标题: Reading 66: Yield Measures, Spot Rates, and Forward Rates-LOS [打印本页]
作者: 1215 时间: 2011-3-30 15:31 标题: [2011]Session16-Reading 66: Yield Measures, Spot Rates, and Forward Rates-LOS
Session 16: Fixed Income: Analysis and Valuation
Reading 66: Yield Measures, Spot Rates, and Forward Rates
LOS b: Calculate and interpret the traditional yield measures for fixed-rate bonds and explain their limitations and assumptions.
A bond is selling at a discount relative to its par value. Which of the following relationships holds?
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A) |
yield to maturity < coupon rate < current yield. | |
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B) |
current yield < coupon rate < yield to maturity. | |
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C) |
coupon rate < current yield < 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: 1215 时间: 2011-3-30 15:31
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?
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: 1215 时间: 2011-3-30 15:31
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?
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: 1215 时间: 2011-3-30 15:32
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?
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: 1215 时间: 2011-3-30 15:32
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?
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: 1215 时间: 2011-3-30 15:32
The yield to call is a less conservative yield measure than the yield to maturity whenever the price of a callable bond is quoted at a value:
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A) |
equal to or greater than par value plus one year's interst. | |
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B) |
equal to par value less one year's interest. | |
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|
The more conservative yield measure is the one that results in a lower yield. The YTM on a discount bond will always be less than its yield to call.
作者: 1215 时间: 2011-3-30 15:32
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?
N = 6; PMT = 50; FV = 1,030; PV = $1,081.11; CPT → I = 3.91054
3.91054 × 2 = 7.82
作者: 1215 时间: 2011-3-30 15:32
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?
PMT = 60; N = 10; FV = 1,120; PV = 1,110; CPT → I = 5.47546
(5.47546)(2) = 10.95
作者: 1215 时间: 2011-3-30 15:33
If a bond sells at a discount its:
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A) |
coupon rate is less than the market rate of interest. | |
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B) |
current yield is greater than its YTM. | |
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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: 1215 时间: 2011-3-30 15:33
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)?
N = 8; PMT = 120; PV = -1,150; FV = 1,100; CPT → I/Y.
What is the bond's yield to maturity (YTM)?
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?
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: 1215 时间: 2011-3-30 15:33
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.
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Rate of return |
Current yield |
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: 1215 时间: 2011-3-30 15:34
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.
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YTM |
Compared to zero coupon bond |
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: 1215 时间: 2011-3-30 15:34
The bond's yield-to-maturity is:
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A) |
both of these are correct. | |
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B) |
the discount rate that equates the present value of the cash flows received with the price of the bond. | |
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C) |
based on the assumption that the bond is held to maturity and all coupons are reinvested at the yield-to-maturity. | |
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: 1215 时间: 2011-3-30 15:34
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:
PMT = 100
FV = 1,000
N = 5
PV = 1,000 ? 72 = 928
compute I = 11.997% or 12.00%
作者: 1215 时间: 2011-3-30 15:35
If a $1,000 bond has a 14% coupon rate and a current market price of 950, what is the current market yield?
(0.14)(1,000) = $140 coupon
140/950 × 100 = 14.74
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