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Slide 13.1

Investments

Chapter 13: Interest Rates and Bond Valuation

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Slide 13.2

Definition: Bonds and Yields

• Bonds

Represent a claim on future cash flows (coupon payments and par value).

• Yield to MaturityThe annualized discount rate that makes the present value of the future cash flows equal to the current price of the bond.

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Slide 13.3

Other Measures of Bond Yields

• Coupon yield / nominal yield.

• Current yield.

• Yield to call.

• Realised yield.

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Slide 13.4

Yield Curve: I

Bond prices are related inversely to market interest rates.

This relation is NOT tautological, however:

bond prices and market interest rates are determined simultaneously by the underlying

economic forces that drive the supply and demand for money.

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Slide 13.5

Yield Curve: II

• The market generally has various interest rates for various maturities.

• The relationship between the market interest rate and the time to maturity is known as the yield curve.

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Slide 13.6

Yield Curve: III

Exhibit 13.1 Examples of actual yield curves

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Slide 13.7

Spot and Forward Rates

• The Spot RateThe yield to maturity of a zero-coupon bond that has a stated maturity.

• The Forward RateThe yield to maturity of a zero-coupon bond that an investor agrees to purchase atsome future specified date.

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Slide 13.8Spot- & forward rates for pure discount bonds

Spot rate is the yield (return) of a pure discount bond, which is sold att discount, since discount bonds, P < F.

%10r9.90

100)r1()r1(

1009.90 1

If a one-year pure discount bond, just issued, is sold at P = €90.9 and has an F = €100, the spot rate is:

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Slide 13.9

Forward rate is the interest rate an investor will pay to buy a bond in the future, no matter its true interest rate (or its bond price), that date.

%12r9.892

1000)r1(

If I sign a forward contract to buy next year a two-years bond at a P = SEK892.9 (with F = SEK1000, to be paid in two years from now), the forward rate is:

Spot & forward rates for pure discount bonds

If the interest rate next year becomes 10%, the price of the bond will be SEK909. In that case, I gain since I buy the bond at SEK892.9.

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Slide 13.10

Forward rates are derived from spot rates and provide a good information on the expected interest rates in the future.

Maturity (n) Spot (Rm) Forward (fn)

1 5 -

2 5.8 6.606

3 6.3 7.307

4 6.4 6.701

5 6.45 6.65

Spot- & forward rates for pure discount bonds

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Slide 13.11Spot- & forward rates for pure discount bonds

If we graph the spot yield curve, it is 5 % for 1-year and 6.45 % for 5-years. But why is it f2 = 6.606 % ?

Strategy 1: Save 1 $ directly in 2-years and get: 1(1 + R2)

2 = 1(1.058)2 = 1.11936.

Strategy 2: (a) Save first 1 $ for 1-year, and (b) sign a contract to invest your $ and its return in an implied rate, (i.e. f2), in order to get the same as in strategy 1.

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Slide 13.12

[1(1.05)]*[1 + rimpl] = 1.11936 , i.e. 1 + rimpl = 1.11936 / 1.05, => rimpl = f2 = 0.06606.

11)11(

)1(

nnR

nnR

nf

Alternatively, R2 = (R1 + f2) / 2.

The Formula to estimate implied forward rates (fn)

from one periods’ spot rates (Rn) is:

Spot- & forward rates for pure discount bonds

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Slide 13.13

Calculating Spot and Forward Rates

Exhibit 13.2 Spot and forward rates for annually compounded, zero-coupon bondsSource: From Introduction to Investments, 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.

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Slide 13.14

Explaining Yield Curves

• The Expectations Hypothesis:

- The Local Expectations Hypothesis.

- The Unbiased Expectations Hypothesis.

• The Liquidity Preference Hypothesis.

• The Market Segmentation Hypothesis.

- The Preferred Habitat Hypothesis.

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Slide 13.15

Credit Risk

• The risk that a company issuing bonds fails to pay the coupon payments or par value in a timely manner.

• Firms that assess the credit risk of bonds are known as credit rating agencies.

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Slide 13.16 Bond Ratings

Exhibit 13.4 Bond rating categories by companySource: From Introduction to Investments, 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.

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Slide 13.17

Junk Bonds

• Bonds rated below BBB or Baa (speculative-grade bonds).

• Junk bonds have two attractive features:

1. They offer relatively high yields (if bankruptcy does not occur).2. They have low correlations with changes

in overall interest rates.

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Slide 13.18

Embedded Options in Bonds

• The Call Feature

The bond issuer has the right to buy bonds back at a stated redemption price.

• The Conversion Feature

The bond issuer has the right to convert bonds in common or preferred stocks.

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Slide 13.19 Convertible Bonds

• A convertible bond is similar to a bond with warrants.

• The most important difference is that a bond with warrants can be separated into different securities and a convertible bond cannot.

• Recall that the minimum (floor) value of convertible:– Straight or “intrinsic” bond value– Conversion value

• The conversion option has value.

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Slide 13.20

The Value of Convertible Bonds

The value of a convertible bond has three components:

1. Straight bond value

2. Conversion value

3. Option value

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Slide 13.21

Convertible Bond Problem• Litespeed, Inc., just issued a zero coupon

convertible bond due in 10 years.• The conversion ratio is 25 shares.• The appropriate interest rate is 10%.• The current stock price is $12 per share.• Each convertible is trading at $400 in the market.

– What is the straight bond value?– What is the conversion value?– What is the option value of the bond?

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Slide 13.22

Convertible Bond Problem (continued)– What is the straight bond value?

– What is the conversion value?25 shares × $12/share = $300

– What is the option value of the bond?$400 – 385.54 = $14.46

54.385$)10.1(

000,1$10

SBV

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Slide 13.23The Value of Convertible Bonds

Convertible Bond Value

Stock Price

Straight bond value

Conversion Value

= conversion ratio

floor value

floor value

Convertible bond values

Option value