Chapter 4: The Meaning of Interest Rates

What are Cash Flows?

Cash payments to the holder of a security.

What is Present Value?

Today’s value of a payment to be received in the future, when the interest rate is i.

What is a Simple Loan?

A credit market instrument that provides the borrower with an amount of funds that must be repaid to the lender at the maturity date, along with an additional payment (interest).

What are the four types of credit market instruments?

A simple loan, a fixed-payment loan, a coupon bond, and a discount bond

What is a Fixed-Payment Loan?

A credit market instrument that provides the borrower with an amount of money that is repaid through fixed periodic (usually monthly) payments made over a set number of years.

What is a Coupon Bond?

A credit market instrument that pays the owner a fixed interest payment every year until the maturity date, at which time a specified final amount is repaid.

What is a Coupon Bond Identified by?

The bond’s face value, the issuer, the maturity date, and the coupon rate

What is a Discount Bond?

A credit market instrument that is bought at a price below its face value and whose face value is repaid at the maturity date; it does not make any interest payments.

When do simple loans and discount bonds make payments?

Only at their maturity dates

When do fixed-payment loans and coupon bonds make payments?

Periodically and a the date of maturity.

What is Yield to Maturity?

The interest rate that equates the present value of payments received from a credit market instrument with its value today.

What is the relation of interest rate and yield to maturity for simple loans?

They are the same

What is a Perpetuity (Consol)?

A perpetual bond with no maturity date and no repayment of principal and that makes periodic, fixed coupon payments.

What is a Current Yield?

An approximation of the yield to maturity; equal to the yearly coupon payment divided by the price of a coupon bond.

What is the Rate of Return?

The payments to the owner of a security plus the change in the security’s value, expressed as a fraction of its purchase price.

Why does the return on a bond not necessarily always equal the YTM on that bond?

Since if the price of the bond experiences sizable fluctuations, it can produce substantial capital gains or losses.

What are the two components of a bond’s holding-period return?

Coupon (interest) income and capital gain or loss from price changes.

When does a bond’s return equal its initial yield to maturity?

When the bond’s time to maturity equals the investor’s holding period (approximately exact for coupon bonds, exact for zero-coupon bonds).

Why do bond prices fall when interest rates rise?

Existing fixed coupon payments become less attractive relative to new bonds, so the market price must fall to raise the yield.

Why do long-maturity bonds experience larger price drops when interest rates rise?

More distant cash flows are discounted at the higher rate, making price more sensitive to interest-rate changes.

Can a bond with a high coupon rate produce a negative return?

Yes, if the capital loss from rising interest rates exceeds the coupon income.

What is interest-rate risk?

The risk that changes in interest rates will affect bond prices and therefore returns.

What does duration measure?

A bond’s sensitivity to interest-rate changes, and thus its interest-rate risk.

Why is the “no interest-rate risk when maturity equals holding period” statement only literally true for zero-coupon bonds?

Coupon bonds require reinvestment of interim payments at uncertain interest rates.

What is reinvestment risk?

The risk that future reinvestment occurs at uncertain interest rates when the holding period exceeds the bond’s maturity.

When does an investor benefit from rising interest rates?

When the holding period is longer than the bond’s maturity, because reinvestment occurs at higher rates.

When does an investor lose from rising interest rates?

When the holding period is shorter than the bond’s maturity, due to capital losses from falling bond prices.

What is the nominal interest rate?

The quoted interest rate on a loan or bond that does not adjust for inflation.

What is the real interest rate?

The interest rate adjusted for changes in the price level, reflecting changes in purchasing power

What is the ex ante real interest rate?

The real interest rate adjusted using expected inflation; the rate relevant for decision-making.

What is the ex post real interest rate?

The real interest rate adjusted using actual, realized inflation after the fact.

State the Fisher equation in its common approximation.

Nominal interest rate ≈ real interest rate + expected inflation.

Why does inflation reduce the real return to lending?

Because rising prices reduce the purchasing power of future dollar payments.

What is the after-tax real interest rate?

The nominal interest rate after taxes, minus expected inflation.

Why is the after-tax real interest rate always lower than the Fisher real interest rate?

Because taxes reduce nominal interest income before adjusting for inflation.

Why are nominal interest rates misleading for evaluating true borrowing costs or returns?

Because they ignore inflation and taxes, which determine real purchasing power.