Spring-03 Investments Zvi Wiener tel: Term Structure of Interest Rates BKM Ch 15

Zvi WienerBKM Ch 15 slide 2 Yields Maturity Upward Sloping Downward Sloping Flat Yield Curves

Zvi WienerBKM Ch 15 slide 3 Expected Interest Rates in Coming Years (Table 15.1) Expected One-Year Rates in Coming Years YearInterest Rate 0 (today) 8% 110% 211% 311%

Zvi WienerBKM Ch 15 slide 4 Pricing of Bonds using forward Rates PV n = Present Value of $1 in n periods r 1 = One-year rate for period 1 r 2 = One-year rate for period 2 r n = One-year rate for period n

Zvi WienerBKM Ch 15 slide 5 Forward Rates y 1 =8% y 2 =8.995% y 3 =9.660% y 4 =9.993% r 1 =8% r 2 =10% r 3 =11% r 4 =11%

Zvi WienerBKM Ch 15 slide 6 f n = one-year forward rate for period n y n = yield for a security with a maturity of n Forward Rates from Observed Long-Term Rates

Zvi WienerBKM Ch 15 slide 7 Forward rates Take a forward loan at S of 1 and repay it at T

Zvi WienerBKM Ch 15 slide 8 Instantaneous forward rates

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Zvi WienerBKM Ch 15 slide 11 Example of Forward Rates using Table 15.2 Numbers 4 yr = yr = 9.660fn = ? (1.0993) 4 = (1.0966) 3 (1+f n ) ( ) / ( ) = (1+f n ) f n = or 11% Note: this is expected rate that was used in the prior example.

Zvi WienerBKM Ch 15 slide 12 Downward Sloping Spot Yield Curve Zero-Coupon RatesBond Maturity 12% % % %4 9.25%5

Zvi WienerBKM Ch 15 slide 13 Forward Rates for Downward Sloping Yield Curve 1yr Forward Rates 1yr[(1.1175) 2 / 1.12] - 1 = yrs[(1.1125) 3 / (1.1175) 2 ] - 1 = yrs[(1.1) 4 / (1.1125) 3 ] - 1 = yrs[(1.0925) 5 / (1.1) 4 ] - 1 =

Zvi WienerBKM Ch 15 slide 14 Expectations Liquidity Preference Upward bias over expectations Market Segmentation Preferred Habitat Theories of Term Structure

Zvi WienerBKM Ch 15 slide 15 Expectations Theory Observed long-term rate is a function of today’s short-term rate and expected future short-term rates. Long-term and short-term securities are perfect substitutes. Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.

Zvi WienerBKM Ch 15 slide 16 Long-term bonds are more risky. Investors will demand a premium for the risk associated with long-term bonds. The yield curve has an upward bias built into the long-term rates because of the risk premium. Forward rates contain a liquidity premium and are not equal to expected future short-term rates. Liquidity Premium Theory

Zvi WienerBKM Ch 15 slide 17 Liquidity Premiums and Yield Curves Yields Maturity Liquidity Premium Forward Rates Observed Yield Curve

Zvi WienerBKM Ch 15 slide 18 Liquidity Premiums and Yield Curves Yields Maturity Liquidity Premium Forward Rates Observed Yield Curve

Zvi WienerBKM Ch 15 slide 19 Short- and long-term bonds are traded in distinct markets. Trading in the distinct segments determines the various rates. Observed rates are not directly influenced by expectations. Preferred Habitat: Modification of market segmentation Investors will switch out of preferred maturity segments if premiums are adequate. Market Segmentation and Preferred Habitat

Zvi WienerBKM Ch 15 slide 20 Using Spot Rates to Price Coupon Bonds A coupon bond can be viewed as a series of zero coupon bonds. To find the value each payment is discount at the zero coupon rate. Once the bond value is found, one can solve for the yield. It’s the reason that similar maturity and default risk bonds sell at different yields to maturity.

Zvi WienerBKM Ch 15 slide 21 Chapter 15 Weblinks This site contains a good source for current rates, the current and past yield curves, and explanations of how the shape of the yield curve can affect economic performance. It also has a summary of current economic factors that are influencing rates. The site listed above has price and yield curve information and the ability to chart Treasury securities over time The site listed above has price and yield curve information and the ability to chart Treasury securities over time. The site listed above has price and yield curve information and the ability to chart Treasury securities over time. Historical information on interest rates and other economic factors are available in the Federal Reserve Economic Data Base (FRED) at the address shown above. Data in FRED can be downloaded in a spreadsheet format.

Zvi WienerBKM Ch 15 slide 22 Summary Term structure of interest rates Zero-coupon Government or LIBOR-Swap Spread for risky bonds OAS for bonds with embedded options Forward rates Expectation, Liquidity, Segmentation Impact of taxation

Zvi WienerBKM Ch 15 slide 23 Home At you can download SPOTYA.XLS file that demonstrates the bootstrapping technique used for derivation of zero coupon curve from coupon bonds.

Zvi WienerBKM Ch 15 slide 24 Home Assignment Required: problems 3, 5, 9, 13, 17 (3 rd ed). problems 4, 6, 12, 17, 22 (5 th ed). closely follow financial news! Recommended: read ML publication on world bond markets visit recommended web links

Zvi WienerBKM Ch 15 slide 25 TreasuriesInvestment gradeSwap ParSpeculative grade144A Strips, zerosYield VolatilityCallable LIBORPuttable SpreadCP, CD TIPSFloater SecuritizationGNMA, MBA ConvertibleDefault risk

Zvi WienerBKM Ch 15 slide 26 End

Zvi WienerBKM Ch 15 slide 27 Rating companies Moody’s Investor Service Standard & Poor’s Duff and Phelps Fitch Rating Categories Investment grade Speculative grade Default Risk and Ratings Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

Zvi WienerBKM Ch 15 slide 28 Straight bond Floater

Zvi WienerBKM Ch 15 slide 29 How to treat Floaters Floater is similar to a constantly renewed loan with fixed spread (!). Thus the yield of a floater is equal to the yield on the basis plus the spread. Note that some of the Israeli government bonds have funny linkage to other bonds.

Zvi WienerBKM Ch 15 slide 30 Reverse (Inverse) Floater USD 5 year interest rates are 5%, however short term interest rates are Libor =2%. Libor = London Interbank offered rate on Bloomberg see FWCV + currency One can construct so-called reverse floater:

Zvi WienerBKM Ch 15 slide 31 Reverse Floater Years bond loan L 0 -L 1 -L 2 -L L 4 Reverse Fl L 1 10-L 2 10-L L 4 bond

Zvi WienerBKM Ch 15 slide 32 Features of Corporate Bonds (indentures) Corporate trustee – represents bondholders Term bonds – maturity Under 10 years – notes Some bonds have specific collateral Others are debentures Guaranteed bonds (third party’s guarantees)

Zvi WienerBKM Ch 15 slide 33 SEC rule 144A Allows to trade private placements among qualified institutions.

Zvi WienerBKM Ch 15 slide 34 Medium Term Notes (MTN) Notes are registered with the SEC under Rule 415 (the shelf registration) and are offered continuously to investors by an agent of the issuer. Maturities vary from 9 months to 30 years. Can be either fixed or floating. Very flexible way to raise debt!

Zvi WienerBKM Ch 15 slide 35 Primary Market (MTN) Issuer posts spreads over Treasuries for a variety of maturities. Then an agent tries to find an investor. Minimal size is between $1M and $25M. The schedule can be changed at any time! Often structured MTNs are used (caps, floors, etc.) = structured notes.

Zvi WienerBKM Ch 15 slide 36 Structured Notes Many institutional investors can use swaps and structured notes to participate in markets that were prohibited. Another use of structured notes is in risk management. Financial Engineering is used to create securities satisfying the needs of investors.

Zvi WienerBKM Ch 15 slide 37 Commercial Papers Short term debt issued with less documentation typically by large and stable corporations for up to 270 days. Much cheaper borrowing than banks. Bridge financing. Rollover Risk An alternative to CD.

Zvi WienerBKM Ch 15 slide 38 Commercial Papers Short term unsecured promissory note An alternative to short term bank borrowing A typical round-lot transaction is $100,000 In the USA maturity is up to 270 days Requires less paperwork Those with maturity up to 90 days can be used as collateral for FED discount window.

Zvi WienerBKM Ch 15 slide 39 Commercial Papers Typically rolled over Rollover risk is backed by an unused bank credit line In order to issue CP one need either a high rating or good collateral Sometimes credit enhancement is used (LOC) CP issued in the USA by foreigners are called Yankee CP

Zvi WienerBKM Ch 15 slide 40 Commercial Papers Between 71 an 89 there was one default on CP. 3 defaults occurred in 89 and 4 in 90 Direct paper is sold without an agent Secondary market is thin There is a special rating for CP, P-1,3, A-1,3 discount instruments, used by money market

Zvi WienerBKM Ch 15 slide 41 Bankruptcy and Creditor Rights liquidation (Chapter 7) - all assets will be distributed reorganization (Chapter 11) - a new corporate entity will result a company that files for protection becomes a debtor in possession and continues to operate under the supervision of the court

Zvi WienerBKM Ch 15 slide 42 Bankruptcy and Credit Rights Absolute priority rule - senior creditors are paid in full before junior creditors are paid anything. Works in liquidation but often does not work in reorganization.

Zvi WienerBKM Ch 15 slide 43 Merton’s model DVDV $ equity debt firm

Zvi WienerBKM Ch 15 slide 44 Government Sponsored Enterprises Federal Home Loan Bank System Federal National Mortgage Association Federal Home Loan Mortgage Corporation Federal Farm Credit Bank System