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Bond Valuation and Yields

This set of notes contains concepts such as Bond valuations and Yields...
Course

Financial Analytics (FIN3134)

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Students shared 24 documents in this course
Academic year: 2022/2023
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Virginia Polytechnic Institute and State University

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Bond Valuation and Yields

● Bond valuation refers to the process of determining the fair price of a bond.

● The fair price of a bond is the present value of the future cash flows that the bond will

generate. These cash flows include the principal (also known as the face value or par

value) and the interest payments.

● The yield of a bond is the rate of return that an investor will receive if they hold the bond

until it matures. There are several different types of bond yields, including the coupon

yield, the current yield, and the yield to maturity.

Practice Problems:

1. A bond has a face value of $1,000, a coupon rate of 5%, and 10 years until maturity. If

the required rate of return (also known as the discount rate) is 8%, what is the fair price

of the bond?

Answer: The present value of the principal is $1,000 / (1 + 0)^10 = $385. The present

value of the interest payments is (5% x $1,000) / (1 + 0) + (5% x $1,000) / (1 + 0)^2 + ... +

(5% x $1,000) / (1 + 0)^10 = $386. The total present value is $385 + $386 =

$772.

2. A bond has a face value of $1,000, a coupon rate of 8%, and 5 years until maturity. If the

bond is currently trading for $950, what is the yield to maturity?

Answer: The yield to maturity is the discount rate that makes the present value of the bond's cash

flows equal to the price at which it is trading. We can use the formula for the present value of a

bond (described in the first practice problem) to solve for the yield to maturity. Plugging in the

values given, we have: $950 = $1,000 / (1 + y)^5 + (8% x $1,000) / (1 + y) + (8% x $1,000) / (

+ y)^2 + ... + (8% x $1,000) / (1 + y)^5. Solving this equation for y, we find that the yield to

maturity is approximately 10%.

Yield Curve

● A yield curve is a graph that plots the yields of bonds with different maturities on the y-axis and the maturities of the bonds on the x-axis. ● The shape of the yield curve can provide insight into the market's expectations for future interest rates. ○ A upward-sloping yield curve (also known as a normal yield curve) indicates that investors expect interest rates to increase in the future. ○ A downward-sloping yield curve (also known as an inverted yield curve) indicates that investors expect interest rates to decrease in the future. ○ A flat yield curve indicates that investors expect little change in interest rates in the future.

● The slope of the yield curve can also have an impact on the prices of bonds. For example, if the yield curve is steep, then longer-term bonds will tend to be more expensive than shorter-term bonds because they offer higher yields.

Practice Problems: 1. Which of the following yield curves would you expect to see in a market where investors expect interest rates to increase in the near future? A. Upward-sloping yield curve B. Downward-sloping yield curve C. Flat yield curve Answer: A. Upward-sloping yield curve

  1. A bond fund holds a mix of bonds with different maturities. If the yield curve is steep, which of the following statements is most likely to be true? A. The fund's average duration will be short. B. The fund's average duration will be long. C. The fund's average duration will not be affected by the shape of the yield curve. Answer: B. The fund's average duration will be long. The average duration of a bond fund is a measure of the fund's sensitivity to changes in interest rates. A steep yield curve typically indicates that longer-term bonds are more expensive relative to shorter-term bonds, so a bond fund holding a mix of bonds with different maturities is likely to have a higher average duration when the yield curve is steep.
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Bond Valuation and Yields

Course: Financial Analytics (FIN3134)

24 Documents
Students shared 24 documents in this course

University: Virginia Polytechnic Institute and State University

Was this document helpful?
Bond Valuation and Yields
●Bond valuation refers to the process of determining the fair price of a bond.
●The fair price of a bond is the present value of the future cash flows that the bond will
generate. These cash flows include the principal (also known as the face value or par
value) and the interest payments.
●The yield of a bond is the rate of return that an investor will receive if they hold the bond
until it matures. There are several different types of bond yields, including the coupon
yield, the current yield, and the yield to maturity.
Practice Problems:
1. A bond has a face value of $1,000, a coupon rate of 5%, and 10 years until maturity. If
the required rate of return (also known as the discount rate) is 8%, what is the fair price
of the bond?
Answer: The present value of the principal is $1,000 / (1 + 0.08)^10 = $385.95. The present
value of the interest payments is (5% x $1,000) / (1 + 0.08) + (5% x $1,000) / (1 + 0.08)^2 + ... +
(5% x $1,000) / (1 + 0.08)^10 = $386.67. The total present value is $385.95 + $386.67 =
$772.62.
2. A bond has a face value of $1,000, a coupon rate of 8%, and 5 years until maturity. If the
bond is currently trading for $950, what is the yield to maturity?
Answer: The yield to maturity is the discount rate that makes the present value of the bond's cash
flows equal to the price at which it is trading. We can use the formula for the present value of a
bond (described in the first practice problem) to solve for the yield to maturity. Plugging in the
values given, we have: $950 = $1,000 / (1 + y)^5 + (8% x $1,000) / (1 + y) + (8% x $1,000) / (1
+ y)^2 + ... + (8% x $1,000) / (1 + y)^5. Solving this equation for y, we find that the yield to
maturity is approximately 10.24%.
Yield Curve
●A yield curve is a graph that plots the yields of bonds with different maturities on the y-axis and
the maturities of the bonds on the x-axis.
●The shape of the yield curve can provide insight into the market's expectations for future interest
rates.
○A upward-sloping yield curve (also known as a normal yield curve) indicates that
investors expect interest rates to increase in the future.
○A downward-sloping yield curve (also known as an inverted yield curve) indicates that
investors expect interest rates to decrease in the future.
○A flat yield curve indicates that investors expect little change in interest rates in the
future.

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