Chapter 16
Fixed-Income Securities: Valuation and Risks
Learning Objectives
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Why buy bonds
The risks of investing in bonds
How bonds are priced
Bond pricing theorems
Assessing interest rate risk
Assessing credit risk
Risk and required returns
Why Invest in Bonds?
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Income
Capital gains potential
Paper versus real losses
Diversification
Tax advantages
Income
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Bonds historically have produced higher current income than other
investment instruments
Income from bonds is also more stable over time
Average Annual Income: 1970-1996
8%
6%
4%
2%
0%
Stock dividend
yield
Coupon rate
Potential for Capital Gains
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Between 1987 and 1996 T-bonds had an CAAR of 14.5% compared to
15.6% for stocks
In periods of falling interest rates, bonds can produce spectacular returns
Paper versus Real Losses
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Unlike stocks, bonds mature at a future date certain
When bonds mature, the investor receives the face, or par, value
This is true regardless of what the bond sold for prior to maturity
Diversification
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Bond returns and stock returns have had a low degree of correlation
historically
Bonds can further diversify a portfolio of common stocks
Correlation of Historical Returns between Bonds and:
Small stocks 0.04
Large stocks 0.19
Tax Advantages
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The 1986 Tax Reform Act eliminated many tax sheltered
investments
Interest from municipal bonds remains exempt from federal
income taxes
Risks from Bonds
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Credit risk
Interest rate risk
Reinvestment risk
Purchasing power risk
Call risk
Liquidity risk
Foreign exchange risk
Credit Risk
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Credit risk is the possibility that the investor will not receive
interest or principal payments when due
The credit risk of bonds varies widely
Treasury bonds have no credit risk
Some corporate bonds--called junk bonds--have much more credit risk
Interest Rate Risk
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Bond prices move inversely with interest rates, rates risk
The value of the bond declines
Opportunity cost
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All bonds expose investors to interest rate risk, but some have
more than others
Reinvestment Risk
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Most bonds pay coupon interest
Must reinvest these coupons
If interest rates decline, the actual return will be less than the promised
return
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Interest rate risk and reinvestment risk tend to offset one another
Immunization techniques attempt to strike a balance between the
two
Purchasing Power Risk
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Impact on cash flows of inflation
Must earn at least the rate of inflation to stay “even”
What if actual inflation exceeds the expected inflation?
Rising inflation means higher interest rates
Call Risk
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Many corporate and municipal bonds can be called back prior to
maturity
Usually called when rates are low meaning the investor reinvests
his or her money at lower rates
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Some bonds offer call protection
Liquidity Risk
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Some bonds trade in poor secondary markets
Wide spread between bid and ask prices
Difficult to sell prior to maturity
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Liquidity risk is a problem for many small municipal bond issues
Foreign Exchange Risk
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U.S. investors can invest in bonds denominated in foreign
currencies (e.g., Japanese Yen or British Pound)
If the dollar strengthens against the other currency, the investor’s
return--measured in dollars--falls
Basics of Bond Pricing
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Step 1: Calculate cash flows
Annual cash flows = Coupon rate x Face value
6% x $1,000 = $60
Face value returned when bond matures
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Step 2: Find the present value of these cash flows discounted at the yield
to maturity (promised rate of return), 7%
Price of bond = PV of coupons + PV of face value
= $60(7.0236) + $1,000(0.5083)
= $929.76
Two Complications
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Semi-annual coupon payments
Price = C/2(P/A, r/2, 2T) + F(P/F, r/2, 2T)
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Accrued interest
All bonds trade on a price + accrued interest basis
Accrued interest affects the price of a bond slightly
Example : 10 year bond with a 6% coupon, 7% yield to maturity
and a face value of $1,000
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Assuming annual coupons the price of the bond equals:
$929.76
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Assuming semi-annual coupons, the price of the bond equals:
$928.94
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Assuming semi-annual coupons, and 90 days until the next
coupon payment (bond matures in 14 years and 9 months), the
price of the bond equals: $945.05
Yield to Maturity
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Yield to maturity is the rate at which a bond’s cash flows are
discounted
Also called the promised rate of return
Changes as market interest rates change
Yield to maturity and coupon rate
If P(b) < F, then YTM > CR (discount bond)
If P(b) = F, then YTM = CR
If P(b) > F, then YTM < CR (premium bond)
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Current yield = Coupon divided by price
Yield to call
Actual Return & Yield to Maturity
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If you buy a bond and hold it until maturity, will your actual
return equal the bond’s yield to maturity?
No, unless you can reinvest the coupons at the yield to maturity
If reinvestment rate is less than YTM, actual return will be less than
YTM
If reinvestment rate is greater than YTM, actual return will be greater
than YTM
Five Bond Pricing Theorems
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Bond prices move inversely to changes in interest rates
The longer the maturity of a bond, the more price sensitive the bond
The price sensitivity of bonds increases as maturity increases, but at a
decreasing rate
Bonds with lower coupons are more price sensitive
Yield decreases have a greater impact on bond prices than similar yield
increases
Assessing Interest Rate Risk
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Interest rate risk is defined as the price sensitivity of a bond
Which bond is more price sensitive?
Bond A: 10% coupon, 10 year maturity
Bond B: 5% coupon, 5 year maturity
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We can’t say without some sort of summary measure of interest rate risk
Such a measure is called duration
Duration
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Duration measures the amount of time before the investor receives the
“average” dollar from a bond
Duration is a function of a bond’s coupon rate, time to maturity and yield
to maturity; duration:
Increases as the coupon rate decreases
Increases as the time to maturity increases
Decreases as yield to maturity increases
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The longer the duration of a bond, the more sensitive its price to a given
change in interest rates.
Credit Risk
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Defined as the risk of not receiving promised cash flows in a timely
fashion
Different bonds expose investors to differ amounts of credit risk
Bond ratings are one tool investors use to assess credit risk
Most publicly traded bonds are rated
Major rating organizations are S&P and Moody’s
Bond Ratings
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Highest ratings are AAA or Aaa
Bonds rated BBB (Baa) or above are considered to be
investment grade
Bonds rated below BBB (Baa) are classified as speculative
grade; also called junk bonds
Bond Ratings: Key Questions
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What determines bond ratings?
Has the historical default rate been higher for bonds with lower
ratings?
Are bond ratings adjusted in a timely fashion?
Risk and Required Returns for Bonds
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Let r be equal to the promised (required or expected) rate of return on a
bond
r = f(i, p, ir, rr, dr, cr, Ir, fxr), where
i is the real rate of interest
p is the expected rate of inflation
ir is interest rate risk
rr is reinvestment risk
dr is default risk
cr is call risk
lr is liquidity risk
fxr is foreign exchange risk (if any)