Chapter 4: Understanding Interest Rates

Summary
1. The yield to maturity, which is the measure that most accurately reflects the interest rate, is the interest rate that equates the present value of future payments of a debt instrument with its value today. Application of this principle reveals that bond prices and interest rates are negatively related: when the interest rate rises, the price of the bond must fall, and vice versa.

2. Two less accurate measures of interest rates are commonly used to quote interest rates on coupon and discount bonds. The current yield, which equals the coupon payment divided by the price of a coupon bond, is a less accurate measure of the yield to maturity the shorter the maturity of the bond. The yield on a discount basis (also called the discount yield) understates the yield to maturity on a discount bond, and the understatement worsens with the distance from maturity of the discount security. Even though these measures are misleading guides to the size of the interest rate, a change in them always signals a change in the same direction for the yield to maturity.

3. The return on a security, which tells you how well you have done by holding this security over a stated period of time, can differ substantially from the interest rate as measured by the yield to maturity. Long-term bond prices have substantial fluctuations when interest rates change and thus bear interest-rate risk. The resulting capital gains and losses can be large, which is why long-term bonds are not considered to be safe assets with a sure return.

4. The real interest rate is defined as the nominal interest rate minus the expected rate of inflation. It is a better measure of the incentives to borrow and lend than the nominal interest rate, and it is a more accurate indicator of the tightness of credit market conditions than the nominal interest rate.

-The ytm is an accurate measurement of interest rates. ytm=interest rate

I)Measuring Interest Rate
1. Present Value
-Present discounted value: a dollar paid to you one year later is less valuable than a dollar paid today
-The process of calculating today's value of dollars received in the future --> discounting the future --> PV=CF/(1+i)^n; CF = cash flow payment

2. Four types of Credit Market Instruments
-Simple loan: repaid to lender at maturity date along with interest
*Commercial loans to business
-Fixed-payment loan: repaid by making the same payment every period, consisting of part of the principal and interest for a number of years.
*Ex. borrowed 1000, require to pay 126 every year for 25 years.
*Installment loans, mortgages
-Coupon bond: pays a fixed interest payment (coupon payment) until maturity date when a specified final amount (face value) is repaid.
*Ex. FV=1000, pay a coupon payment of 100/yr for ten years and at maturity date, pay 1000.
*Identified by three info: issuer, maturity date, coupon rate.
*US Treasury bonds and notes, corporate bonds
-Discount bond: bought at a price below face value and face value is repaid at maturity.
*No interest payments
*T-bills, US saving bonds, long-term 0-coupon bonds
-Require payments at different times: Simple loans and discount bonds may payment only at maturity dates; fixed payment and coupon bonds have periodic payments.
-For simple loans, simple interest rate equals the ytm.

-Table 1
*When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate.
*The price of a coupon bond and the yield to maturity are negatively related; that is, as the yield to maturity rises, the price of the bond falls. As the yield to maturity falls, the price of the bond rises.
*The yield to maturity is greater than the coupon rate when the bond price is below its face value.

-Consol or perpetual bond: no maturity date and no repayment of principal; makes fixed coupon payments forever.
-Long-term coupon bonds (>20 yrs), acts like perpetual bonds because cash flow in the far future have very small present value.
-Current bond prices and interest rates are negatively correlated: when interest rate rises, the price of bond falls.

II) Yield on a Discount Basis
1. Yield to maturity is hard to calculate
2. Alternative method: yield on a discount basis.
3. It uses the % gain on the face value of the bill (F-P)/F rather than the % gain on the purchase of the bill (F-P)/P.
4. It puts the yield on an annual basis 360 days.
5. Understates interest rate: year; #3 above.
-Always understate the yield to maturity and this becomes more severe the longer the maturity of the discount bond.
6. It is negatively related to the price of the bond just like ytm.
7. DB and ytm always move together

III) Distinction between interest rates and returns
1. How well a person does by holding a bond --> return
2. Rate of return = payments to the owner plus the change in its value, expressed as a fraction of its purchase price.
3. The return on a bond will not necessarily equal the yield to maturity on that bond.

4. Table 2
-The only bond whose return equals the initial ytm is one whose time to maturity is the same as the holding period (last bond in table 2)
-A rise in interest rates is associated with a fall in bond prices, resulting in capital losses on bonds whose terms to maturity are longer than the holding period.
-The more distant a bond's maturity, the greater the size of the percentage price change associated with an interest-rate change.
-The more distant a bond's maturity, the lower the rate of return that occurs as a result of the increase in the the interest rate.
-Even though a bond has a substantial initial interest rate, its return can turn out to be negative if interest rates rise.

5. Maturity and the Volatility of Bond Returns: Interest Rate Risk
-Prices and returns for long-term bonds are more volatile than those for short-term bonds.

IV) The Distinction Between Real and Nominal Interest Rates
1. When the real interest rate is low, there are greater incentives to borrow and fewer incentives to lend.
2. Returns vs. real returns