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标题: Fixed Income【Reading 58】Sample [打印本页]
作者: prashantsahni    时间: 2012-3-31 13:59     标题: [2012 L1] Fixed Income【Session 16 - Reading 58】Sample

A 6-year annual interest coupon bond was purchased one year ago. The coupon rate is 10% and par value is $1,000. At the time the bond was bought, the yield to maturity (YTM) was 8%. If the bond is sold after receiving the first interest payment and the bond's yield to maturity had changed to 7%, the annual total rate of return on holding the bond for that year would have been:
A)
11.95%.
B)
7.00%.
C)
8.00%.

Price 1 year ago N = 6, PMT = 100, FV = 1,000, I = 8, Compute PV = 1,092 Price now N = 5, PMT = 100, FV = 1,000, I = 7, Compute PV = 1,123
% Return = (1,123.00 + 100 − 1,092.46)/1,092.46 x 100 = 11.95%
作者: prashantsahni    时间: 2012-3-31 14:00

An investor purchased a 10-year zero-coupon bond with a yield to maturity of 10% and a par value of $1,000. What would her rate of return be at the end of the year if she sells the bond? Assume the yield to maturity on the bond is 9% at the time it is sold and annual compounding periods are used.
A)
19.42%.
B)
16.00%.
C)
15.00%.


Purchase price: I = 10; N = 10; PMT = 0; FV = 1,000; CPT → PV = 385.54
Selling price: I = 9; N = 9; PMT = 0; FV = 1,000; CPT → PV = 460.43
% Return = (460.43 − 385.54) / 385.54 × 100 = 19.42%
作者: kim226    时间: 2012-3-31 14:02

If an investor holds a bond for a period less than the life of the bond, the rate of return the investor can expect to earn is called:
A)
approximate yield.
B)
bond equivalent yield.
C)
expected return, or horizon return.


The horizon return is the total return of a given horizon such as 5 years on a ten year bond.
作者: kim226    时间: 2012-3-31 14:03

A 30-year, 12% bond that pays interest annually is discounted priced to yield 14%. However, interest payments will be invested at 12%. The realized compound yield on this bond must be:
A)
greater than 14.0%.
B)
12.0%.
C)
between 12.0% and 14.0%.


Since you are reinvesting the current income at 12%, you will have a return of at least 12%.  And since the bond is priced to yield 14%, you will earn no more than 14%.
作者: kim226    时间: 2012-3-31 14:04

An investor purchased a 6-year annual interest coupon bond one year ago. The coupon interest rate was 10% and the par value was $1,000. At the time he purchased the bond, the yield to maturity was 8%. If he sold the bond after receiving the first interest payment and the yield to maturity continued to be 8%, his annual total rate of return on holding the bond for that year would have been:
A)
8.00%.
B)
7.82%.
C)
9.95%.


Purchase price N = 6, PMT = 100, FV = 1,000, I = 8
compute PV = 1,092.46
Sale price N = 5, PMT = 100, FV = 1,000, I = 8
compute PV = 1,079.85
% return = [(1,079.85 - 1,092.46 + 100) / 1,092.46] x 100 = 8%
作者: kim226    时间: 2012-3-31 14:04

A bond has a par value of $1,000, a time to maturity of 20 years, a coupon rate of 10% with interest paid annually, a current price of $850, and a yield to maturity (YTM) of 12%. If the interest payments are reinvested at 10%, the realized compounded yield on this bond is:
A)
10.0%.
B)
10.9%.
C)
12.0%.

The realized yield would have to be between the reinvested rate of 10% and the yield to maturity of 12%. While no calculation is necessary to answer this question, the realized yield can be calculated as follows. The value of the reinvested coupons at the maturity date is: N = 20; I/Y = 10; PMT = 100; PV = 0; CPT FV = 5,727.50. Adding the principal repayment, total cash at maturity is $6,727.50.
Realized yield: N = 20; PMT = 0; PV = -850; FV = 6727.5; CPT I/Y = 10.8975.
作者: kim226    时间: 2012-3-31 14:10

Consider the purchase of an existing bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100.What is the bond's yield to call (YTC)?
A)
10.55%.
B)
10.05%.
C)
9.26%.


N = 8; PMT = 120; PV = -1,150; FV = 1,100; CPT → I/Y.
What is the bond's yield to maturity (YTM)?
A)
10.55%.
B)
9.26%.
C)
10.34%.


N = 28; PMT = 120; PV = -1,150; FV = 1,000; CPT → I/Y.
What rate should be used to estimate the potential return on this bond?
A)
10.34%.
B)
the YTM.
C)
the YTC.


The yield to call should be used since the bond could be called in the future. Because the bond is callable using yield to maturity would give a falsely increased rate of return.
作者: kim226    时间: 2012-3-31 14:12

Consider the purchase of an existing bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100.What is the bond's yield to call (YTC)?
A)
10.55%.
B)
10.05%.
C)
9.26%.


N = 8; PMT = 120; PV = -1,150; FV = 1,100; CPT → I/Y.
What is the bond's yield to maturity (YTM)?
A)
10.55%.
B)
9.26%.
C)
10.34%.


N = 28; PMT = 120; PV = -1,150; FV = 1,000; CPT → I/Y.
What rate should be used to estimate the potential return on this bond?
A)
10.34%.
B)
the YTM.
C)
the YTC.


The yield to call should be used since the bond could be called in the future. Because the bond is callable using yield to maturity would give a falsely increased rate of return.
作者: kim226    时间: 2012-3-31 14:13

To estimate the actual return of a bond when a callable bond's market price is higher than par use:
A)
YTM.
B)
HPR.
C)
YTC.


To estimate the return at the point of a call the yield to call (YTC) measure is used.  This is different than the YTM because the YTC uses the call price as the future value and uses the time to first call instead of the time to maturity.
作者: kim226    时间: 2012-3-31 14:14

An investor is interested in buying a 4-year, $1,000 face value bond with a 7% coupon and semi-annual payments. The bond is currently priced at $875.60. The first put price is $950 in 2 years. The yield to put is closest to:
A)
8.7%.
B)
11.9%.
C)
10.4%.


N = 2 × 2 = 4; PV = -875.60; PMT = 70/2 = 35; FV = 950; CPT → I/Y = 5.94 × 2 = 11.88%.
作者: kim226    时间: 2012-3-31 14:14

Which statement describes a premium bond and discount bond?
Premium bondDiscount bond
A)
Coupon rate > current yield < yield-to-maturityCoupon rate < current yield < yield-to-maturity
B)
Coupon rate < current yield > yield-to-maturityCoupon rate < current yield < yield-to-maturity
C)
Coupon rate > current yield > yield-to-maturityCoupon rate < current yield < yield-to-maturity


If the coupon rate > market yield, then bond will sell at a premium.
If the coupon rate < market yield, then bond will sell at a discount.
If the coupon rate = market yield, then bond will sell at par.
In addition, if the bond is selling at a premium, the current yield will be between the coupon rate and market rate.
作者: kim226    时间: 2012-3-31 14:14

Harmon Moving has a 13.25% coupon semiannual coupon bond currently trading in the market at $1,229.50. The bond has eight years remaining until maturity, but only two years until first call on the issue at 107.50% of $1,000 par value. Which of the following is closest to the yield to first call on the bond?
A)
4.72%.
B)
5.16%.
C)
9.14%.


To compute yield to first call, enter: FV = $1,075; N = 2 × 2 = 4; PMT = $66.25; PV = –1,229.50, CPT → I/Y = 2.36%, annualized as (2.36)(2) = 4.72%.
作者: kim226    时间: 2012-3-31 14:15

A 20-year bond with a par value of $1,000 and an annual coupon rate of 6% currently trades at $850. It has a promised yield of:
A)
7.9%.
B)
7.5%.
C)
6.8%.


N = 20; FV = 1,000; PMT = 60; PV = -850; CPT → I = 7.5
作者: kim226    时间: 2012-3-31 14:16

A 20-year bond with a par value of $1,000 and an annual coupon rate of 6% currently trades at $850. It has a promised yield of:
A)
7.9%.
B)
7.5%.
C)
6.8%.


N = 20; FV = 1,000; PMT = 60; PV = -850; CPT → I = 7.5
作者: kim226    时间: 2012-3-31 14:16

If a bond sells at a discount its:
A)
coupon rate is less than the market rate of interest.
B)
current yield is greater than its YTM.
C)
coupon rate is greater than its current yield.


When a bond sells at a discount, the market rate goes above the coupon rate and the bond's price falls below par. The current yield is the coupon rate / price, so as price falls below 1000 the current yield rises above the coupon rate. The YTM considers the current yield plus the capital gain associated with the discount.
作者: kim226    时间: 2012-3-31 14:16

PG&E has a bond outstanding with a 7% semiannual coupon that is currently priced at $779.25. The bond has remaining maturity of 10 years but has a first put date in 4 years at the par value of $1,000. Which of the following is closest to the yield to first put on the bond?
A)
7.73%.
B)
14.46%.
C)
14.92%.


To compute yield to first put, enter: FV = $1,000; N = 2 × 4 = 8; PMT = $35; PV = -$779.25; CPT → I/Y = 7.23%, annualized as (7.23)(2) = 14.46%.
作者: kim226    时间: 2012-3-31 14:17

A 10% coupon bond, annual payments, maturing in 10 years, is expected to make all coupon payments, but to pay only 50% of par value at maturity. What is the expected yield on this bond if the bond is purchased for $975?
A)
6.68%.
B)
8.68%.
C)
10.68%.


PMT = 100; N = 10; FV = 500; PV = -975; CPT → I = 6.68
作者: kim226    时间: 2012-3-31 14:17

If interest rates and risk factors remain constant over the remainder of a coupon bond's life, and the bond is trading at a discount today, it will have a:
A)
positive current yield and a capital gain.
B)
negative current yield and a capital gain.
C)
positive current yield, only.


A coupon bond will have a positive current yield. If it is trading at a discount, it will have a capital gain because its value at maturity will be greater than its price today.
作者: kim226    时间: 2012-3-31 14:18

A 20-year, 9% annual coupon bond selling for $1,098.96 offers a yield of:
A)
8%.
B)
10%.
C)
9%.


N = 20, PMT = 90, PV = -1,098.96, FV = 1,000, CPT I/Y
作者: kim226    时间: 2012-3-31 14:18

A $1,000 par value, 10%, semiannual, 20-year debenture bond is currently selling for $1,100. What is this bond's current yield and will the current yield be higher or lower than the yield to maturity?
Current YieldCurrent Yield vs. YTM
A)
9.1%   higher
B)
8.9%   lower
C)
8.9%   higher


Current yield = annual coupon payment/price of the bond
CY = 100/1,100 = 0.0909
The current yield will be between the coupon rate and the yield to maturity. The bond is selling at a premium, so the YTM must be less than the coupon rate, and therefore the current yield is greater than the YTM.
The YTM is calculated as: FV = 1,000; PV = -1,100; N = 40; PMT = 50; CPT → I = 4.46 × 2 = 8.92
作者: kim226    时间: 2012-3-31 14:19

A zero coupon bond with a face value of $1,000 has a price of $148. It matures in 20 years. Assuming annual compounding periods, the yield to maturity of the bond is:
A)
9.68%.
B)
14.80%.
C)
10.02%.


PV = -148; N = 20; FV = 1,000; PMT = 0; CPT → I = 10.02.
作者: kim226    时间: 2012-3-31 14:19

Calculate the current yield and the yield-to-first call on a bond with the following characteristics:
Current YieldYield-to-Call
A)
8.93%5.51%
B)
9.83%19.80%
C)
8.93%11.02%


To calculate the CY and YTC, we first need to calculate the present value of the bond: FV = 1,000; N = 5 × 2 = 10; PMT = (1000 × 0.0875) / 2 = 43.75; I/Y = (9.25 / 2) = 4.625; CPT → PV = -980.34 (negative sign because we entered the FV and payment as positive numbers). Then, CY = (Face value × Coupon) / PV of bond = (1,000 × 0.0875) / 980.34 = 8.93%.
And the YTC calculation is: FV = 1,025 (price at first call); N = (2 × 2) = 4; PMT = 43.75 (same as above); PV = –980.34 (negative sign because we entered the FV and payment as positive numbers); CPT → I/Y = 5.5117 (semi-annual rate, need to multiply by 2) = 11.02%.
作者: kim226    时间: 2012-3-31 14:20

When a bond's coupon rate is greater than its current yield, and its current yield is greater than its yield to maturity, the bond is a:
A)
discount bond.
B)
par value bond.
C)
premium bond.


For a premium bond, coupon rate > current yield > yield to maturity.
For a par bond, coupon rate = current yield = yield to maturity.
For a discount bond, coupon rate < current yield < yield to maturity.
作者: kim226    时间: 2012-3-31 14:20

A coupon bond pays annual interest, has a par value of $1,000, matures in 4 years, has a coupon rate of $100, and a yield to maturity of 12%. The current yield on this bond is:
A)
10.65%.
B)
11.25%.
C)
9.50%.


FV = 1,000; N = 4; PMT = 100; I = 12; CPT → PV = 939.25.
Current yield = coupon / current price
100 / 939.25 × 100 = 10.65
作者: kim226    时间: 2012-3-31 14:20

An 11% coupon bond with annual payments and 10 years to maturity is callable in 3 years at a call price of $1,100. If the bond is selling today for 975, the yield to call is:
A)
9.25%.
B)
10.26%.
C)
14.97%.


PMT = 110, N = 3, FV = 1,100, PV = 975
Compute I = 14.97
作者: kim226    时间: 2012-3-31 14:21

Which of the following statements concerning the current yield is CORRECT? It:
A)
is of great interest to aggressive bond investors seeking capital gains.
B)
is of great interest to conservative bond investors seeking current income.
C)
can be deteremined by dividing coupon income by the face value of a bond.


The current yield of a bond only considers interest income. The capital gains/losses and reinvestment income are not considered.  The formula for current yield is the annual cash coupon payment divided by the bond price.
作者: kim226    时间: 2012-3-31 14:22

A 15-year, 10% annual coupon bond is sold for $1,150. It can be called at the end of 5 years for $1,100. What is the bond's yield to call (YTC)?
A)
8.0%.
B)
9.2%.
C)
8.4%.


Input into your calculator:
N = 5; FV = 1,100; PMT = 100; PV = -1,150; CPT → I/Y = 7.95%.
作者: kim226    时间: 2012-3-31 14:22

A 20-year, 9% semi-annual coupon bond selling for $1,000 offers a yield to maturity of:
A)
11%.
B)
9%.
C)
10%.


N = (20 × 2) = 40
pmt = 90/2 = 45
PV = -1000
FV = 1000
cpt i = ? = 4.5×2 = 9%
作者: kim226    时间: 2012-3-31 14:22

A 20-year, $1,000 face value, 10% semi-annual coupon bond is selling for $875. The bond's yield to maturity is:
A)
5.81%.
B)
11.43%.
C)
11.62%.


N = 40 (2 × 20 years); PMT = 50 (0.10 × 1,000) / 2; PV = -875; FV = 1,000; CPT → I/Y = 5.811 × 2 (for annual rate) = 11.62%.
作者: kim226    时间: 2012-3-31 14:23

If a $1,000 bond has a 14% coupon rate and a current market price of 950, what is the current market yield?
A)
15.36%.
B)
14.74%.
C)
14.00%.


(0.14)(1,000) = $140 coupon
140/950 × 100 = 14.74
作者: kim226    时间: 2012-3-31 14:23

A coupon bond which pays interest $100 annually has a par value of $1,000, matures in 5 years, and is selling today at a $72 discount from par value. The yield to maturity on this bond is:
A)
7.00%.
B)
12.00%.
C)
8.33%.


PMT = 100
FV = 1,000
N = 5
PV = 1,000 − 72 = 928
compute I = 11.997% or 12.00%
作者: kim226    时间: 2012-3-31 14:24

A 12% coupon bond with semiannual payments is callable in 5 years. The call price is $1,120. If the bond is selling today for $1,110, what is the yield-to-call?
A)
11.25%.
B)
10.95%.
C)
10.25%.


PMT = 60; N = 10; FV = 1,120; PV = 1,110; CPT → I = 5.47546
(5.47546)(2) = 10.95
作者: kim226    时间: 2012-3-31 14:24

Consider a 5-year, semiannual, 10% coupon bond with a maturity value of 1,000 selling for $1,081.11. The first call date is 3 years from now and the call price is $1,030. What is the yield-to-call?
A)
7.28%.
B)
3.91%.
C)
7.82%.


N = 6; PMT = 50; FV = 1,030; PV = $1,081.11; CPT → I = 3.91054
3.91054 × 2 = 7.82
作者: kim226    时间: 2012-3-31 14:25

A bond is selling at a discount relative to its par value. Which of the following relationships holds?
A)
yield to maturity < coupon rate < current yield.
B)
coupon rate < current yield < yield to maturity.
C)
current yield < coupon rate < yield to maturity.

When a bond is selling at a discount, it means that the bond has a larger YTM (discount rate that will equate the PV of the bond's cash flows to its current price) than its current yield (coupon payment/current market bond price) and coupon payment.

作者: kim226    时间: 2012-3-31 14:26

Which of the following describes the yield to worst? The:
A)
yield given default on the bond.
B)
lowest of all possible prices on the bond.
C)
lowest of all possible yields to call and yields to put.


Yield to worst involves the calculation of yield to call and yield to put for every possible call or put date, and determining which of these results in the lowest expected return.
作者: kim226    时间: 2012-3-31 14:27

A $1,000 bond with an annual coupon rate of 10% has 10 years to maturity and is currently priced at $800. What is the bond's approximate yield-to-maturity?
A)
12.6%.
B)
11.7%.
C)
13.8%.


FV = 1,000, PMT = 100, N = 10, PV = -800
Compute I = 13.8
作者: kim226    时间: 2012-3-31 14:27

What is the yield to call on a bond that has an 8% coupon paid annually, $1,000 face value, 10 years to maturity and is first callable in 6 years? The current market price is $1,100. The call price is the face value plus 1-year’s interest.
A)
7.14%.
B)
7.02%.
C)
6.00%.


N = 6; PV = -1,100.00; PMT = 80; FV = 1,080; Compute I/Y = 7.02%.
作者: kim226    时间: 2012-3-31 14:28

Tony Ly is a Treasury Manager with Deeter Holdings, a large consumer products holding company. The Assistant Treasurer has asked Ly to calculate the current yield (CY) and the Yield-to-first Call (YTC) on a bond the company holds that has the following characteristics:
If Ly calculates correctly, the CY and YTC are approximately:
CYYTC
A)
7.80%   15.82%
B)
7.80%   15.72%
C)
7.78%   15.82%


To calculate the CY and YTC, we first need to calculate the present value of the bond: FV = 1,000, N = 14 = 7 × 2, PMT = 35 =(1000 × 0.07)/2, I/Y = 4.5 (9 / 2), Compute PV = -897.77 (negative sign because we entered the FV and payment as positive numbers).
Then, CY = (Face value × Coupon) / PV of bond = (1,000 × 0.07) / 897.77 = 7.80%.
And finally, YTC  calculation: FV = 1,060 (price at first call), N = 4 (2 × 2), PMT = 35 (same as above), PV = -897.77 (negative sign because we entered the FV and payment as positive numbers), ComputeI/Y = 7.91 (semi-annual rate, need to multiply by 2) = 15.82%.
作者: kim226    时间: 2012-3-31 14:28

In capital markets, stock dividends and bond coupons generally provide what is referred to as:
A)
internal yield.
B)
current yield.
C)
capital gain yield.


Current yield is based on actual cash received during the investment horizon and is typically composed of dividends and interest.
作者: kim226    时间: 2012-3-31 14:29

Find the yield to maturity of a 6% coupon bond, priced at $1,115.00. The bond has 10 years to maturity and pays semi-annual coupon payments.
A)
8.07%.
B)
4.56%.
C)
5.87%.


N = 10 × 2 = 20; PV = -1,115.00; PMT = 60/2 = 30; FV = 1,000.
Compute I = 2.28 (semiannual) × 2 = 4.56%
作者: kim226    时间: 2012-3-31 14:29

A 20 year, 8% semi-annual coupon, $1,000 par value bond is selling for $1,100. The bond is callable in 4 years at $1,080. What is the bond's yield to call?
A)
8.13.
B)
6.87.
C)
7.21.


n = 4(2) = 8; PMT = 80/2 = 40; PV = -1,100; FV = 1,080
Compute YTC = 3.435(2) = 6.87%
作者: kim226    时间: 2012-3-31 14:30

What is the current yield for a 5% three-year bond whose price is $93.19?
A)
5.00%.
B)
2.68%.
C)
5.37%.


The current yield is computed as follows:
Current yield = 5% x 100 / $93.19 = 5.37%
作者: karoliukas    时间: 2012-3-31 14:34

A coupon bond that pays interest annually is selling at par, matures in 5 years, and has a coupon rate of 12%. The yield to maturity on this bond is:
A)
12.00%.
B)
60.00%.
C)
8.33%.


N = 5; PMT = 120; PV = -1,000; FV = 1,000; CPT → I = 12
Hint: the YTM equals the coupon rate when a bond is selling at par.
作者: karoliukas    时间: 2012-3-31 14:34

A 20-year, 10% semi-annual coupon bond selling for $925 has a promised yield to maturity (YTM) of:
A)
10.93%.
B)
11.23%.
C)
9.23%.


N = 40, PMT = 50, PV = -925, FV = 1,000, CPT I/Y.
作者: karoliukas    时间: 2012-3-31 14:35

A 30-year, 10% annual coupon bond is sold at par. It can be called at the end of 10 years for $1,100. What is the bond's yield to call (YTC)?
A)
8.9%.
B)
10.0%.
C)
10.6%.


N = 10; PMT = 100; PV = 1,000; FV = 1,100; CPT → I = 10.6.
作者: karoliukas    时间: 2012-3-31 14:35

The bond's yield-to-maturity is:
A)
the discount rate that equates the present value of the cash flows received with the price of the bond.
B)
based on the assumption that the bond is held to maturity and all coupons are reinvested at the yield-to-maturity.
C)
both of these are correct.


The yield to maturity (YTM) is the interest rate that will make the present value of the cash flow from a bond equal to its market price plus accrued interest and is the most popular of all yield measures used in the bond marketplace.
作者: karoliukas    时间: 2012-3-31 14:36

A 6% semi-annual pay bond, priced at $860 has 10 years to maturity. Find the yield to maturity and determine if the price of this bond will be lower or higher than a zero coupon bond.
YTMCompared to zero coupon bond
A)
8.07%   higher price
B)
8.07%   lower price
C)
4.03%   higher price

N = 2 × 10 = 20; PV = -$860.00; PMT = $30; FV = $1,000. Compute I/Y = 4.033 × 2 = 8.07%.
The price of this bond will most likely be higher than a zero coupon bond because this bond pays coupons to the holder.
作者: karoliukas    时间: 2012-3-31 14:36

What rate of return will an investor earn if they buy a 20-year, 10% annual coupon bond for $900? They plan on selling this bond at the end of five years for $951.  Calculate the rate of return and the current yield at the end of five years.
Rate of returnCurrent yield
A)
9.4%11.00%
B)
12.0%10.51%
C)
12.0%11.00%


Realized (horizon) yield = rate of return based on reinvestment rate on selling price at the end of the holding period horizon.
PV = 900; FV = 951; n = 5; PMT = 100; compute i = 12%
Current Yield = annual coupon payment / bond price
CY = 100 / $951 = 0.1051 or 10.51%
作者: karoliukas    时间: 2012-3-31 14:37

A five-year bond with a 7.75% semiannual coupon currently trades at 101.245% of a par value of $1,000. Which of the following is closest to the current yield on the bond?
A)
7.53%.
B)
7.65%.
C)
7.75%.


The current yield is computed as: (Annual Cash Coupon Payment) / (Current Bond Price). The annual coupon is: ($1,000)(0.0775) = $77.50. The current yield is then: ($77.50) / ($1,012.45) = 0.0765 = 7.65%.
作者: karoliukas    时间: 2012-3-31 14:37

Suppose that IBM has a $1,000 par value bond outstanding with a 12% semiannual coupon that is currently trading at 102.25 with seven years to maturity. Which of the following is closest to the yield to maturity (YTM) on the bond?
A)
11.21%.
B)
11.52%.
C)
11.91%.


To find the YTM, enter PV = –$1,022.50; PMT = $60; N = 14; FV = $1,000; CPT → I/Y = 5.76%. Now multiply by 2 for the semiannual coupon payments: (5.76)(2) = 11.52%.
作者: karoliukas    时间: 2012-3-31 14:38

When computing the yield to maturity, the implicit reinvestment assumption is that the interest payments are reinvested at the:
A)
prevailing yield to maturity at the time interest payments are received.
B)
coupon rate.
C)
yield to maturity at the time of the investment.


The reinvestment assumption states that reinvestment must occur at the YTM in order for an investor to earn the YTM.  The assumption also states that payments are received in a prompt and timely fashion resulting in immediate reinvestment of those funds.
作者: karoliukas    时间: 2012-3-31 14:38

In which of the following conditions is the bond selling at a premium? The coupon rate:
A)
current rate and yield-to-maturity are all the same.
B)
is greater than current yield, which is greater than yield-to-maturity.
C)
is less than current yield, which is less than yield-to-maturity.


When a bond is selling at a premium the nominal yield, coupon payment divided by face value, will be greater than current yield and current yield will be greater than YTM.
作者: karoliukas    时间: 2012-3-31 14:38

A bond will sell at a discount when the coupon rate is:
A)
less than the current yield and the current yield is less than the yield to maturity.
B)
greater than the current yield and the current yield is greater than the yield to maturity.
C)
less than the current yield and the current yield is greater than the yield to maturity.


When a bond sells at a discount the nominal yield, coupon yield divided by the face value, will be less than current yield and current yield will be less than YTM.
作者: karoliukas    时间: 2012-3-31 14:38

Which of the following statements concerning the yield-to-maturity on a bond is CORRECT? Yield to maturity (YTM) is:
A)
based on the assumption that any payments received are reinvested at the current yield.
B)
the discount rate that will set the present value of the payments equal to the bond price.
C)
below the current yield minus capital gain when the bond sells at a discount, and above the current yield plus capital loss when the bond sells at a premium.


Reinvestments occur at the YTM. The YTM will find the present value of a future value and associated payments.
作者: karoliukas    时间: 2012-3-31 14:39

The yield to maturity (YTM) is:
A)
the discount rate that will set the present value of the payments equal to the bond price.
B)
neither of these answers are correct.
C)
below the coupon rate when the bond sells at a discount, and about the coupon rate when the bond sells at a premium.


The YTM is a measure that will take into account present value, future value, periodic payments, and periods until maturity to find the rate of return that is being earned.  If the YTM is given, the result will be finding the present value of the future value and periodic cash flows.
作者: karoliukas    时间: 2012-3-31 14:40

Which of the following is a limitation of the cash flow yield measure? The cash flow yield measure:
A)
assumes that interest rates do not change over the life of the security.
B)
assumes that the projected cash flows are reinvested at the cash flow yield.
C)
assumes a flat yield curve.


Cash flow yield has two major deficiencies: (i) it is implicitly assumed that the cash flows will be reinvested at the cash flow yield prevailing when the MBS or ABS is priced, and (ii) it is assumed that the MBS or ABS will be held until maturity.
作者: karoliukas    时间: 2012-3-31 14:40

Regarding the computation of the cash flow yield for an agency security, which of the following is the best reason why the assumption that the projected cash flows are actually realized is very restrictive?
A)
Interest rate risk.
B)
Prepayments.
C)
Default risk.


Prepayments instill uncertainty into the assumed cash flows used to compute cash flow yield.
作者: karoliukas    时间: 2012-3-31 14:41

In which of the following cases is the bond selling at a discount? The coupon rate is:
A)
greater than current yield and current yield is greater than yield-to-maturity.
B)
smaller than current yield and current yield is smaller than yield-to-maturity.
C)
smaller than current yield and current yield is greater than yield-to-maturity.


When a bond is selling at a discount the nominal yield, coupon payment divided by face value, will be less than current yield and current yield will be less than YTM.
作者: karoliukas    时间: 2012-3-31 14:41

An investor purchases a 4-year, 6%, semiannual-pay Treasury note for $9,485. The security has a par value of $10,000. To realize a total dollar return equal to 7.515% (its yield to maturity), all payments must be reinvested at a return of:
A)
more than 7.515%.
B)
7.515%.
C)
less than 7.515%.


The reinvestment assumption that is embedded in any present value-based yield measure implies that all coupons and principal payments must be reinvested at the specific rate of return, in this case, the yield to maturity. Thus, to obtain a 7.515% total dollar return, the investor must reinvest all the coupons at a 7.515% rate of return. Total dollar return is made up of three sources, coupons, principal, and reinvestment income.
作者: karoliukas    时间: 2012-3-31 14:42

All else being equal, which of the following bond characteristics will lead to higher levels of coupon reinvestment risk?
A)
Longer maturities and lower coupon levels.
B)
Longer maturities and higher coupon levels.
C)
Shorter maturities and higher coupon levels.


Other things being equal, the amount of reinvestment risk embedded in a bond will increase with higher coupons because there is a greater dollar amount to reinvest, and with longer maturities because the reinvestment period is longer.
作者: karoliukas    时间: 2012-3-31 14:43

If the coupon payments are reinvested at the coupon rate during the life of the issue, then the yield to maturity:
A)
is less than the realized yield.
B)
may be greater or less than the realized yield.
C)
is greater than the realized yield.


For the realized yield to equal the YTM, coupon reinvestments must occur at that YTM. Whether reinvesting the coupons at the coupon rate will result in a realized yield higher or lower than the YTM depends on whether the bond is at a discount (coupon < YTM) or a premium (coupon>YTM).
作者: karoliukas    时间: 2012-3-31 14:43

Jane Walker has set a 7% yield as the goal for the bond portion of her portfolio. To achieve this goal, she has purchased a 7%, 15-year corporate bond at a discount price of 93.50. What amount of reinvestment income will she need to earn over this 15-year period to achieve a compound return of 7% on a semiannual basis?
A)
$459.
B)
$624.
C)
$574.


935(1.035)30 = $2,624
Bond coupons: 30 × 35 = $1,050
Principal repayment: $1,000
2,624 − 1,000 – 1050 = $574 required reinvestment income
作者: karoliukas    时间: 2012-3-31 14:43

All else being equal, which of the following bond characteristics will lead to lower levels of coupon reinvestment risk?
A)
Shorter maturities and lower coupon levels.
B)
Longer maturities and higher coupon levels.
C)
Shorter maturities and higher coupon levels.


Other things being equal, the amount of reinvestment risk embedded in a bond will decrease with lower coupons because the there will be a lesser dollar amount to reinvest and with shorter maturities because the reinvestment period is shorter.
作者: karoliukas    时间: 2012-3-31 14:46

All else being equal, which of the following bond characteristics will lead to lower levels of coupon reinvestment risk?
A)
Shorter maturities and lower coupon levels.
B)
Longer maturities and higher coupon levels.
C)
Shorter maturities and higher coupon levels.


Other things being equal, the amount of reinvestment risk embedded in a bond will decrease with lower coupons because the there will be a lesser dollar amount to reinvest and with shorter maturities because the reinvestment period is shorter.
作者: karoliukas    时间: 2012-3-31 14:47

What is the bond-equivalent yield given if the monthly yield is equal to 0.7%?
A)
8.55%.
B)
8.65%.
C)
8.40%.

The bond equivalent yield (BEY) is computed as follows:
BEY = 2 × [(1 + monthly yield)6 − 1] = 2 × [(1 + 0.007)6 − 1] = 8.55%
作者: karoliukas    时间: 2012-3-31 14:47

What is the annual-pay yield for a bond with a bond-equivalent yield of 5.6%?
A)
5.68%.
B)
5.60%.
C)
5.52%.


The annual-pay yield is computed as follows:
Annual-pay yield = [(1 + 0.056 / 2)2 – 1
作者: karoliukas    时间: 2012-3-31 14:48

The yield to maturity for a semiannual-pay, 10-year corporate bond is 5.25%. What is the bond's annual equivalent yield?
A)
5.32%.
B)
5.00%.
C)
5.25%.


The annual equivalent yield is equal to [1 + (nominal yield/number of payments per year)]number of payments per year – 1 = (1 + 0.0525/2)2 - 1 = 5.32%.
作者: karoliukas    时间: 2012-3-31 14:48

What is the semiannual-pay bond equivalent yield on an annual-pay bond with a yield to maturity of 12.51%?
A)
12.14%.
B)
12.00%.
C)
12.51%.


The semiannual-pay bond equivalent yield of an annual-pay bond = 2 × [(1 + yield to maturity on the annual-pay bond)0.5 – 1] = 12.14%.
作者: karoliukas    时间: 2012-3-31 14:49

The yield to maturity on an annual-pay bond 5.6%, what is the bond equivalent yield for this bond?
A)
5.52%.
B)
5.43%.
C)
5.60%.


The bond-equivalent yield is computed as follows:
Bond-equivalent yield = 2[(1 + 0.056)0.5 – 1] = 5.52%
作者: karoliukas    时间: 2012-3-31 14:49

What is the bond-equivalent yield if the monthly yield is equal to 0.5%?
A)
6.08%.
B)
6.00%.
C)
6.12%.

The bond equivalent yield (BEY) is computed as follows:
BEY = 2 × [(1 + monthly yield)6 − 1] = 2 × [(1 + 0.005)6 − 1] = 6.08%
作者: karoliukas    时间: 2012-3-31 14:50

Sysco Foods has a 10-year bond outstanding with an annual coupon of 6.5%. If the bond is currently priced at $1,089.25, which of the following is closest to the bond-equivalent yield of the bond?
A)
5.26%.
B)
5.33%.
C)
5.42%.


First, find the annual yield to maturity of the bond as: FV = $1,000; PMT = $65; N = 10; PV = –1,089.25; CPT → I/Y = 5.33%. Then, find the BEY as: 2 × [(1 + YTM)0.5 – 1] = 0.0526 = 5.26%.
作者: karoliukas    时间: 2012-3-31 14:51

Consider a 6-year $1,000 par bond priced at $1,011. The coupon rate is 7.5% paid semiannually. Six-year bonds with comparable credit quality have a yield to maturity (YTM) of 6%. Should an investor purchase this bond?
A)
Yes, the bond is undervalued by $38.
B)
No, the bond is overvalued by $64.
C)
Yes, the bond is undervalued by $64.


FV = 1,000
PMT = 37.5
N = 12
I/Y = 3%
CPT PV = 1,074.66
1,074.66 – 1,011 = 64
作者: karoliukas    时间: 2012-3-31 14:51

Corinne Mueller is explaining how to derive the theoretical Treasury spot rate curve from the prices of Treasury coupon bonds. She states the following:
Statement 1: To calculate a theoretical Treasury spot rate curve from the yields on coupon bonds, we must know at least two actual Treasury spot rates.
Statement 2: To compute the theoretical 3-year Treasury spot rate, first determine the spot rates for each of the bond’s coupon periods from 0.5 to 2.5 years. Discount each coupon payment to its present value using the theoretical spot rate for each period. The theoretical 3-year spot rate is the discount rate on the final coupon and principal payment that sets the sum of the present values of all the bond’s cash flows equal to its price.
With respect to Mueller’s statements:
A)
only one is correct.
B)
both are correct.
C)
both are incorrect.


Statement 1 is incorrect. If we know one actual spot rate, we can calculate the theoretical spot rate for the next longer period. With these two spot rates we can calculate the next theoretical spot rate, and so on up the coupon curve. Statement 2 is a correct description of the methodology for computing a theoretical Treasury spot rate.
作者: karoliukas    时间: 2012-3-31 14:52

An investor gathers the following information about a 2-year, annual-pay bond:
Using the above spot rates, the current price of the bond is closest to:
A)
$983.
B)
$1,000.
C)
$1,010.


The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $40 (0.04 × 1,000). The bond price = 40/(1.02) + 1,040/(1.05)2 = $982.53.
作者: karoliukas    时间: 2012-3-31 14:53

Which of the following statements regarding zero-coupon bonds and spot interest rates is least accurate?
A)
Price appreciation creates all of the zero-coupon bond's return.
B)
Zero-coupon bonds have no coupons.
C)
Spot interest rates will never vary across the term structure.


Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond’s return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. Spot rates are defined as interest rates used to discount a single cash flow to be received in the future.
作者: karoliukas    时间: 2012-3-31 14:53

An investor gathers the following information about a 3-year, annual-pay bond:
Using the above information, the 3-year spot rate is closest to:
A)
4.37%.
B)
4.27%.
C)
8.20%.


The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $80 (0.08 × 1,000) and the face value is $1,000. Hence, bond price of 1,100= 80/(1.05)+ 80/(1.06)2 + 1,080/(1 + 3-year spot rate)3. Using the yx key on our calculator, we can solve for the 3-year spot rate of 4.27%.
作者: karoliukas    时间: 2012-3-31 14:54

The 3-year spot rate is 10%, and the 4-year spot rate is 10.5%. What will the 1-year rate be 3 years from now?
A)
12.0%.
B)
10.0%.
C)
11.0%.


[(1 + Z4)4 / (1 + Z3)3] − 1 = 12.01% = 12%.
作者: karoliukas    时间: 2012-3-31 14:54

Given the following spot rate curve:

Spot Rate
1-yr zero = 9.50%
2-yr zero = 8.25%
3-yr zero = 8.00%
4-yr zero = 7.75%
5-yr zero = 7.75%

What will be the market price of a five-year, 9% annual coupon rate bond?
A)
$1,067.78.
B)
$1,000.00.
C)
$1,047.68.


90 / (1 + 0.095) + 90 / (1 + 0.0825)2 + 90 / (1 + 0.08)3 + 90 / (1 + 0.0775)4 + 1,090 / (1 + 0.0775)5 = $1,047.68.
作者: karoliukas    时间: 2012-3-31 14:55

Using the following spot rates, what is the price of a three-year bond with annual coupon payments of 5%?
A)
$98.87.
B)
$93.27.
C)
$97.47.


The bond price is computed as follows:
Bond price = (5 / 1.0478) + (5 / 1.05562) + (105 / 1.05983) = $97.47
作者: karoliukas    时间: 2012-3-31 14:55

An analyst observes that the current 6-month T-Bill rate is 8% (4% semi-annually) and the one-year T-Bill rate is 9% (4.5% semi-annually). There is an existing 1.5-year, 9% semi-annual coupon bond selling for $990. What is the annualized 1.5-year spot rate?
A)
8.8%.
B)
9.5%.
C)
9.8%.


45 / (1.04) + 45 / (1.045)2 + 1045 / (1 + Z3)3 = 990
(1045 / 905.53 )0.3333 − 1 = Z3 = 4.89%
Annualized = 9.8%.
作者: karoliukas    时间: 2012-3-31 14:55

Assume that a callable bond's call period starts two years from now with a call price of $102.50. Also assume that the bond pays an annual coupon of 6% and the term structure is flat at 5.5%. Which of the following is the price of the bond assuming that it is called on the first call date?
A)
$100.00.
B)
$102.50.
C)
$103.17.


The bond price is computed as follows:
Bond price = 6/1.055 + (102.50 + 6)/1.0552 = $103.17
作者: karoliukas    时间: 2012-3-31 14:56

Can spot interest rates be used to value a callable bond?
A)
Yes.
B)
No.
C)
It depends on the slope of the term structure.


Any complex debt instruments (like callable bonds, putable bonds, and mortgage-backed securities) can be viewed as the sum of the present value of its individual cash flows where each of those cash flows are discounted at the appropriate zero-coupon bond spot rate. It should be noted that while the appropriate spot interest rate can be used to discount each cash flow, determining the actual pattern of cash flows is uncertain due to the possibility of the bond being called away.
作者: Kingpin804    时间: 2012-3-31 14:57

One of the most commonly used yield spread measures is the nominal spread. Which of the following is NOT a limitation of nominal spread? The nominal spread:
A)
assumes a flat yield curve.
B)
assumes all cash flows can be discounted at the same rate.
C)
is difficult to calculate.


The nominal spread is easy to calculate – it is simply the yield to maturity on a bond minus the yield to maturity on a Treasury security of a similar maturity. Because the nominal yield is based on the yield to maturity, it suffers the same shortcomings as yield to maturity. The yield measures assume that all cash flows can be discounted at the same rate (i.e., assumes a flat yield curve). They also assume that all coupon payments will be received in a prompt and timely fashion, and reinvested to maturity, at a rate of return that is equal to the appropriate solving rate (i.e., the bond's YTM or its BEY).
作者: Kingpin804    时间: 2012-3-31 14:57

One of the most commonly used yield spread measures is the nominal spread. Which of the following is a limitation of nominal spread? The nominal spread assumes:
A)
an upward sloping yield curve.
B)
all coupon payments are reinvested at a rate equal to the risk free rate.
C)
a flat yield curve.


The nominal spread is easy to calculate – it is simply the yield to maturity on a bond minus the yield to maturity on a Treasury security of a similar maturity. Because the nominal yield is based on the yield to maturity, it suffers the same shortcomings as yield to maturity. The yield measures assume that all cash flows can be discounted at the same rate (i.e., assumes a flat yield curve). They also assume that all coupon payments will be received in a prompt and timely fashion, and reinvested to maturity, at a rate of return that is equal to the appropriate solving rate (i.e., the bond’s YTM or its BEY).
作者: Kingpin804    时间: 2012-3-31 14:57

The zero volatility spread (Z-spread) is the spread that:
A)
is added to the yield to maturity of a similar maturity Treasury bond to equal the yield to maturity of the risky bond.
B)
is added to each spot rate on the Treasury yield curve that will cause the present value of the bond's cash flows to equal its market price.
C)
results when the cost of the call option in percent is subtracted from the option adjusted spread.


The zero volatility spread (Z-spread) is the interest rate that is added to each zero-coupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value. The nominal spread is the spread that is added to the YTM of a similar maturity Treasury bond that will then equal the YTM of the risky bond. The zero volatility spread (Z-spread) is the spread that results when the cost of the call option in percent is added to the option adjusted spread.
作者: Kingpin804    时间: 2012-3-31 14:58

Which of the following statements regarding the option adjusted spread (OAS) is least accurate? The option adjusted spread:
A)
is the spread added to the Treasury spot rate curve that the bond would have if it were option-free.
B)
is the spread that accounts for non-option characteristics like credit risk, liquidity risk, and interest rate risk.
C)
for a putable bond is the Z-spread minus the cost of the option.


Since the buyer of a putable bond must pay extra for the put option, the OAS spread for a putable bond is the Z-spread plus the put option cost in percent.
作者: Kingpin804    时间: 2012-3-31 14:59

Which of the following statements regarding the option adjusted spread (OAS) is least accurate? The option adjusted spread:
A)
is the spread added to the Treasury spot rate curve that the bond would have if it were option-free.
B)
is the spread that accounts for non-option characteristics like credit risk, liquidity risk, and interest rate risk.
C)
for a putable bond is the Z-spread minus the cost of the option.


Since the buyer of a putable bond must pay extra for the put option, the OAS spread for a putable bond is the Z-spread plus the put option cost in percent.
作者: Kingpin804    时间: 2012-3-31 14:59

One of the most commonly used yield spread measures is the nominal spread. Which of the following is least likely a limitation of nominal spread? The nominal spread assumes:
A)
all cash payments will be received in a prompt and timely manner.
B)
all cash flows can be discounted at the same rate.
C)
an upward sloping yield curve.


The nominal spread is easy to calculate – it is simply the yield to maturity on a bond minus the yield to maturity on a Treasury security of a similar maturity. Because the nominal yield is based on the yield to maturity, it suffers the same shortcomings as yield to maturity. The yield measures assume that all cash flows can be discounted at the same rate (i.e., assumes a flat yield curve). They also assume that all coupon payments will be received in a prompt and timely fashion, and reinvested to maturity, at a rate of return that is equal to the appropriate solving rate (i.e., the bond’s YTM or its BEY).
作者: Kingpin804    时间: 2012-3-31 15:00

The zero volatility spread (Z-spread) is the spread that:
A)
is added to the yield to maturity of a similar maturity Treasury bond to equal the yield to maturity of the risky bond.
B)
is added to each spot rate on the Treasury yield curve that will cause the present value of the bond's cash flows to equal its market price.
C)
results when the cost of the call option in percent is subtracted from the option adjusted spread.


The zero volatility spread (Z-spread) is the interest rate that is added to each zero-coupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value. The nominal spread is the spread that is added to the YTM of a similar maturity Treasury bond that will then equal the YTM of the risky bond. The zero volatility spread (Z-spread) is the spread that results when the cost of the call option in percent is added to the option adjusted spread.
作者: Kingpin804    时间: 2012-3-31 15:01

The following information is available for two bonds:

The embedded option cost for Bond:

A)
X is 5bp.
B)
X is 13bp.
C)
X is 8bp.


Option cost (Bond X) = Z-spread – OAS = 68bp – 55bp = 13bp
Option cost (Bond Y) = Z-spread – OAS = 78bp – 100bp = - 22bp
作者: Kingpin804    时间: 2012-3-31 15:01

Which of the following statements on spreads is NOT correct?
A)
The Z-spread may be used for bonds that contain call options.
B)
The Z-spread will equal the nominal spread if the term structure of interest rates is flat.
C)
The option-adjusted spread (OAS) is the difference between the Z-spread and the option cost.


The Z-spread is used for risky bonds that do NOT contain call options in an attempt to improve on the shortcomings of the nominal spread. The other statements are correct.
作者: Kingpin804    时间: 2012-3-31 15:01

An analyst has gathered the following information:

Which of the following statements regarding spreads on bond A is CORRECT?

A)
The nominal spread is approximately 25 basis points.
B)
The Z-spread is approximately 85 basis points.
C)
The nominal spread is approximately 85 basis points.


The nominal spread is 8.50% − 7.65% = 0.85%. Note that the Z-spread, calculated by trial and error, is approximately 48 basis points.
作者: Kingpin804    时间: 2012-3-31 15:02

Kwagmyre Investments, Ltd., hold two bonds: a callable bond issued by Mudd Manufacturing Inc. and a putable bond issued by Precarious Builders. Both bonds have option adjusted spreads (OAS) of 135 basis points (bp). Kevin Grisly, a junior analyst at the firm, makes the following statements (each statement is independent). Apparently, Grisly could benefit from a CFA review course, because the only statement that could be accurate is:
A)
Given a nominal spread for Precarious Builders of 110 bp, the option cost is -25 bp.
B)
The Z-spread for Mudd's bond is based on the YTM.
C)
The spread over the spot rates for a Treasury security similar to Mudd's bond is 145 bp.

The “spread over the spot rates for a Treasury security similar to Mudd’s bond” refers to the Z-spread on the bond.For a callable bond, the OAS < Z-spread, so this could be a true statement because 135bp < 145 bp.

The other statements are false. The option cost is calculated using the OAS and the Z-spread, not the nominal spread. The static spread (or Z-spread)is the spread over each of the spot rates in a given Treasury term structure, not the spreadover the Treasury’s YTM.

Following is a more detailed discussion:

The option-adjusted spread (OAS) is used when a bond has embedded options. The OAS can be thought of as the difference between the static or Z-spread and the option cost. For the exam, remember the following relationship between the static spread (Z-spread), the OAS, and the embedded option cost:

Z Spread - OAS = Option Cost in % terms


Remember the following option value relationships:
作者: Kingpin804    时间: 2012-3-31 15:02

Assume that an option-free 5% coupon bond with annual coupon payments has two years to maturity. A callable bond that is the same in every respect as the option-free bond is priced at 91.76. With the term structure flat at 6% what is the value of the embedded call option?
A)
-8.24.
B)
4.58.
C)
6.41.


The option value is the difference between the option-free bond price and the corresponding callable bond price.
The value of the option free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign).
The option value = 98.17 – 91.76 = 6.41.
作者: Kingpin804    时间: 2012-3-31 15:02

Assume an option-free 5% coupon bond with annual coupon payments has two years remaining to maturity. A putable bond that is the same in every respect as the option-free bond is priced at 101.76. With the term structure flat at 6% what is the value of the embedded put option?
A)
1.76.
B)
3.59.
C)
-3.59.


The value of the embedded put option of the putable bond is the difference between the price of the putable bond and the price of the option-free bond.
The value of the option-free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign).
The option value = 101.79 − 98.17 = 3.59.
作者: Kingpin804    时间: 2012-3-31 15:03

The six-year spot rate is 7% and the five-year spot rate is 6%. The implied one-year forward rate five years from now is closest to:
A)
6.5%.
B)
12.0%.
C)
5.0%.


1r5= [(1 + R6)6 / (1 + R5)5] - 1 = [(1.07)6/(1.06)5] – 1 = [1.5 / 1.338] - 1 = 0.12
作者: Kingpin804    时间: 2012-3-31 15:03

Suppose the 3-year spot rate is 12.1% and the 2-year spot rate is 11.3%. Which of the following statements concerning forward and spot rates is most accurate? The 1-year:
A)
forward rate two years from today is 13.2%.
B)
forward rate one year from today is 13.7%.
C)
forward rate two years from today is 13.7%.


The equation for the three-year spot rate, Z3, is (1 + Z1)(1 + 1f1)(1 + 1f2) = (1 + Z3)3. Also, (1 + Z1)(1 + 1f1) = (1 + Z2)2. So, (1 + 1f2) = (1 + Z3)3 / (1 + Z2)2, computed as: (1 + 0.121)3 / (1 + 0.113)2 = 1.137. Thus, 1f2 = 0.137, or 13.7%.
作者: Kingpin804    时间: 2012-3-31 15:03

Given the following spot and forward rates, how much should an investor pay for each $100 of a 3-year, annual zero-coupon bond?
The investor should pay approximately:
A)
$76.
B)
$44.
C)
$83.


The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.
Using the formula: (1 + Z3)3 = (1 + 1f0)(1 + 1f1)(1 + 1f2)
where Z = spot rate and nfm = the n year rate m periods from today, (1f0 = the 1 year spot rate now).
(1 + Z3)3 = (1.0375) × (1.095) × (1.158)
Z3 = 1.3155601/3 − 1 = 0.095730, or 9.57%

Then, the value of the zero coupon bond = 100 / (1.09573)3 = 76.01, or approximately $76,
or, using a financial calculator, N = 3; I/Y = 9.57; FV = 1,000; PMT = 0; CPT → PV = 76.20 or approximately $76.
作者: Kingpin804    时间: 2012-3-31 15:04

Given the following spot and forward rates, how much should an investor pay for a 3-year, annual zero-coupon bond with a face value of $1,000?
The investor should pay approximately:
A)
$724.
B)
$720.
C)
$884.


The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.

Using the formula: (1 + Z3)3 = (1 + 1f0) × (1 + 1f1) × (1 + 1f2)

Where Z = spot rate and nfm = The n year rate m periods from today, (1f0 = the 1 year spot rate now)

(1 + Z3)3 = (1.035) × (1.115) × (1.1975)
Z3 = 1.38191/3 − 1 = 0.11386, or 11.39%

Then, the value of the zero coupon bond = 1,000 / (1.1139)3 = 723.62, or approximately $724.
or, using a financial calculator, N = 3; I/Y = 11.39; FV = 1,000; PMT = 0; CPT → PV = 723.54, or approximately $724.
作者: Kingpin804    时间: 2012-3-31 15:04

Given the one-year spot rate S1 = 0.06 and the implied 1-year forward rates one, two, and three years from now of: 1f1 = 0.062; 1f2 = 0.063; 1f3 = 0.065, what is the theoretical 4-year spot rate?
A)
6.75%.
B)
6.00%.
C)
6.25%.


S4 = [ (1.06) (1.062) (1.063) (1.065) ].25 − 1 = 6.25%.



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