360 91 10094 45 X2 492985 42 sell Profit X2 X1 631 95
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Hedging with TB futures
V need to pay 500 000 in 3 months and V wanted to lock in the current interest rate 5 65 3 months later the interest rate rose to 6 1 Calculate the gains from this strategy

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Hedging with TB futures
Current 500000 X1 500000 360 91 5 65 X1 492859 03 sell 3 month later 500000 X2 500000 360 91 6 1 X2 492290 28 buy Profit X1 X2 568 75
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Arbitrage with TB futures and repo
Similar to stock index futures there is also an arbitrage mechanism in TB futures market to restore prices when they deviate from theoretical level However the arbitrage process cannot be complete without repurchase agreement repo

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Example of repurchase agreement
Donnie Darko is a government securities dealer who needs to finance 10million of a TB that it purchased and plans to hold overnight One of his customers has excess funds for funding Donnie would agree to deliver sell 10million of the TB to the customer for an amount determined by the repo rate and buy repurchase the same TB for 10million Suppose the repo rate is 6 5
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Repo interest
Formula for calculating repo interest I F I repo rate days 360 Where I interest F face value I 10000000 I 6 5 1 360 I 1805 23 So Donnie would have to sell the TB for about 9 998 195 and buy it back for the face value 10million
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A note on repo
Donnie can normally retain the TB and just pay the interest in the end The TB is however used as collateral for the borrowing Due to the collateral repo rates are sometimes used as risk free rates By retaining the TB repurchasers could have a leveraged position

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Reconciling futures and TB prices
Discount yield for 45 day TB is 5 75 Discount yield for 136 day TB is 5 9 P45 100 5 75 45 360 99 2813 Yield for 45 days 100 99 2813 99 2813 0 007239 P136 100 5 9 136 360 97 7711 Yield for 136 days 100 97 7711 97 7711 0 022797
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The structure of interest rates
1 Rt k 1 Rt 1 Rk Where Rt k interest rate on period t k Rt interest rate on period t Rk interest rate on period k 1 Invest in a security with 136 day maturity 2 Invest in a security with 45 day maturity then invest in another security with 91 day maturity In theory 1 and 2 should give identical yield
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Implied futures price
Theoretical price of a 91 day TB Futures contract mature in 45 days 1 022797 1 007239 1 R91 R91 0 015446 P91 100 1 015446 98 4789 Futures discount yield 1 0 984789 1 360 91 0 060175 6 0175
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Arbitrage opportunity
Discount yield for 45 day TB is 5 75 Discount yield for 136 day TB is 5 9 Discount yield for 91 day TB futures deliverable in 45 days is 5 9 The price of 91 day TB futures contract is 1 P91 100 360 91 5 9 P91 98 5086
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Arbitrage opportunity
Compared to the implied futures price 98 4789 the actual futures contracts are overpriced So Sell 91 day futures contracts Buy 136 day TB Short sell 45 day TB using Repo
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Repo interest
45 day TB discount yield 5 75 F I 977 711 11

I 977 711 11 5 75 45 360 7027 299

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Arbitrage
Today Short sell 45 day TB Buy 136 day TB Sell futures 94 1 Net cash flow
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977 711 11 977 711 11 0 0
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Arbitrage
45 days later Deliver TB on short futures contract Repay Repo principal Repo interest payment Total profit
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985 086 977 711 11 7027 30 347 59
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Futures underpriced
Suppose in the previous example the discount yield for 91 day TB futures deliverable in 45 days is 6 25 The price of the futures contract is 1 P91 100 360 91 6 25 P91 98 4201 underpriced

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Futures underpriced
Strategy Buy futures Buy 45 day TB Short sell 136 day TB by repo Since the price of 45 day TB is 99 2813 for simplicity assume the arbitrageur use repo to borrow 992 813 to buy 10000 45 day TB and 136 day TB can be infinitely divisible to cover this amount without the transfer of collateral this is plausible
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Futures underpriced
At the time of the settlement of futures contract the amount from repayment of 45 day TB is 1 million some fraction of futures contract was needed when the arbitrage position was opened i e buy 1 million futures 98 4201

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Futures underpriced
Today Short sell 136 day TB Buy 45 day TB Sell futures 93 75 Net cash flow
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992 813 992 813 0 0
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Futures underpriced
45 days later Receive 91 day TB from futures Repayment of 45 day TB plus interest Net cash flow
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1 000 000 1 000 000 0
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Futures underpriced
136 days later Repay Repo principal Repo interest payment Principal of 91 day TB Interest of 91 day TB Total profit
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992 813 22 128 7 1 000 000 15798 61 856 91
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