Question 1

The duration of a ten-year, 10 percent coupon bond when the interest rate is 10 percent is 6.76 years. What happens to the price of the bond if the interest rate falls to 8 percent?

Accepted Answer

Using the bond price formula, we can calculate the initial price of the bond:
P = (C × [1 - (1 + r)-n]/r) + (F/(1 + r)-n)
Where:
C = Annual coupon payment = 10% × $1,000 = $100
r = Annual interest rate = 10%
n = Number of periods = 10 years
F = Face value = $1,000
P = ($100 × [1 - (1 + 0.1)-10]/0.1) + ($1,000/(1 + 0.1)-10)
P = $1,000

Using the modified duration formula, we can calculate the duration of the bond when the interest rate is 8%:
D = [(C × n) / (1 + r)2] + [(F × n) / (1 + r)n+1] / P
Where:
r = Annual interest rate = 8%
All other variables remain the same as before
D = [(100 × 10) / (1 + 0.08)2] + [(1,000 × 10) / (1 + 0.08)11] / 1,000
D = 7.189

Using the following formula, we can calculate the percentage change in price:
ΔP/P = -D × Δr
Where:
Δr = Change in interest rate = 8% - 10% = -0.02
All other variables remain the same as before
ΔP/P = -7.189 × (-0.02)
ΔP/P = 0.144

Therefore, the percentage change in price is 14.4%, which corresponds to a price increase of 12.3% (since 1 + 0.123 = 1.144). The correct answer is B.

Question 2

The current yield is the yearly coupon payment divided by the current market price.

Accepted Answer

This is the correct definition of current yield.

Question 3

A discount bond

Accepted Answer

A discount bond is also called a zero-coupon bond because it is sold at a discount to its face value and does not pay periodic interest payments. Therefore, the only way an investor can earn a return on this bond is by holding it until maturity and receiving the face value. It is different from a coupon bond, which pays periodic interest payments. It is also not specific to a certain type of bond issuer, so it is not called a corporate bond or fixed-payment bond.

Question 4

The change in the bond's price relative to the initial purchase price is

Accepted Answer

The rate of capital gain signifies the change in the bond's price relative to the initial purchase price. The current yield calculates the annual income earned from the bond relative to its current market price, while the coupon payment is the fixed amount paid to bondholders. The yield to maturity is the total return that the bondholder can expect if the bond is held until maturity. Therefore, the best choice is option D.

Question 5

Prices for long-term bonds are more volatile than for shorter-term bonds.

Accepted Answer

Long-term bonds are subject to more interest rate risk and inflation risk over time, making their prices more sensitive to changes in market conditions.

Question 6

The current yield is the best measure of an investor's return from holding a bond.

Accepted Answer

The current yield only considers the annual interest payments in relation to the bond's current market price, ignoring potential capital gains or losses and reinvestment rates, which are also important for the overall return.

Question 7

Increasing duration implies that interest-rate risk has increased.

Accepted Answer

Increasing duration means that the investment is exposed to changes in interest rates for a longer period of time, therefore increasing the degree of interest-rate risk associated with the investment.

Question 8

When the lender provides the borrower with an amount of funds that must be repaid to the lender at the maturity date, along with an additional payment for the interest, it is called a ________.

Accepted Answer

This type of loan is commonly referred to as a simple loan.

Question 9

A long-term bond's price is less affected by interest rate movements than a short-term bond's price.

Accepted Answer

A long-term bond's price is more sensitive to interest rate movements than a short-term bond's price. This is because the longer the term of a bond, the greater the potential for changes in interest rates to affect its value.

Question 10

The return on a bond is equal to the yield to maturity when

Accepted Answer

The return on a bond is equal to the yield to maturity when the holding period and the maturity of the bond are identical. This means that if you hold a bond until it matures, the return you receive will be equal to the yield to maturity.

Question 11

A bond's current market value is equal to the present value of the coupon payments plus the present value of the face amount.

Accepted Answer

This is the basic formula for calculating the value of a bond, where the present value of future cash flows (coupon payments and face amount) is discounted at the bond's yield to maturity.

Question 12

Bonds whose term to maturity is shorter than the holding period are also subject to

Accepted Answer

Bonds with shorter term to maturity may expose investors to reinvestment risk, which occurs when the investor must reinvest the proceeds from the bond at a lower interest rate than the original bond. This risk increases when the holding period is longer than the bond's maturity. Default risk is not necessarily a concern with shorter-term bonds.

Question 13

The interest rate that is adjusted for actual changes in the price level is called the

Accepted Answer

The ex post real interest rate is the interest rate that has been adjusted for actual changes in the price level, making it the best choice for this question. The expected interest rate refers to the interest rate that is anticipated in the future, while the ex ante real interest rate is the interest rate that has been adjusted for expected changes in the price level. Therefore, neither B nor C are the correct choices for this question.

Question 14

(I)The average lifetime of a debt security's stream of payments is called duration. (II)The duration of a portfolio is the weighted average of the durations of the individual securities, with the weights reflecting the proportion of the portfolio invested in each.

Accepted Answer

Both statements are true. Duration is indeed the average lifetime of a debt security's stream of payments, and the duration of a portfolio is calculated as the weighted average of the durations of the individual securities held in the portfolio, with the weights reflecting the proportion of the portfolio invested in each security.

Question 15

Interest-rate risk is the uncertainty that an investor faces because the interest rate at which a bond's future coupon payments can be invested is unknown.

Accepted Answer

The answer of Interest-rate risk is the uncertainty that an...

Question 16

All else being equal, the greater the interest rate the greater the duration is.

Accepted Answer

Duration typically decreases as interest rates increase because higher rates mean future cash flows are discounted more heavily, reducing their present value and thus the sensitivity of the bond's price to changes in interest rates.

Question 17

Reinvestment risk is the risk that

Accepted Answer

Reinvestment risk refers to the risk that future coupon payments from a bond may have to be reinvested at a rate lower than the bond's yield to maturity. This can occur when interest rates decline after the bond is purchased, and the investor is forced to reinvest their coupon payments at a lower rate. This can lead to lower overall returns on the investment.

Question 18

Discounting the future is the procedure used to find the future value of a dollar received today.

Accepted Answer

Discounting the future is the procedure used to find the present value of a dollar received in the future.

Question 19

A ________ is a type of loan that has the same cash flow payment every year throughout the life of the loan.

Accepted Answer

A fixed-payment loan is a type of loan where the borrower agrees to make equal payments of principal and interest over the life of the loan. This type of loan is also known as an installment loan or an amortizing loan. The fixed payment ensures that the borrower knows exactly how much they will owe each month, making budgeting and financial planning easier.

Question 20

Unless a bond defaults, an investor cannot lose money investing in bonds.

Accepted Answer

While it is true that bonds provide steady income and are generally considered to be less risky than investing in stocks, there are still market risks associated with investing in bonds. Changes in interest rates, inflation, credit ratings, and other factors can all affect the value of a bond, even if it does not default. Therefore, there is still a possibility of losing money when investing in bonds.

Quiz 3: What Do Interest Rates Mean and What Is Their Role in Valuation