Bond Valuation and Risk: How Bond Prices Move and Why

Book: Financial Markets and Institutions, 11th Edition Author: Jeff Madura Publisher: Cengage Learning, 2015 ISBN: 978-1-133-94788-2

Chapter 8 is where Madura gets into the math behind bond prices. If Chapter 7 was about the types of bonds, this chapter explains how to figure out what they are worth, why their prices change, and how investors manage the risk. It is the most technical chapter so far, but the concepts are fundamental to understanding how fixed-income investing works.

How Bond Prices Are Determined

The price of a bond is the present value of its future cash flows. Those cash flows are the coupon payments plus the par value returned at maturity. The formula is straightforward:

Bond Price = Sum of (Coupon Payments / (1+k)^t) + (Par Value / (1+k)^n)

Where k is the investor’s required rate of return and n is the number of periods to maturity.

For example, a bond with a $1,000 par value, $100 annual coupon, and 3 years to maturity priced at a 12 percent required return would be worth $951.97. The investor pays less than par value because they need a 12 percent return, but the coupon rate is only 10 percent.

This leads to three key relationships:

1. If the coupon rate is below the required return, the bond sells at a discount (below par).
2. If the coupon rate equals the required return, the bond sells at par.
3. If the coupon rate is above the required return, the bond sells at a premium (above par).

Most real bonds pay semiannual coupons. The math adjusts by halving the coupon, halving the discount rate, and doubling the number of periods. Same concept, just split into six-month chunks.

What Makes Bond Prices Move

Bond prices change when the required rate of return changes. And the required return has two components: the risk-free rate and the credit risk premium.

Change in Bond Price = f(Change in Risk-Free Rate, Change in Risk Premium)

Factors Affecting the Risk-Free Rate

Madura identifies four drivers:

Inflation expectations. Higher expected inflation pushes interest rates up, which pushes bond prices down. Oil prices matter here. Higher oil prices mean higher production costs, which feeds inflation. A weakening dollar also raises import prices and fuels inflation.

Economic growth. Strong economic growth puts upward pressure on interest rates because more borrowers compete for funds. Weak growth does the opposite. This is why bond prices sometimes rally when bad economic news comes out. Investors expect rates to fall.

Money supply. When the Fed increases the money supply, there are more loanable funds, which can push rates down. But if that extra money triggers inflation fears, rates could go up instead. It depends on the context. During the credit crisis, the Fed pumped money into the system and rates fell because inflation was not a concern.

Budget deficit. A bigger deficit means the government borrows more, competing for funds and pushing rates up.

Factors Affecting the Risk Premium

The risk premium depends mainly on economic conditions. Strong economies mean firms are more likely to repay their debts, so risk premiums shrink. Weak economies increase the chance of default, so premiums expand.

During the 2008 credit crisis, the risk-free rate fell (Fed policy), but corporate bond yields actually went up because the risk premium exploded. Investors demanded much higher compensation for lending to corporations when the economy was falling apart. The gap between Baa-rated corporate bonds and Treasury bonds widened dramatically.

Longer maturities also carry higher risk premiums. A company might look fine for the next month, but who knows what happens over 15 years?

Measuring Bond Price Sensitivity

Not all bonds react the same way to interest rate changes. Two methods help measure sensitivity.

Bond Price Elasticity

This measures the percentage change in bond price relative to the percentage change in required return. A higher elasticity means the bond is more sensitive.

Key finding: zero-coupon bonds are the most sensitive to interest rate changes. That makes sense. All of their value comes from a single payment far in the future. Bonds with high coupon rates are less sensitive because you get cash sooner.

Duration

Duration measures the weighted average time until a bond’s cash flows are received. It is measured in years. A zero-coupon bond’s duration equals its maturity. A coupon bond’s duration is always less than its maturity because some payments arrive before maturity.

For example, a bond with a 7 percent coupon, three years to maturity, and a 9 percent yield has a duration of 2.8 years. A zero-coupon bond with the same maturity has a duration of exactly 3 years.

Modified duration estimates the percentage price change for a 1 percentage point change in yield. If a bond has a modified duration of 8.514, a 1 percent rise in yields causes about an 8.5 percent drop in price.

There is a catch, though. Modified duration assumes a linear relationship between yields and prices. In reality, the relationship is curved. This is called convexity. For small yield changes, duration works well. For large changes, it overestimates price declines and underestimates price increases.

Portfolio managers use duration to match their assets and liabilities. If a pension fund’s asset duration is higher than its liability duration, rising rates will hurt the fund because asset values drop faster than liability values.

Bond Investment Strategies

Madura describes four common approaches:

Matching strategy. Build a portfolio that generates income matching your expected expenses. A retiree might do this, or a pension fund covering future payouts.

Laddered strategy. Spread your money evenly across different maturities (5, 10, 15, 20 years). When the shortest bonds mature, reinvest in new long-term bonds. This gives you diversified interest rate exposure, though it does not eliminate rate risk.

Barbell strategy. Put money in very short-term and very long-term bonds, skipping the middle. Short bonds provide liquidity. Long bonds provide higher yields. It is a balance between safety and return.

Interest rate strategy. Actively shift your portfolio based on where you think rates are headed. If you expect rates to drop, load up on long-term bonds to capture the biggest price gains. If you expect rates to rise, shorten your maturities to limit losses. This sounds great in theory, but Madura notes that even sophisticated investors struggle to consistently predict rate movements.

International Bonds

Foreign bonds can offer higher yields, but they add risks. Interest rates in different countries move independently. A U.S. investor buying British bonds might get a 10 percent coupon, but if the pound weakens against the dollar, the dollar value of those coupon payments shrinks.

Madura uses a scenario analysis showing how cash flows from a British bond vary under three exchange rate scenarios: stable pound, weak pound, and strong pound. The differences are substantial.

International bond diversification can reduce interest rate risk, credit risk, and exchange rate risk. But the benefits shrink during global crises when correlations spike and everything drops together.

The European debt crisis of 2010-2012 is covered in detail. Greece, Portugal, and Spain could not repay their debts. Because they use the euro, they could not print money to stimulate their economies. Their only options were austerity (cutting spending, raising taxes) or default. The European Central Bank stepped in with loans, but with strict conditions. The crisis showed how debt problems in one country spread to others through economic integration.

My Take

The big lesson from this chapter is that bonds are not the safe, boring investment people think they are. Interest rate changes can cause serious price swings, especially for long-term, low-coupon bonds. And duration is the single most important concept for understanding that sensitivity.

The 2008 crisis examples are powerful. The Fed cut the risk-free rate, but corporate bond prices still fell because the risk premium went through the roof. That is the kind of nuance you miss if you only look at interest rates in the news.

The interest rate strategy section is also a nice reality check. Everyone thinks they can predict rates. Almost nobody can do it consistently. The laddered and barbell strategies are more practical for most investors because they do not require you to be right about the future.

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