Intermediate Investments F303 1

Bonds and Risk

• Liquidity Risk

• Default Risk– Bond rating agencies

– Investment grade v. junk bonds

– Covenants and other indentures

• Interest Rate Risk

Intermediate Investments F303 2

Relationship Between Bond Pricing and Yield

• If you can only remember one thing, remember this:

“There is an inverse relationship between bond prices and interest rates (yields). If interest rates go up, bond prices go down. If interest rates go down, bond prices go up!”

Intermediate Investments F303 3

Bond Pricing Examples

• What is the current market price of a US Treasuy strip that matures in exactly 5 years and has a par value of $1,000. Assume the yield to maturity is 7.5%?

• What is the market price of a US Treasury that has a coupon rate of 9%, a par value of $1,000 and matures exactly 10 years from today if the required yield to maturity is 10% compounded semi-annually?– What if the yield was 8%

– What is the yield was 9%

– What if the yield was 12%

Intermediate Investments F303 4

Another Example

• What is the Yield to Maturity of a US Treasury Strip that pays $1,000 in exactly 7 years and is currently selling for $591.11– If the YTM changes by +/- 1.2%, what happens to the

price of the Strip?

• Back to Example from Last Class – Coupon rate 8% / Term 30 years /Par Value $1,000

– At 6% BEY, Price = $1,276.76, or +276.76

– At 10% BEY, Price = $810.71 or – $189.29

Intermediate Investments F303 5

Convexity Consider the following table of bond prices at

different given interest rates and time to maturity:

Time 4% 6% 8% 10% 12%

1 year 1,038.83$ 1,019.13$ 1,000.00$ 981.41$ 963.33$ 10 years 1,327.03 1,148.77 1,000.00 875.38 770.60 20 years 1,547.11 1,231.15 1,000.00 828.41 699.07 30 years 1,695.22 1,276.76 1,000.00 810.71 676.77

1 year 38.83$ 19.13$ -$ (18.59)$ (36.67)$ 10 years 327.03$ 148.77$ -$ (124.62)$ (229.40)$ 20 years 547.11$ 231.15$ -$ (171.59)$ (300.93)$ 30 years 695.22$ 276.76$ -$ (189.29)$ (323.23)$

Intermediate Investments F303 6

Convexity(cont)

• Bond prices will drop slower from an increase in interest rates, than they rise from a decrease in interest rates

• The longer the maturity, the greater the sensitivity of price fluctuations to changes in interest rates

• This is why short-term treasuries are considered to be the risk free rate. They are not subject to default risk and the maturities are so short, they are really not subject to much interest rate risk

Intermediate Investments F303 7

Bond Yields and Pricing Zero Coupon Bonds

Consider three zero-coupon bonds, all with a face value of $100 and a yield to maturity of 10% compounded annually. See the following table:

What happens if the yield drops to 9%? Or increases to 11%? How would the price respond?

Time Bond 1 Bond 2 Bond 3Value 90.91 75.13 62.09 1 100.00 23 100.00 45 100.00

Intermediate Investments F303 8

Bond Yields and Pricing Zero Coupon Bonds

Yield Bond 1 Bond 2 Bond 31year 3 year 5 year

10.0% 90.91 75.13 62.09 9.0%% change11.0%% change

Intermediate Investments F303 9

Bond Yields and Pricing Coupon Bonds

Consider two bonds with 10% annual coupons. One bond matures in 5 years and other in 10 years

What is the response of these bonds to changes in yield from 8% to 9%? To 7%?

Yield 5 year bond 10 year bond8% 1,079.85 1,134.20 9%% change7%% change

Intermediate Investments F303 10

The Yield Curve

• The graphical relation between the yield to maturity and the term to maturity is called the Yield Curve or the Term Structure of Interest Rates

• What does it mean if the yield curve is:– Flat

– Rising

– “Hump shaped”

Intermediate Investments F303 11

Theories Regarding Yield Curve Behavior

• Liquidity Preference Theory –

• Expectations Theory –

Intermediate Investments F303 12

How the Expectations Theory Leads to Finding Forward Rates of Interest

• Difference between the Spot rate and the Forward Rate of interest –

• Determining the Forward Rate of Interest – the theory holds that over any holding period, holding period returns will be equalized across bonds of all maturities. So, future short-term interest rates can be determined by finding the rate that makes the expected return to bonds of different maturities equal

Intermediate Investments F303 13

An example

• Let’s assume that you have a one-year bond that provides an 8% return. Two year bonds have a return of 8.55%. What does this infer about the Forward Rate of Interest?– You have 2 choices, invest in the 1 year bond and re-

invest the proceeds at the prevailing spot rate when it matures or invest in the two year bond. Since the outcomes of these two strategies should be equal, what is the anticipated spot rate in the future: the forward rate of interest?

Intermediate Investments F303 14

Another Example

• Suppose you want to borrow $20,000 in two years in order to buy a new car. You know with certainty that you will re=pay the loan at the end of the 3rd year. You have two options:– Borrow $17,884 now at 6%. If you do this, you can

invest the proceeds at 5.75%, the current Risk free rate, for two years, then repay the loan at the end of three years.

– You can wait for two years, borrow $20,000 at the prevailing rate of interest for a one year loan

• How does finding the forward rate of interest influence your decision?