Ch 6 Short Answer
Calculate the holding period return for a $1,000 face value bond with a $60 annual coupon purchased for $970.00 and sold three years later for $1,060.00.
9.02%. Here we have to consider the present value of the three coupon payments as well as the present value of the capital gain that results from purchasing the bond for $970 and selling it for $1,060.
Which bond will have a higher yield to maturity, a $1,000 face value bond, with a 5.0% coupon rate that sells for $900; or a $1,000 face value bond, with a $50 annual coupon that sells for $1,050? Explain your choice.
Coupon Payment/(1+I) + Face value/(1+I) = purchase price The bond that is selling for $900 will. Both bonds have the same coupon rate, 5%, and they have the same maturity, so the bondholder's returns from the coupons are equal. What differentiates the two is that the bondholder who purchases the bond for $900 will also receive a capital gain which increases his/her yield to maturity.
issue bonds, would you prefer to be in a country where the average inflation rate is 3% inflation but fluctuates wildly, or in a country with a higher, 4% expected inflation rate that is stable (meaning it's always 4%). Explain.
Even though the 4% expected rate is higher, it is stable. As we saw, the inflation risk isn't really the risk from inflation; it is the risk that results from unexpected changes in inflation which then can significantly alter the real interest rate, and therefore the real returns bondholders receive. Because bondholders tend to be risk-averse, they would want to be compensated for the inflation risk, and since the inflation risk results from the fluctuations in the rate of inflation, the returns required by bondholders in the country where the average expected rate is 3% but volatile are likely to be higher than the required returns on the bonds in the higher but stable inflation country. This explains, at least partially, why the central banks in many developed countries strive for inflation stability. Stable prices will lead to lower inflation risk and a more efficient bond market.
Suppose that a bond is purchased at a discount (meaning that it is sold for less than face value). Could the yield to maturity ever be less than the coupon rate? Could the holding period return be less than the coupon rate? Explain.
If a bond is purchased for less than face value, the yield to maturity will always exceed the coupon rate. For the yield to maturity to be less than the coupon rate the price of the bond would have to exceed the face value. On the other hand, the holding period return could be less than the coupon rate. Even if a bond is purchased for less than face value, there is no guarantee it will sell before the maturity date for an amount that is at or above the face value; in fact it could sell for an amount well below the actual purchase price.
Explain why holding period return, as an economic measure, does not have the same significance as current yield or yield to maturity.
One of the things economists do is try to explain behavior, or decisions people make. Current yield and yield to maturity are a priori measures, meaning we can calculate these prior to actually making the purchase of the bond. The holding period return cannot be calculated a priori, it is only calculated after the bond is purchased; to a certain degree it represents a "sunk" cost.
. Compute the change in the price of a five-year (until maturity) $1,000 face value zero- coupon bond that currently yields 7% when expected inflation increases from 3% to 4%.
The bond currently will sell for $712.99. Once the expected inflation increases by 1%, the bondholders would want to keep the same real return, which would drive the bond yield up to 8%. This increase in bond yield will drive the price down to $680.58, or a decrease of more than 4.8% of the bond's price.
Explain the relationship between coupon rate (or coupon yield) and current yield.
The coupon rate is simply the annual coupon divided by the face value. The current yield is the annual coupon divided by the price of the bond. The only time these should equal each other is when the price of the bond equals the face value. If the price is greater than the face value the current yield should be less than the coupon rate. If the price of the bond is less than the face value, the current yield should be greater than the coupon rate.
In mid-2004 there was speculation that the Federal Reserve would be raising interest rates before the end of the year. How would this news affect the bond market and why?
The speculated increase in interest rates by the Federal Reserve would cause the value of bonds to decrease. As we saw in the text, an increase in the expected future interest rate makes bonds less attractive. This will lower the demand for bonds, causing bond prices to decrease and yields to increase. Moreover, the change in bond prices and yields will occur before the actual interest rate changes since existing and prospective bondholders will act on their expectations
You win your state lottery. The lottery officials offer you the option of taking your winnings in one lump-sum payment, or fixed annual payments for the next 20 years. The sum of the 20 annual payments is larger than the lump-sum payment. Before deciding, what are the key factors you will want to consider that could influence your decision?
You should start by finding the interest rate that equates the present value of the 20 payments with the lump sum. Next, compare this rate to the interest rate you think you could safely earn on the lump-sum if you invested it. If the market offers a higher interest rate, then this is a reason you may wish to take the lump sum. Although morbid, you should also consider your own life expectancy. If you do not think you are going to live another 20 years, you would certainly want to take your winnings early. Lifestyle is also important as is the degree of risk aversion you exhibit. One advantage to taking the payments over 20 years is that it is a form of expenditure discipline that may prevent you from going through the funds quickly (though it is highly likely that you will find plenty of sources that will loan you funds for the assignment of the winnings to them).
Notice the following model of a bond market. In each situation given, explain what happens to the bond price and yield and why. Supply and Demand Model a) Expected inflation increases b) The return on bonds rises relative to other assets c) The federal government deficit increases
a) If expected inflation increases the demand for bonds will decrease and the supply will increase. Both of these will reinforce each other, causing the bond prices to fall and interest rates to increase. b) If the return on bonds rises relative to other assets, the bond demand curve will shift to the right, causing bond prices to increase and interest rates to decrease. c) If the federal budget deficit increases, the bond supply curve will shift to the right, causing the bond prices to fall and interest rates to increase.
