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Bond Yields and Interest Rates

(chapter 17)

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Maturity: time when bond principal and all interest will be paid in full- Term-to-Maturity: years remaining until maturity

Par Value: face amount, or principle of bond- Discount and Premium to par

Coupon Rate: rate promised based on par value of bond principal—determines interest paid

Current Yield: rate based on interest paid divided by current bond price

KEY TERMS

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Rates and basis points- 100 basis points are equal to one percentage point

Short-term riskless rate- Provides foundation for other rates- Approximated by rate on Treasury bills- Other rates differ because of

Maturity differentialsSecurity risk premiums

Interest Rates

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Real rate of interest- Rate that must be offered to persuade individuals to save

rather than consume- Rate at which real capital physically reproduces itself

Nominal interest rate - Function of the real rate of interest and expected inflation

premium Bonds benefits from a weak economy

- Interest rates decline and bond prices increase Important relationship is between bond yields and inflation rates

- Investors react to expectations of future inflation rather than current actual inflation

Determinants of Interest Rates

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Market interest rates on riskless debt real rate +expected inflation- Fisher Hypothesis

Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate

Real interest rate is an ex ante concept

Determinants of Interest Rates

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Term structure of interest rates- Relationship between time to maturity and yields

Yield curves- Graphical depiction of the relationship between yields and time

for bonds that are identical except for maturity Upward-sloping yield curve

- typical, interest rates rise with maturity Downward-sloping yield curves

- Unusual, predictor of recession? Term structure theories

- Explanations of the shape of the yield curve and why it changes shape over time

The Term Structure of Interest Rates

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Yield curve and the term structure of interest rates

Term structure – relationship between interest rates (or yields) and maturities.

The yield curve is a graph of the term structure.

The November 2005 Treasury yield curve is shown at the right.

0

1

2

3

4

5

6

0.25 0.5 2 5 10 30Maturity (years)

Yield (% )

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What is the relationship between the Treasury yield curve and the yield curves for

corporate issues? Corporate yield curves are higher than that

of Treasury securities, though not necessarily parallel to the Treasury curve.

The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.

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What determines the yield curve?: Pure (unbiased) Expectations Hypothesis

The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates.

If interest rates are expected to increase, L-T rates will be higher than S-T rates, and vice-versa. Thus, the yield curve can slope up, down, or even bow.

Assumes that the maturity risk premium for Treasury securities is zero. Long-term rates are an average of current and future short-term rates. Most evidence supports the general view that lenders prefer S-T securities, and

view L-T securities as riskier.

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An example:Observed Treasury rates and the PEH

Maturity Yield1 year 6.0%2 years 6.2%

If expectations hypothesis holds, what does the market expect will be the interest rate on one-year securities, one year from now?

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Forward rates Forward rates are rates that are expected to prevail in the future For example a two year bond would carry an interest that is an

average of the current rate for one year and the forward one year rate one year from now

(1+R2)^2= (1+R1)*(1+r1) r1=(1+R2)^2/(1+R1) -1 r1 = (1+0.062)^2/(1+0.06) -1 = 6.4%

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Yield to maturity- Most commonly used- Promised compound rate of return received from a

bond purchased at the current market price and held to maturity

- Equates the present value of the expected future cash flows to the initial investment

- Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM

Measuring Bond Yields

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Yields Yield spread = Yield – Treasury yield Yield spreads are a function of bond

characteristics(see previous slide) Yield spread varies inversely to the business cycles Premium bond: if the bond yield is lower than the

coupon rate Discount bond: if the bond yield is greater than the

coupon rate Current yield: bond’s annual coupon divided by bond

price

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Factors affecting the Yield spreads Differences in quality Differences in time to maturity Differences in call features Differences in coupon interests Differences in marketability Differences in tax treatments Cross country differences

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What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for

$887?

Must find the ytm that solves this model.

10101

NN1B

ytm)(11,000

ytm)(190 ...

ytm)(190 $887

ytm)(1FV

ytm)(1C ...

ytm)(1C V

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Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates

Ex: Total ending wealth = $1,340.1Purchase price (par) = $1,000Three years holding, coupon paid semi annualRCY = 0.05 simiannual and 10% bond equivalent annual

Realized Compound Yield

0121

.ndrice of boPurchase p

ngwealthTotal endi RCYn/

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What is interest rate (or price) risk?(no calculations for the exam)

Interest rate risk is the concern that rising kd will cause the value of a bond to fall.

% change 1 yr rd 10yr % change+4.8% $1,048 5% $1,386 +38.6%

$1,000 10% $1,000-4.4% $956 15% $749 -25.1%

The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

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What is reinvestment rate risk?(no calculations for the exam)

Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You

intend to invest the money and live off the interest.

If you choose to invest in series of 1-year bonds, that pay a 8% coupon you receive $80,000 in income and have $1,000,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $30,000.

If you choose a 30-year bond that pay a 10 % coupon you receive $100,000 in income; you can lock in a 10% interest rate, and $100,000 annual income for 30 years

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Conclusions about interest rate and reinvestment rate risk

CONCLUSION: Nothing is riskless!

Short-term AND/OR High coupon bonds

Long-term AND/OR Low coupon bonds

Interest rate risk

Low High

Reinvestment rate risk High Low

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Interest Rate Risk : Malkiel’s Theorems Malkiel’s theorems are a set of relationships

among bond prices, time to maturity, and interest rates.

Theorem One : Bond prices move inversely with yields.

Theorem Two : Long-term bonds have more risk. Theorem Three : Higher coupon bonds have less

risk.

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Learning objectives

Know the key characteristics of a bondEverything except:Sections NOT on the exam: No calculations using the 5 TVM keys to value a bond; Yield to call p. 456; Realized Compound Yield p 457End of chapter questions 17.1 to 20, 24