chapter 6 Flashcards
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In the Global Financial Crisis box in Section 6.2, Bloomberg.com reported that the three-month Treasury bill sold for a price of $ 100.002556 per $ 100 face value. What is the yield to maturity of this bond, expressed as an EAR?
a. The three-month yield to maturity
b. The annual yield to maturity
In the Global Financial Crisis box in Section 6.2, Bloomberg.com reported that the three-month Treasury bill sold for a price of $ 100.002556 per $ 100 face value. What is the yield to maturity of this bond, expressed as an EAR?
a. The three-month yield to maturity
y = ( FV / PV ) - 1
y = (100.002556 / 100 ) - 1 = .00002556 = -.002556%
(don’t forget the negative sign)
b. The annual yield to maturity
multiply the 3-month yield to 4. = -.010224
For each of the following pairs of Treasury securities (each with $ 1 comma 000 par value), identify which will have the higher price:
a. A three-year zero-coupon bond or a five-year zero-coupon bond?
b. A three-year zero-coupon bond or a three-year 4 % coupon bond?
c. A two-year 5 % coupon bond or a two-year 6 % coupon bond?
For each of the following pairs of Treasury securities (each with $ 1 comma 000 par value), identify which will have the higher price:
a. A three-year zero-coupon bond or a five-year zero-coupon bond?
– 3 yr zero-coupon bond because the FV is received sooner and the PV is higher.
b. A three-year zero-coupon bond or a three-year 4 % coupon bond?
– 4% coupon bond because it earns interest whereas the zero coupon bond is a pure discount bond
c. A two-year 5 % coupon bond or a two-year 6 % coupon bond?
– 6% coupon bond because the coupon interest payments are higher even though the timing is the same.
The yield to maturity of a $ 1,000 bond with a 6.8 % coupon rate, semiannual coupons, and two years to maturity is 8.4 % APR, compounded semiannually. What is its price?
The yield to maturity of a $ 1,000 bond with a 6.8 % coupon rate, semiannual coupons, and two years to maturity is 8.4 % APR, compounded semiannually. What is its price?
CPN = PMT in TVM CPN = FV * (coupon rate / compounding) CPN = 1000 * (6.8 / 2) CPN = 1000 * (3.4%) = 1000 * .034 = $34
TVM N = 4 : (2 * 2 ) bec semi-annual I = 4.2 : (8.4% / 2) PV = goal --> -971.10 PMT = 34 FV = 1000 : face value P/Y = 1 C/Y = 1
actual formula:
Price = CPN/y * [1 - (1/1+y)^n] + FV / (1+y)^n
Suppose a ten-year, $ 1,000 bond with an 8.5 % coupon rate and semiannual coupons is trading for $ 1 comma 034.29.
a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?
b. If the bond’s yield to maturity changes to 9.8 % APR, what will be the bond’s price?
Suppose a ten-year, $ 1,000 bond with an 8.5 % coupon rate and semiannual coupons is trading for $ 1,034.29.
a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?
P = CPN/y * [1 - 1/(1+y)^n = FV / (1+y)^n
TVM: N = 20 : 10-year semi annual compounding I = GOAL ---> 8.00 % (4.00% * 2) PV = 1034.29 : coupons are trading for PMT = 42.50 : (1000 * 8.5% /2) FV = 1000 P/Y = 1 C/Y = 1
b. If the bond’s yield to maturity changes to 9.8 % APR, what will be the bond’s price?
TVM: N = 20 : 10-year semi annual compounding I = 4.9% (9.8% /2) PV = GOAL ---> -918.30 PMT = 42.50 : (1000 * 8.5% /2) FV = 1000 P/Y = 1 C/Y = 1
note: if P/Y and C/Y is changed to 2 (semi-annual) then I can stay at 9.8%
Suppose a five-year, $ 1,000 bond with annual coupons has a price of $ 903.41 and a yield to maturity of 5.7 %. What is the bond’s coupon rate?
What is the bond’s coupon rate?
a.k.a. r in r = CPN/FV
Suppose a five-year, $ 1,000 bond with annual coupons has a price of $ 903.41 and a yield to maturity of 5.7 %. What is the bond’s coupon rate?
What is the bond’s coupon rate?
Step 1
TVM: N = 5: annual I = 5.7 PV = -903.41 PMT = GOAL ---> 34.26 FV = 1000 P/Y = 1 C/Y = 1
Step 2
r = CPN / FV r = 34.26 /1000 = .03426 = 3.426%
The prices of several bonds with face values of $ 1,000 are summarized in the following table:
Bond Prices A: 970 B: 1040 C: 1153.28 D: 1000
The prices of several bonds with face values of $ 1,000 are summarized in the following table:
Bond
A: 970 - this is discount because prices < FV
B: 1040 - this premium because prices > FV
C: 1153.28 - same here premium because price > FV
D: 1000 - this is at par because is price == FV
You have purchased a 8% coupon bond for $1 comma 030. What will happen to the bond’s price if market interest rates rise?
You have purchased a 8% coupon bond for $1,030. What will happen to the bond’s price if market interest rates rise?
If market interest rates rise, the bond’s price will DECREASE
Your company currently has $ 1,000 par, 5.25 % coupon bonds with 10 years to maturity and a price of $ 1,081. If you want to issue new 10-year coupon bonds at par, what coupon rate do you need to set? Assume that for both bonds, the next coupon payment is due in exactly six months.
Your company currently has $ 1,000 par, 5.25 % coupon bonds with 10 years to maturity and a price of $ 1,081. If you want to issue new 10-year coupon bonds at par, what coupon rate do you need to set? Assume that for both bonds, the next coupon payment is due in exactly six months.
TVM: N = : 20 : semi annual I = GOAL ---> 4.24% PV = -903.41 PMT = 26.25 : ( 1000 * 0.0525/2 ) FV = 1000 P/Y = 1 C/Y = 1
I = APR = 2.12% * 2 = 4.24%
Consider the following bonds: Bond Coupon Rate (annual payments) Maturity (years) A: 0.0 % 15 B: 0.0 % 10 C: 4.0 % 15 D: 8.0 % 10
Which of the bonds A to D is most sensitive to a 1 % drop in interest rates from 6.0 % to 5.0 %? Which bond is least sensitive?
Consider the following bonds: Bond Coupon Rate (annual payments) Maturity (years) A: 0.0 % 15 B: 0.0 % 10 C: 4.0 % 15 D: 8.0 % 10
Which of the bonds A to D is most sensitive to a 1 % drop in interest rates from 6.0 % to 5.0 %? Which bond is least sensitive?
Bond A is the most sensitive because:
The most sensitive has the longest maturity and no coupons. The least sensitive has the shortest maturity and highest coupon rate. Intuitively, higher coupon rates and a shorter maturity typically lower a bond’s interest rate sensitivity
With that said:
Bond D is the least sensitive.
