Ch4 - The meaning of interest rates

What is the formula used to calculate the yield to maturity on a 20-year coupon bond with a current yield of 12% and $1,000 face value that sells for $2,500?

$2,500 = $120/(1 + i) + C/(1 + i)2 + · · · + C/(1 + i)20 + $1,000/(1 + i)20. Solving for i gives the yield to maturity.

What are the risks associated with fixed income?

1. Interest rate risk: When interest rate rise, bond prices fall, meaning the bonds you hold lose value. 2. Inflation risk: Bonds provide a fixed amount of income at regular intervals. But if the rate of inflation outpaces this fixed income, the investor loses purchasing power. 3. Credit risk: The possibility that an issuer could default on its debt obligation. 4. Liquidity risk: An investor might want to sell a fixed income asset, but unable to find a buyer

Explain discount, par, and premium.

Discount: p < face value Par: p = face value Premium: p > face value

What is yield to maturity?

It is the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today. For simple loans, the simple interest rate equals the yield to maturity.

A $1,100-face-value bond has a 5% coupon rate, its current price is $1,040, and it is expected to increase to $1070 next year. Calculate the current yield, the expected rate of capital gains, and the expected rate of return.

The coupon payment, C = $55. Thus, the current yield is $55/$1040 = 0.053, or 5.3%. The expected rate of capital gain, g = ($1070 − $1040)/$1040 = 30/1040 = 0.028, or 2.9%. The expected rate of return, R = iC + g = 5.3% + 2.9% = 8.2%.

When is the current yield a good approximation of the yield to maturity?

The current yield will be a good approximation to the yield to maturity whenever the bond price is very close to par or when the maturity of the bond is over about ten years. This is because cash flows farther in the future have such small present discounted values that the value of a long-term coupon bond is close to a perpetuity with the same coupon rate.

What is real interest rate?

The nominal interest rate minus the expected inflation rate. When the real interest rate is low, there are greater incentives to borrow and fewer incentives to lend

Suppose today you buy a coupon bond that you plan to sell one year later. Which part of the rate of return formulation incorporates future changes into the bond?

The rate of capital gain is the part of the rate of return formula that incorporates future changes in the price of the bond. The other part of the formula, the current yield, is composed of the coupon payment (completely determined by the bond's face value and coupon rate) and the price you paid for the bond today. The rate of capital gain incorporates the future price of the bond and is therefore the part of the formula that reflects the consequences of future price changes.

In what case is the return of a bond equal to the yield to maturity?

The return on a bond, is equal to the yield to maturity in only one special case—when the holding period and the term to maturity of the bond are identical

True or False: With a discount bond, the return on the bond is equal to the rate of capital gain.

True. The return on a bond is the current yield iC plus the rate of capital gain, g. A discount bond, by definition, has no coupon payments, thus the current yield is always zero (the coupon payment of zero divided by current price) for a discount bond.

Do bondholders fare better when the yield to maturity increases or when it decreases? Why?

When the yield to maturity increases, this represents a decrease in the price of the bond. If the bondholder were to sell the bond at a lower price, the capital gains would be smaller (capital losses larger) and therefore the bondholder would be worse off.

If interest rates decline, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?

You would rather be holding long-term bonds because their price would increase more than the price of the short-term bonds, giving them a higher return. Longer-term bonds are more susceptible to higher price fluctuations than shorter-term bonds, and hence have greater interest-rate risk.

What is the relationship between bond prices and interest rates?

current bond prices and interest rates are negatively related: When the interest rate rises, the price of the bond falls, and vice versa

What is the key things that are generally true of bonds?

• The only bonds whose returns will equal their initial yields to maturity are those whose times to maturity are the same as their holding periods (see, for example, the 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 their holding periods. • The more distant a bond's maturity date, the greater the size of the percentage price change associated with an interest rate change. • The more distant a bond's maturity date, the lower the rate of return that occurs as a result of an increase in the interest rate. • Even though a bond may have a substantial initial interest rate, its return can turn out to be negative if interest rates rise.