chapter 10 and 11: theoretical questions

Question 1

Would a dollar tomorrow be worth more to you today when the interest rate is 20% or when it is 10%?

Answer 1

when the interest rate is 10%

It would be worth 1/(1 + 0.20) = $0.83 when the interest rate is 20%, rather than 1/(1 + 0.10) = $0.91 when the interest rate is 10%

Question 2

To help pay for college, you have just taken out a $1000 government loan that makes you pay $126 per year for 25 years. However, you don’t have to start making these payments until you graduate from college two years from now.

Why is the yield to maturity necessarily less than 12%? (This is the yield to maturity on a normal $1000 fixed-payment loan on which you pay $126 per year for 25 years.

Answer 2

you got the loan two years prior (so you have to pay it back in full by the maturity date in 27 years

If the interest rate were 12%, the present discounted value of the payments on the government loan are necessarily less than the $1000 loan amount because they do not start for two years

hus the yield to maturity must be lower than 12% in order for the present discounted value of these payments to add up to $1000

Question 3

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?

Note: Check Equations 7 and 8 in this chapter

Answer 3

The rate of capital gain is the part of the rate of return formula that incorporates future changes in the price of the bond

Question 4

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

Answer 4

whenever the bond price is very close to par or when the maturity of the bond is over about 10 years

because cash flows further 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

Question 5

Under what conditions will a discount bond have a negative nominal interest rate?

Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?

Answer 5

Whenever the current price P is greater than face value F of a discount bond, the yield to maturity will be negative

It is possible for a coupon bond to have a negative nominal interest rate as long as the coupon payment and face value are low relative to the current price

It is impossible for a perpetuity to have a negative nominal interest rate, since this would require either the coupon payment or the price to be negative

Question 6

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?

Answer 6

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

Question 7

Retired persons often have much of their wealth placed in savings accounts and other interest-bearing investments, and complain whenever interest rates are low

Do they have a valid complaint?

Answer 7

their real return on savings accounts will be unaffected if the inflation drops (so deflation) at the same rate

in practice, expected inflation as reflected by the cost of living for seniors and retired persons often is much higher than standard measures of inflation, thus low nominal rates can adversely affect the wealth of senior citizens and retired persons