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THE STRUCTURE OF INTEREST RATES

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THE STRUCTURE OF INTEREST RATES

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    1. CHAPTER 6 THE STRUCTURE OF INTEREST RATES

    2. Finance 308 2 Interest Rate Changes & Differences Between Interest Rates Can Be Explained by Several Variables Term to Maturity. Default Risk. Tax Treatment. Marketability. Call or Put Features. Convertibility.

    3. Finance 308 3 Need to Understand Yields Individual and institutional investors must understand why quoted yields vary so they can determine whether the extra yield is worth the risk. Financial managers of corporations or government agencies in need of funds must understand why quoted yields vary, so they can estimate the yield they would have to offer in order to sell new debt securities.

    4. Finance 308 4 Selected Rates of Interest, February 9, 2005 (Wall Street Journal)

    5. Finance 308 5 Selected Rates of Interest, February 9, 2005 (Wall Street Journal)

    6. Finance 308 6 Yield Curve The Term to Maturity of a financial claim is the length of time until the principal amount becomes payable. The relationship between yield and Term to Maturity on securities that differ only in length of time to maturity is called the Term Structure of Interest Rates. Shown by the Yield Curve. The Yield Curve is the graph of the relationship between interest rates on particular securities and their yield to maturity. Same default risk.

    7. Finance 308 7 Term (Maturity) Structure May Be Studied Visually by Plotting a Yield Curve at a Point in Time The yield curve may be ascending, flat, or descending. Several theories explain the shape of the yield curve.

    8. Finance 308 8 Yield Curves in the 2000s

    9. Finance 308 9 Yield Curve (February 10, 2005)

    10. Finance 308 10 The Expectations Theory of the Term Structure The slope of the yield curve reflects investors’ expectations about future interest rates. Ascending: future interest rates are expected to increase. Descending: future interest rates are expected to decrease. Long-term interest rates represent the geometric average of current and expected future (implied, forward) interest rates.

    11. Finance 308 11 The Expectations Theory of Term Structure (concluded) Investors are assumed to trade in a very efficient market with excellent information and minimal trading costs. Other theories discussed later presume less efficient markets.

    12. Finance 308 12 Expectations Theory Notations

    13. Finance 308 13 Term Structure Formula from Expectation Theory

    14. Finance 308 14 An Implied One Year Forward Rate From the Term Structure Formula

    15. Finance 308 15 Finding a One-Year Implied Forward Rate Using term structure of interest rates from January 29, 1999, find the one-year implied forward rate for year three. 1-year Treasury bill 4.51% 2-year Treasury note 4.58% 3-year Treasury note 4.57%

    16. Finance 308 16 Expectations Theory Calculations

    17. Finance 308 17 Liquidity Premium Theory Long-term securities have greater risk and investors require greater premiums to give up liquidity. Long-term securities have greater price variability. Long-term securities have less marketability. The liquidity premium explains an upward sloping yield curve. Investors are not indifferent between purchasing long-term vs. short term securities

    18. Finance 308 18 Liquidity Premium Theory (Concluded) Today’s long-term rates reflect the geometric average of intervening short-term rates plus a premium that investors demand for holding long-term securities instead of a series of short-term risky investments. The liquidity premium increases as maturity increases, because the longer the maturity of a security, the greater its price risk. Thus, an investor would not be indifferent between a 5-year bond and a series of five 1-year bonds.

    19. Finance 308 19 Market Segmentation Theory Maturity preferences by investors may affect security prices (yields), explaining variations in yields by time Market participants have strong preferences for securities of particular maturity and buy and sell securities consistent with their maturity preferences. If market participants do not trade outside their maturity preferences, then discontinuities are possible in the yield curve.

    20. Finance 308 20 Market Segmentation Theory (Concluded) For instance, commercial banks may prefer short-term investments while pension funds and life insurance companies make generally long-term investments that coincide with their long-term liabilities.

    21. Finance 308 21 Preferred Habitat Theory The Preferred Habitat Theory is an extension of the Market Segmentation Theory. The Preferred Habitat Theory allows market participants to trade outside of their preferred maturity if adequately compensated for the additional risk. The Preferred Habitat Theory allows for humps or twists in the yield curve, but limits the discontinuities possible under Segmentation Theory.

    22. Finance 308 22 Which Theory is Right? Day-to-day changes in the term structure are most consistent with the Preferred Habitat Theory. However, in the long-run, expectations of future interest rates and liquidity premiums are important components of the position and shape of the yield curve.

    23. Finance 308 23 Yield Curves and the Business Cycle Interest rates are directly related to the level of economic activity. An ascending yield curve notes the market expectations of economic expansion and/or inflation. A descending yield curve forecasts lower rates possibly related to slower economic growth or lower inflation rates. Security markets respond to updated new information and expectations and reflect their reactions in security prices and yields.

    24. Finance 308 24 Interest-rate and Yield-curve Patterns Over the Business Cycle

    25. Finance 308 25 Default Risk Is the Probability of the DSU Not Honoring the Security Contract Losses may range from “interest a few days late” to a complete loss of principal. Risk averse investors want adequate compensation for expected default losses. Measured as the difference paid on a risky security and the rate paid on a default-free security, all other factors held constant.

    26. Finance 308 26 Default Risk, cont. Investors charge a default risk premium (above riskless or less risky securities) for added risk assumed DRP = i - irf The default risk premium (DRP) is the difference between the promised or nominal rate and the yield on a comparable (same term) riskless security (Treasury security). Investors are satisfied if the default risk premium is equal to the expected default loss.

    27. Finance 308 27 Risk Premiums (2/02) Exhibit 6.5

    28. Finance 308 28 Default Risk, Cont. Default Risk Premiums Increase (Widen) in Periods of Recession and Decrease in Economic Expansion In good times, risky security prices are bid up; yields move nearer that of riskless securities. With increased economic pessimism, investors sell risky securities and buy “quality” widening the DRP. “Flight to Quality” during periods of recession

    29. Finance 308 29 Default Risk, cont. Credit Rating Agencies Measure and Grade Relative Default Risk Security Issuers Cash flow, level of fixed contractual cash payments, profitability, and variability of earnings are indicators of default riskiness. As conditions change, rating agencies alter rating of businesses and governmental debtors.

    30. Finance 308 30 Corporate Bond-Rating Systems

    31. Finance 308 31 Tax Effects on Yields The Taxation of Security Gains and Income Affects the Yield Differences Among Securities The after-tax return, iat, is found by multiplying the pre-tax return by one minus the marginal tax rate. iat = ibt(1-t) Municipal bond interest income is currently tax exempt. (See footnote 4, on page 147.) Capital gains for individuals are taxed differently than ordinary income such as corporate bond interest. Maximum rate of 15% for gains on securities held by individuals for more than one year (effective May 5, 2003).

    32. Finance 308 32 Should you buy a municipal or a corporate bond?

    33. Finance 308 33 Differences in Marketability Affect Interest Yields Marketability -- The costs and rapidity with which investors can resell a security. Cost of trade. Physical transfer cost. Search costs. Information costs. Liquidity. Securities with good marketability have higher prices (in demand) and lower yields.

    34. Finance 308 34 Contract Options and Yields Varied Option Provisions May Explain Yield Differences Between Securities An option is a contract provision which gives the holder the right, but not the obligation, to buy,sell, redeem, or convert an asset at some specified price within a defined future time period.

    35. Finance 308 35 Contract Options and Yields A Call Option Permits the Issuer (Borrower) to Call (Refund) the Obligation Before Maturity Borrowers will “call” if interest rates decline. Investors in callable securities bear the risk of losing their high-yielding security. With increased call risk, investors demand a call interest premium (CIP). CIP = ic – inc > 0 A callable bond, ic, will be priced to yield a higher return (by the CIP) than a noncallable, inc, bond.

    36. Finance 308 36 Call Option on Bonds Most corporate and municipal bonds and some U.S. Government bonds contain a call option in their contracts. Similar to a Mortgage Many corporate bonds have a Deferred Call provision rather than an Immediate Call provision. With corporate bonds, the premium initially set is usually one year’s interest above the par value. A municipality may be able to call its bonds without any premiums being paid.

    37. Finance 308 37 Contract Options and Yields A put option permits the investor (lender) to terminate the contract at a designated price before maturity Investors are likely to “put” their security or loan back to the borrower during periods of increasing interest rates. The difference in interest rates between putable and nonputable contracts is called the put interest discount (PID). PID = ip – inp < 0 The yield on a putable bond, ip, will be lower than the yield on the nonputable bond, inp, by the PID.

    38. Finance 308 38 Contract Options and Yields A Conversion Option Permits the Investor to Convert a Security Contract Into Another Security Convertible bonds generally have lower yields, icon, than nonconvertibles, incon. The conversion yield discount (CYD) is the difference between the yields on convertibles relative to nonconvertibles. CYD = icon – incon < 0. Investors accept the lower yield on convertible bonds because they have an opportunity for increased rates of return through conversion.

    39. Finance 308 39 Conclusion Term Structure of Interest Rates Expectations Liquidity Premium Market Segmentation Preferred Habitat Use of Yield Curve Default Risk Tax Equivalent Yield Options Put Call Convertible

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