Deck 3: Interest Rates and Security Valuation

Question 1

For a given interest rate change, a 20-year bond's price change will be twice that of a 10-year bond's price change.

Answer 1

False

Question 2

Suppose two bonds of equivalent risk and maturity have different prices such that one is a premium bond and one is a discount bond. The premium bond must have a greater expected return than the discount bond.

Answer 2

False

Question 3

The required rate of return on a bond is

A) the interest rate that equates the current market price of the bond with the present value of all future cash flows received.
B) equivalent to the current yield for non par bonds.
C) less than the Err for discount bonds and greater than the Err for premium bonds.
D) inversely related to a bond's risk and coupon.
E) none of the above.

Answer 3

E

Question 4

The duration of a four-year maturity 10% coupon bond is less than four years.

Question 5

Any security that returns a greater percentage of the price sooner is less price-volatile.

Question 6

Duration is

A) the elasticity of a security's value to small coupon changes.
B) the weighted average time to maturity of the bond's cash flows.
C) the time until the investor recovers the price of the bond in today's dollars.
D) greater than maturity for deep discount bonds and less than maturity for premium bonds.
E) the second derivative of the bond price formula with respect to the ytm.

Question 7

The greater a security's coupon, the lower the security's price sensitivity to an interest rate change, ceteris paribus.

Question 8

If interest rates increase, the value of a fixed income contract decreases and vice versa.

Question 9

All else equal, the holder of a fairly priced premium bond must expect a capital loss over the holding period.

Question 10

A zero coupon bond has a duration equal to its maturity and a convexity equal to zero.

Question 11

At equilibrium a security's required rate of return will be less than its expected rate of return.

Question 12

Higher interest rates lead to lower bond convexity, ceteris paribus.

Question 13

Ignoring default risk, if a bond's expected return is greater than its required return, then the bond's market price must be greater than the present value of the bond's cash flows.

Question 14

A fairly priced bond with a coupon less than the expected return must sell at a discount from par.

Question 15

A bond with an 11% coupon and a 9% required return will sell at a premium to par.

Question 16

The higher a bond's coupon, the lower the bond's price volatility.

Question 17

A ten-year maturity zero coupon bond will have lower price volatility than a ten-year bond with a 10% coupon.

Question 18

If a security's realized return is negative, it must have been true that the expected return was greater than the required return.

Question 19

The longer the time to maturity, the lower the security's price sensitivity to an interest rate change, ceteris paribus.

Question 20

The lower the level of interest rates, the greater a bond's price sensitivity to interest rate changes.

Question 21

An 8-year annual payment 7% coupon Treasury bond has a price of $1,075. The bond's annual Err must be

A) 13.49%
B) 5.80%
C) 7.00%
D) 1.69%
E) 4.25% 1075 = 70 *PVIFA (Err%, 8) + 1000 *PVIF (Err%, 8), trial and error or calculator

Question 22

You bought a stock three years ago and paid $45 per share. You collected a $2 dividend per share each year you held the stock and then you sold the stock for $47 per share. What was your annual compound rate of return?

A) 8.89%
B) 8.51%
C) 5.84%
D) 4.44%
E) 2.96% 45 = 2 x PVIFA (rr%, 3) + 47 x (PVIF (rr%, 3))

Question 23

A 15-year corporate bond pays $40 interest every six months. What is the bond's price if the bond's promised ytm is 5.5%?

A) $1261.32
B) $1253.12
C) $1250.94
D) $1263.45
E) $1264.79 Price = 40* PVIFA (2.75%, 30) + 1000 * PVIF (2.75%, 30)

Question 24

A 12-year annual payment corporate bond has a market price of $925. It pays annual interest of $60 and its required rate of return is 7%. By how much is the bond mispriced?

A) $0.00
B) Overpriced by $7.29
C) Underpriced by $7.29
D) Overpriced by $4.43
E) Underpriced by $4.43 FPV = 60 * PVIFA [7%, 12 yrs] + 1000 * PVIF (7%, 12 yrs) = $920.57

Question 25

The ___________ the coupon and the ______________ the maturity; the __________ the duration of a bond, ceteris paribus.

A) larger; longer; longer
B) larger; longer; shorter
C) smaller; shorter; longer
D) smaller; shorter; shorter
E) none of the above

Question 26

An annual payment bond with a $1,000 par has a 5% quoted coupon rate, a 6% promised ytm, and 6 years to maturity. What is the bond's duration?

A) 5.31 years
B) 5.25 years
C) 4.76 years
D) 4.16 years
E) 3.19 years $\Sigma$ [(t*CF_t/(1.06)^t)]/$950.83

Question 27

A corporate bond returns 12% of its cost (in PV terms) in the first year, 11% in the second year, 10% in the third year and the remainder in the fourth year. What is the bond's duration in years?

A) 3.68 years
B) 2.50 years
C) 4.00 years
D) 3.75 years
E) 3.32 years 3.32 = (12% * 1) + (11% * 2) + (10% * 3) + (67% * 4)

Question 28

A bond that you held to maturity had a realized return of 8%, but when you bought it, it had an expected return of 6%. If no default occurred, which one of the following must be true?

A) The bond was purchased at a premium to par.
B) The coupon rate was 8%.
C) The required return was greater than 6%.
D) The coupons were reinvested at a higher rate than expected.
E) The bond must have been a zero coupon bond.

Question 29

A security has an expected return less than its required return. This security is

A) selling at a premium to par.
B) selling at a discount to par.
C) selling for more than its PV.
D) selling for less than its PV.
E) a zero coupon bond.

Question 30

A 10-year annual payment corporate coupon bond has an expected return of 11% and a required return of 10%. The bond's market price is

A) greater than its PV.
B) less than par.
C) less than its Err.
D) less than its PV.
E) $1000.00.

Question 31

A 10-year annual payment corporate bond has a market price of $1,050. It pays annual interest of $100 and its required rate of return is 9%. By how much is the bond mispriced?

A) $0.00
B) Overpriced by $14.18
C) Underpriced by $14.18
D) Overpriced by $9.32
E) Underpriced by $9.32 PV = 100*PVIFA [9%, 10 yrs] + 1000 *PVIF (9%, 10 yrs) = $1064.18

Question 32

You would want to purchase a security if P ____________ PV or Err ____________ rrr.

A) $\ge$ ; $\le$
B) $\ge$ ; $\ge$
C) $\le$ ; $\ge$
D) $\le$ ; $\le$

Question 33

A semiannual payment bond with a $1,000 par has a 7% quoted coupon rate, a 7% promised ytm, and 10 years to maturity. What is the bond's duration?

A) 10.00 years
B) 8.39 years
C) 6.45 years
D) 5.20 years
E) 7.35 years $\Sigma$ [(t * CF_t/(1.035)^t)]/(2 * $1,000)

Question 34

If an N year security recovered the same percentage of its cost in PV terms each year the duration would be

A) N.
B) 0.
C) sum of the years/N.
D) N!/N².
E) none of the above.

Question 35

A 6-year annual payment corporate bond has a required return of 9.5% and an 8% coupon. Its market value is $20 over its PV. What is the bond's Err?

A) 8.00%
B) 10.21%
C) 9.98%
D) 9.03%
E) 3.53% PV = 933.70 = 80*PVIFA (9.5%, 6 yrs) + 1000 *PVIF (9.5%, 6 yrs); (933.70 + 20) = 80 * PVIFA (Err, 6 yrs) + 1000 * PVIF (Err, 6 yrs), trial and error or calculator

Question 36

A 4-year maturity 0% coupon corporate bond with a required rate of return of 12% has an annual duration of _______________ years.

A) 3.05
B) 2.97
C) 3.22
D) 3.71
E) 4.00

Question 37

A corporate bond has a coupon rate of 10% and a required return of 10%. This bond's price is

A) $924.18
B) $1000.00
C) $879.68
D) $1124.83
E) not possible to determine from the information given

Question 38

An 8-year corporate bond has a 7% coupon rate. What should be the bond's price if the required return is 6% and the bond pays interest semiannually?

A) $1062.81
B) $1062.10
C) $1053.45
D) $1052.99
E) $1049.49 Price = 35.00 * PVIFA (3%, 16) + 1000 * PVIF (3%, 16)

Question 39

The interest rate used to find the present value of a financial security is the

A) expected rate of return.
B) required rate of return.
C) realized rate of return.
D) realized yield to maturity.
E) current yield.

Question 40

Which of the following bond terms are generally positively related to bond price volatility?
I) Coupon rate
II) Maturity
III) ytm
IV) Payment frequency

A) II and IV only
B) I and III only
C) II and III only
D) II only
E) II, III, and IV only

Question 41

An investor is considering purchasing a Treasury bond with a 16-year maturity, a 6% coupon and a 7% required rate of return. The bond pays interest semiannually.
a) What is the bond's modified duration?
b) If annual promised yields decrease 30 basis points immediately after the purchase, what is the predicted price change in dollars based on the bond's duration?

Question 42

Convexity arises because

A) bonds pay interest semiannually.
B) coupon changes are the opposite sign of interest rate changes.
C) duration is an increasing function of maturity.
D) present values are a nonlinear function of interest rates.
E) duration increases at higher interest rates.

Question 43

A 9-year maturity AAA-rated corporate bond has a 6% coupon rate. The bond's promised yield is currently 5.75% and the bond sells for its FPV. The bond pays interest semiannually and has an annual duration of 7.1023 years.
a) What is the bond's convexity?
b) If promised yields decrease to 5.45%, what is the bond's predicted new price, including convexity?
c) Based on your result in b), would you prefer to have a bond with more or less convexity? Explain.

Question 44

A six-year maturity bond has a five-year duration. Over the next year maturity will decline by 1 year and duration will decline by

A) less than one year.
B) more than one year.
C) 1 year.
D) N years.
E) N/(N-1) years.

Question 45

A decrease in interest rates will

A) decrease the bond's PV.
B) increase the bond's duration.
C) lower the bond's coupon rate.
D) change the bond's payment frequency.
E) not affect the bond's duration.

Question 46

An investor owned a 9% annual payment coupon bond for 6 years that was originally purchased at a 9% required return. She did not reinvest any coupons (she kept the money under her mattress). She redeemed the bond at par. What was her annual realized rate of return? What if she did reinvest the coupons but only earned 5% on each coupon? Why are your answers not equal to 9%?

Question 47

A 10-year maturity coupon bond has a 6-year duration. An equivalent 20-year bond with the same coupon has a duration

A) equal to 12 years.
B) less than 6 years.
C) less than 12 years.
D) equal to 6 years.
E) greater than 20 years.

Question 48

A bond that pays interest semiannually has a 6% promised yield and a price of $1045. Annual interest rates are now projected to increase 50 basis points. The bond's duration is 5 years. What is the predicted new bond price after the interest rate change? (Watch your rounding.)

A) $1020.35
B) $1069.65
C) $1070.36
D) $1019.64
E) None of the above ((-5/1.03) *0.0050 *$1045) + $1045

Question 49

The duration of a 180-day T-Bill is (in years)

A) 0.493.
B) 0.246.
C) 1.
D) 0.
E) indeterminate. 180/365

Question 50

What is convexity? How does convexity affect duration-based predicted price changes for interest rates changes?
Convexity is a measure of the nonlinearity (curvature) of a change in a bond's price caused by a change in interest rates. The level of convexity increases for greater interest rate changes. Duration is a linear estimate of a bond's price change as the interest rate changes from its current level. Due to convexity, the greater the interest rate change, the greater the error in using duration to estimate the bond's price change. For a multimillion-dollar bond portfolio, the dollar errors can be quite significant. In abnormal markets, bond investors may face more or less risk than the bond's duration would imply.
Calculus

Question 51

An annual payment bond has a 9% required return. Interest rates are projected to fall 25 basis points. The bond's duration is 12 years. What is the predicted price change?

A) -2.75%
B) 33.33%
C) 1.95%
D) -1.95%
E) 2.75% -12 * (-0.0025/1.09)

Question 52

Which would have a longer duration: a) a 5-year fully amortized installment loan with semiannual payments or b) a 5-year semiannual payment bond, ceteris paribus. Why?

Question 53

Explain the effects of coupon and maturity on volatility.

Question 54

A 15-year, 7% coupon annual payment corporate bond has a PV of $1055.62. However, you pay $1024.32 for the bond. By how many basis points is your Err different from your rrr?

Question 55

Conceptually, why does a bond's price fall when required returns rise on an existing fixed income security?

Question 56

You have 5 years until you need to take your money out of your investments to make a planned expenditure. Right now bonds are promising an 8% return. You buy a 5-year duration bond. After you buy the bond, interest rates fall to 6% and stay there for the full five years. You reinvest the coupons and earn 6%. Will your realized return be more or less than the originally promised 8%? Explain.

Question 57

For large interest rate increases, duration _____________ the fall in security prices, and for large interest rate decreases, duration ______________ the rise in security prices.

A) overpredicts; overpredicts
B) overpredicts; underpredicts
C) underpredicts; overpredicts
D) underpredicts; underpredicts
E) none of the above

Question 58

Is the realized rate of return related to the expected return? The required return? Explain.

Question 59

A bond that pays interest annually has a 6% promised yield and a price of $1025. Annual interest rates are now projected to fall 50 basis points. The bond's duration is 6 years. What is the predicted new bond price after the interest rate change? (Watch your rounding.)

A) $1042.33
B) $995.99
C) $1054.01
D) $987.44
E) None of the above 1025 + [-6 *(-0.0050/1.06) * $1025]

Question 60

How does an increase in interest rates affect a security's duration?

Question 61

The preferred stock of ACE pays a constant $1.00 per share dividend. The common stock of ACME just paid a $1.00 dividend per share, but its dividend is expected to grow at 4% per year forever. ABLE common stock also just paid a dividend of $1.00 per share but its dividend is expected to grow at 10% per year for 5 years and then grow at 4% per year forever. All three stocks have a 12% required return. How much should you be willing to pay for a share of each stock? Which stock will give you the best return? Explain.