THE STRUCTURE OF INTEREST RATES CHAPTER 6 THE STRUCTURE OF INTEREST RATES

Factors that Influence Interest Rate Differences Term to Maturity Default Risk Tax Treatment Marketability Options on Debt Securities: Call, Put or Convertibility option Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. Term Structure Relationship between yield and term to maturity on securities that differ only in length of time to maturity A yield curve is a graphical representation of the term structure; it shows the relationship between maturity and a security's yield at a point in time. The yield curve may be ascending (normal), flat, or descending (inverted). Several theories explain the shape of the yield curve. Copyright© 2008 John Wiley & Sons, Inc.

Yield Curves in the 2000s - Exhibit 6.1 Copyright© 2008 John Wiley & Sons, Inc.

The Expectations Theory The shape of the yield curve is determined solely by expectations of future interest rate movements, and changes in these expectations lead to changes in the shape of the yield curve . Ascending: future interest rates are expected to increase. Descending: future interest rates are expected to decrease. Flat :interest rates are expected to be stable in the future. Copyright© 2008 John Wiley & Sons, Inc.

The Expectations Theory Assumptions of the Theory: 1. Investors are profit maximizers. 2. Investors are risk neutral (indifferent between holding a long term security and holding a series of short -term securities). 3. Markets are assumed to be very efficient with excellent information and minimal trading costs. Copyright© 2006 John Wiley & Sons, Inc.

The Expectations Theory Long-term interest rates are geometric averages of current and expected future (implied, forward) interest rates. Copyright© 2006 John Wiley & Sons, Inc.

tR3 = [(1 + 3%)(1+ 4%) (1+ 5%)]1/3 - 1 = 3.997% Example Example 1: Given the following information: Current one – year rate = 3%, Expected 1 – year rate, a year from now = 4% Expected 1 – year rate, 2 years from now = 5% What is the yield on a 3 – year security? 1 + tR3 = [(1 + 3%)(1+ 4%) (1+ 5%)]1/3 tR3 = [(1 + 3%)(1+ 4%) (1+ 5%)]1/3 - 1 = 3.997% The investor is indifferent between a 3- year security, and the average yield of three 1 – year securities. Copyright© 2006 John Wiley & Sons, Inc.

Copyright© 2006 John Wiley & Sons, Inc. Example Example 2: A commercial bank made a 3 – year term loan at 10 %. The bank’s economics department forecasts that 1 and 2 years in the future, the 1 –year interest rate will be 10% and 14%, respectively. The current 1 – year rate is 8%. Given that the bank’s forecasts are reliable, has the bank set the 3 – year rate correctly? Copyright© 2006 John Wiley & Sons, Inc.

An Implied One Year Forward Rate Copyright© 2008 John Wiley & Sons, Inc.

Finding a One-Year Implied Forward Rate Example 1: Using the following term structure of interest rates, find the one-year implied forward rate two years from now. 1-year Treasury note 1.95% 2-year Treasury note 2.39% 3-year Treasury note 2.71% Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2006 John Wiley & Sons, Inc. Example Example 2: Calculate the one – year forward rate three years from now if three and four years spot rates are 5.5% and 5.8% respectively? Copyright© 2006 John Wiley & Sons, Inc.

Liquidity Premium Theory Long-term securities have greater risk and investors require greater premiums to give up liquidity. Long-term security prices are more sensitive to interest rates (have more price risk). Long-term securities have less marketability. The liquidity premium explains why the yield curve slopes upward most of the time. Liquidity premiums change over time. Copyright© 2008 John Wiley & Sons, Inc.

Market Segmentation Theory Investors are assumed to be risk averse. Maturity preferences by investors may affect security prices (yields), explaining variations in yields by time. The shape of the yield curve is determined by the supply and demand of securities at each maturity. 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 and spikes are possible in the yield curve. Copyright© 2008 John Wiley & Sons, Inc.

Preferred Habitat Theory The Preferred Habitat Theory (PH) is an extension of the Market Segmentation Theory. PH allows market participants to trade outside of their preferred maturity if adequately compensated for the additional risk. PH allows for humps or twists in the yield curve, but limits the discontinuities possible under Segmentation Theory. PH is consistent with a smooth yield curve. Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. Which Theory is Right? It is difficult to conclude that one theory is totally able to explain the shape of the yield. 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. Markets participants tend to favor the preferred Habitat Theory, whereas economists tend to favor the expectation and liquidity premium theories. Copyright© 2008 John Wiley & Sons, Inc.

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. Copyright© 2008 John Wiley & Sons, Inc.

Yield-Curve Patterns Over the Business Cycle Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. Uses of the Yield Curve The slope of the yield curve can be used to assess the market’s expectations about future interest rates! Issuers may use the yield curve to price their securities. Investors can use the yield curve to identify under-priced securities for their portfolios and this strategy known as riding the yield curve. Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2006 John Wiley & Sons, Inc. Uses of the Yield Curve Riding the yield curve: If the yield is expected to increase in the future, investors will prefer to buy short term bonds, while issuers will prefer to issue long term bonds. If the yield is expected to decrease in the future, investors will prefer to buy long term bonds, while issuers will prefer to issue short term bonds. Copyright© 2006 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. Default Risk It is the probability of the borrower 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. Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. 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. Copyright© 2008 John Wiley & Sons, Inc.

Risk Premiums (December 2006) Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. 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, which means that investors tend to buy bonds with high default risk because they seek the highest yielding investments and during expansion, there is little chance of default. During economic recession, investors sell risky securities and buy “quality”, thus widening the DRP. Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. Default Risk, cont. Credit rating agencies such as Moody’s measure and grade relative default risk security issuers. The higher the credit rating, the lower the default risk. Cash flow, level of debt, profitability, and variability of earnings are all indicators of default riskiness. As conditions change, rating agencies revise credit ratings of debtors. Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2006 John Wiley & Sons, Inc. Default Risk, cont. Bonds are called investment - grade bonds if their Moody's and Standard & Poor's rating is Baa (BBB) and above. Bonds are called speculative - grade bonds or junk bonds if their Moody's and Standard & Poor's rating is Below Baa (BBB). Copyright© 2006 John Wiley & Sons, Inc.

Corporate Bond-Rating Systems, Exhibit 6.7 Copyright© 2008 John Wiley & Sons, Inc.

Copyright© 2008 John Wiley & Sons, Inc. Tax Effects on Yields The taxation of security gains and income affects the yield differences among securities The interest rate most relevant to investors is the rate of return earned after taxes. The after-tax return, iat, is found by multiplying the pre-tax return by one minus the investor’s marginal tax rate: iat = ibt(1-t) Municipal bonds’ interest income is tax exempt. Copyright© 2008 John Wiley & Sons, Inc.

To Buy a Municipal or a Corporate Bond? Example: Assume that the current yield on a Municipal bond is 7% (no tax treatment) and the current yield on a taxable Corporate bond is 10% (before tax), which bond should you purchase if your tax is 20%? Copyright© 2006 John Wiley & Sons, Inc.

To Buy a Municipal or a Corporate Bond? Copyright© 2008 John Wiley & Sons, Inc.

Impact of Marketability on Interest Yields Marketability – The costs and speed with which investors can resell a security. Cost of trade. Physical transfer cost. Search costs. Information costs. Securities with good marketability have higher prices and lower yields. Treasury bills are the most marketable securities. Copyright© 2008 John Wiley & Sons, Inc.

Contract Options and Yields Various option provisions may explain yield differences between securities An option is a contract provision which gives the holder or the issuer the right, but not the obligation, to buy, sell, redeem, or convert an asset at some specified price within a defined future time period. Copyright© 2008 John Wiley & Sons, Inc.

Contract Options and Yields A call option permits the issuer (borrower) to call (redeem) the bond before maturity at a prespecified price. Callable bonds are sold at a higher market yield than non-callable bonds because they are to the benefit of the issuer. Hence, bondholder demand a call interest premium (CIP). CIP = ic – inc Borrowers call bonds if interest rates decline. Investors in callable securities bear the risk of losing their high-yielding security. Copyright© 2008 John Wiley & Sons, Inc.

Contract Options and Yields A put option permits the investor (lender) to sell the bond back to the issuer at a prespecified price before maturity. The yield on a putable bond, ip, will be lower than the yield on the nonputable bond, inp, because they are advantage to the bondholder. The difference in interest rates between putable and nonputable contracts is called the put interest discount (PID). PID = ip - inp Investors are likely to put their bonds during periods of increasing interest rates Copyright© 2008 John Wiley & Sons, Inc.

Contract Options and Yields A conversion option permits the investor to convert a bond into another security (usually common stock). Convertible bonds generally have lower yields, icon, than nonconvertibles, inconbecause it is an advantage to the bondholder. The conversion yield discount (CYD) is the difference between the yields on convertibles relative to nonconvertibles. CYD = icon - incon. Bondholders tend to use the conversion option when the stock market prices are rising and bond prices are declining. Copyright© 2008 John Wiley & Sons, Inc.