Fixed Income Analysis

Session 12 Controlling Interest Rate Risks with Derivatives

Controlling Interest Rate Risk with Derivatives

by Frank J. Fabozzi, Shrikant Ramamurthy, and Mark Pitts

Copyright 2007 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express permission of the copyright owner is unlawful. Request for futher information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.

PowerPoint Slides byDavid S. Krause, Ph.D., Marquette University

Chapter 22Controlling Interest Rate Risk with Derivatives

• Major learning outcomes:– Identify the advantages of using interest rate

futures rather than Treasury securities to control the interest rate risk of a portfolio.

– Explain the basic principles of controlling interest rate risk.

Key Learning Outcomes

• Determine the position in a futures contract that adjusts the current dollar duration of a portfolio to that of the target dollar duration.

• Calculate the number of futures contracts that must be bought or sold in order to achieve a portfolio’s target duration.

• Compute the dollar duration of a futures contract.

Key Learning Outcomes

• Explain why hedging is a special case of controlling interest rate risk.

• Describe a short hedge and a long hedge and explain when each hedge is used.

• Explain what a cross hedge is.

• Identify the steps in the hedging process.

• Identify the factors that are important for determining the appropriate hedging instrument.

Key Learning Outcomes

• Describe the typical shape of a credit describe basis risk and explain why hedging with futures substitutes basis risk for price risk.

• Describe which price or rate is locked in when hedging with a futures contract.

• Describe convergence for a futures contract.

• Calculate the number of futures contracts that must be sold to hedge a position against a rise in interest rates.

Key Learning Outcomes

• Explain how the position in a Treasury bond futures contract is adjusted for the cheapest-to-deliver issue.

• Explain why an assumption must be made about the yield spread between a bond to be hedged and the hedging instrument.

• Describe yield beta and explain how it is used to adjust the number of futures contracts in a hedge.

• Identify the major sources of hedging error.

• Show how the cash flows of an entity can be altered using an interest rate swap.

Why Derivatives?

• Selling futures decreases portfolio’s exposure to rate changes

• Advantages of futures to treasuries– Lower transaction costs– Greater leverage allowed (lower margins req.)– Easier to sell short– Can construct longer duration portfolios

Buy or Sell?

• If target dollar duration is greater than current dollar duration then buy futures.

• If target dollar duration is less than current dollar duration then sell futures.

Hedging w/ Interest Rate Futures

• For a perfect hedge you want the target duration to equal 0.

• Short hedge (sell futures)– Protects against decline in cash price of bond

• Long hedge (buy futures)– Protects against rise in cash price of bond

4-Step Process

• Step 1 – Determine the appropriate hedge instrument

– Correlation between future contract & interest rates

– Liquidity

4-Step Process - Continued

• Step 2 – Determine target– Hedges held to delivery• Convergence at maturity (Spot price = Futures price)• Effective price based on the futures rate the day hedge

is set.

– Hedges with short holding periods (1 day)• Lock in the 1-day forward rate ≈ spot rate

4-Step Process - Continued

• Step 3 - Determine the position to take– Hedge ratio is the number of futures contracts

needed for the hedge• CTD - Cheapest-to-deliver

Current dollar duration w/o futuresDollar duration of CTD issueHedge ratio = - x Conversion factor for CTD issue Yield betax

4-Step Process - Continued

• Step 4 – Monitor & evaluate the hedge– Evaluate hedge performance once hedge has been

lifted– 3 Types of error• Dollar duration for hedge instrument was incorrect• The projected basis at time of hedge removal was

incorrect• Parameters estimated from regression can be incorrect

Hedging with Swaps

• Used to more closely match cash flows from assets with cash flows from liabilities

• Dollar duration– Pay floating & receive fixed • Increased dollar duration by roughly the dollar duration

of underlying fixed-rate bond

– Pay fixed & receive floating• Decreases dollar duration by roughly the dollar

duration of the fixed-rate bond

Hedging with Options

• Steps to option hedging– Determine the options contract to use– Find appropriate strike price– Determine the # of contracts

• 3 Basic strategies– Protective put buying– Covered call writing– Collar strategy

Protective Put Buying• Similar to buying insurance– It limits the potential downside– Leaves unlimited upside potential

Covered Call Writing• Give up some or all of the upside potential for

a cushion on the downside

Collar Strategy• Combines protective put buying and covered

call writing– Limits the potential downside but also gives up

the potential upside, using the premiums collected to offset any downside

Selecting the Best Strategy

• Based on the managers view of future markets and risk tolerance– Bearish = Purchase a put– Neutral to Mildly Bearish = Sell covered calls– No view & little risk tolerance = Futures hedge– Bullish = Unhedged

Selecting the Best Strategy

• The best options contract to use in a hedging strategy depends upon the option price, liquidity, and correlation with the bond(s) to be hedged.

• For a cross hedge, the manager converts the strike price for the options that are bought or sold into an equivalent strike price for the actual bonds being hedged.

Selecting the Best Strategy

• When using Treasury bond futures options, the hedge ratio is based on the relative dollar duration of the current portfolio, the cheapest-to-deliver issue, the futures contract at the option expiration date, and the conversion factor for the cheapest-to-deliver issue.

Futures Option Hedging• While there are some mechanical differences in the way

options on physicals and options on futures are traded and there may be substantial differences in their liquidity, the basic economics of the hedging strategies are virtually identical for both contracts.

• Using options on physicals frequently eliminates much of the basis risk associated with an options hedge.

• An interest rate floor can be used to establish a minimum rate for a floating-rate security. An interest rate cap can be used to set a maximum funding cost.

Caps and Floors

• One strategy is to sell a cap and buy a floor or buy a cap and sell a floor– This strategy uses the premium collected to offset

the cost and creates a collar• By taking only one position– Limits the downside while retaining the upside

minus the premium paid for the position