GEN COMBO LOOSELEAF INVESTMENTS; CONNECT ACCESS CARD
11th Edition
ISBN: 9781260201550
Author: Bodie
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 15, Problem 8PS
A
Summary Introduction
To calculate: The expected price of the 4-year bond at the end of the first year, second year, third year and fourth year are to be determined.
Introduction: When the forward rates are equal to the market expectation rates is called as expectation hypothesis. The expected
A
Expert Solution
Answer to Problem 8PS
The expected price of the 4-year bond is shown as −
| Beginning of the year | Expected price |
| 1 | $792.16 |
| 2 | $839.69 |
| 3 | $881.68 |
| 4 | $934.58 |
Explanation of Solution
Expectations theory is the long term interest rate that predicts the short term interest rates. It suggests the investor gets same interest by investing in two different investment having diffrent maturity period.At this condition liquidity premium is zero.
The following method will be used for the calculation of the Yield to maturity (YTM) and the forward rate −
| Maturity | Price of bond | YTM | Forward rate |
| 1 | $943.40 | ||
| 2 | $898.47 | ||
| 3 | $847.62 | ||
| 4 | $792.16 |
On calculation, the values of forward rate and YTM is given as −
| Maturity | Price of bond | YTM | Forward rate |
| 1 | $943.40 | 6.00% | 6.00% |
| 2 | $898.47 | 5.50% | 5.00% |
| 3 | $847.62 | 5.67% | 6.00% |
| 4 | $792.16 | 6.00% | 7.00% |
Now, the following method will be used for the calculation of the expected price −
| Beginning of the year | Expected price calculation | Expected price |
| 1 | $792.16 | $792.16 |
| 2 | $839.69 | |
| 3 | $881.68 | |
| 4 | $934.58 |
The expected price of the 4-year bond is given as −
| Beginning of the year | Expected price |
| 1 | $792.16 |
| 2 | $839.69 |
| 3 | $881.68 |
| 4 | $934.58 |
B
Summary Introduction
To calculate: The rate of return of the bond in first year, second year, third year and fourth year and prove that expected return equals the forward rate for each year.
Introduction: When the forward rates are equal to the market expectation rates is called as expectation hypothesis. The expected rate of return is defined as the amount which is expected on a security at specific period.
B
Expert Solution
Answer to Problem 8PS
The forward rate and expected rate of return is equal.
Explanation of Solution
Expectations theory is the long term interest rate that predicts the short term interest rates. It suggests the investor gets same interest by investing in two different investment having diffrent maturity period. At this condition liquidity premium is zero.
The following formula will be used for the calculation of the return of year bond −
| Beginning of the year | Expected price | Expected rate of return calculation | Expected rate of return |
| 1 | $792.16 | 6.00% | |
| 2 | $839.69 | 5.00% | |
| 3 | $881.68 | 6.00% | |
| 4 | $934.58 | 7.00% |
Now, the comparison between the values of the forward rate and the expected rate of return is given as −
| Forward rate | Expected rate of return |
| 6.00% | 6.00% |
| 5.00% | 5.00% |
| 6.00% | 6.00% |
| 7.00% | 7.00% |
The above table proves that the value of the forward rate is equal to the value of the expected rate of return for each year.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Suppose that the yield curve shows that the one-year bond yield is 8 percent, the two-year yield is 7 percent, and the three-year yield
is 7 percent. Assume that the risk premium on the one-year bond is zero, the risk premium on the two-year bond is 1 percent, and the
risk premium on the three-year bond is 2 percent.
a. What are the expected one-year interest rates next year and the following year?
The expected one-year interest rate next year =
The expected one-year interest rate the following year
b. If the risk premiums were all zero, as in the expectations hypothesis, what would the slope of the yield curve be?
The slope of the yield curve would be (Click to select)
%
%
Required:
a. Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown below at
the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year.
b. What is the rate of return of the bond in years 1, 2, 3, and 4? Conclude that the expected return equals the forward rate for each
year.
Complete this question by entering your answers in the tabs below.
Required A Required B
Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown
below at the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Beginning
Price of Bond
of Year
Expected Price
1
$
935.90
2
$
906.47
3
$
837.12
4
$
775.39
Required A
Required B >
B
Assume that the real risk free rate is 2% and the average expected inflation rate is 3% for each future year. The default risk premium and the liquidity premium for bond x are each 1% and the applicable Maturity Risk premium is 2% what is bond x’s interest rate.
Round to 2 decimal places
Chapter 15 Solutions
GEN COMBO LOOSELEAF INVESTMENTS; CONNECT ACCESS CARD
Ch. 15 - Prob. 1PSCh. 15 - Prob. 2PSCh. 15 - Prob. 3PSCh. 15 - Prob. 4PSCh. 15 - Prob. 5PSCh. 15 - Prob. 6PSCh. 15 - Prob. 7PSCh. 15 - Prob. 8PSCh. 15 - Prob. 9PSCh. 15 - Prob. 10PS
Ch. 15 - Prob. 11PSCh. 15 - Prob. 12PSCh. 15 - Prob. 13PSCh. 15 - Prob. 14PSCh. 15 - Prob. 15PSCh. 15 - Prob. 16PSCh. 15 - Prob. 17PSCh. 15 - Prob. 18PSCh. 15 - Prob. 19PSCh. 15 - Prob. 1CPCh. 15 - Prob. 2CPCh. 15 - Prob. 3CPCh. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 6CPCh. 15 - Prob. 7CPCh. 15 - Prob. 8CPCh. 15 - Prob. 9CPCh. 15 - Prob. 10CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- Suppose 2-year Treasury bonds yield 4.1%,while 1-year bonds yield 3.2%. r* is 1%, and the maturity risk premium is zero.a. Using the expectations theory, what is the yield on a 1-year bond, 1 year from now?Calculate the yield using a geometric average.b. What is the expected inflation rate in Year 1? Year 2?arrow_forwardAssume that the real risk-free rate of return, k*, is 3%, and it will remain at that level far into the future. Also assume that maturity risk premiums (MRP) increase from zero for bonds that mature in one year or less to a maximum of 1%, and MRP increases by 0.2% for each year to maturity that is greater than one year-that is, MRP equals 0.2% for two-year bond, 0.4% for a three-year bond, and so forth. Following are the expected inflation rates for the next five years: Year Inflation Rate (%) 2017 5 2018 6 2019 7 2020 8 2021 9 a) Compute the interest rate for a one-, two-, three-, four-, and five-year bond. b) If inflation is expected to equal 9% every year after 2021, what should be the interest rate for a 10- and 20-year bond? c) Plot the yield curve for the interest rates you computed in part [a] and [b]. d) Based on the curve (in part c), interpret your findings.arrow_forwardd Required: a. Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown below at the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year. b. What is the rate of return of the bond in years 1, 2, 3, and 4? Conclude that the expected return equals the forward rate for each year. Complete this question by entering your answers in the tabs below. Required A Required B Assuming that the expectations hypothesis is valid, compute the expected price of the four-year zero coupon bond shown below at the end of (i) the first year; (ii) the second year; (iii) the third year; (iv) the fourth year. Note: Do not round intermediate calculations. Round your answers to 2 decimal places. Beginning of Year 1 2 3 4 Price of Bond 948.40 921.47 832.62 781.99 $ $ GA $ $ Expected Price $ $ $ 1,150.22 X 1,144.95 X 965.60 x 937.47arrow_forward
- Assume that the real risk-free rate is 2% and the average annual expected inflation rate is 4%. The DRP and LP for Bond A are each 2%, and the applicable MRP is 3%. What is Bond A's interest rate?arrow_forwardAssume that the real risk-free rate is 2% and that the maturityrisk premium is zero. If a 1-year Treasury bond yield is 5% and a 2-year Treasury bondyields 7%, what is the 1-year interest rate that is expected for Year 2? Calculate this yieldusing a geometric average. What inflation rate is expected during Year 2? Comment onwhy the average interest rate during the 2-year period differs from the 1-year interestrate expected for Year 2.arrow_forwardAssume the pure expectation theory holds: If the return on 6 years maturity treasury bill (TB) is 8%, the return on 1-year maturity TB is 6%, the return on a 2 years maturity (TB) is 7%, X is the return on a 3-year maturity bond. a. Calculate X, the forward rate, the return on a 3-year maturity bond, 3 years from today. b. Graph the yield curve c. Based on the yield curve you just derived, what are your expectations of the future performance of the economy?arrow_forward
- Suppose the interest rate on a 1-year T-bond is 6.3 % and that on a 3 year T-bond is 7.3 %. Assuming the pure expectations theory is correct, what is the market's forecast for 2-year rates 1 year from now? Enter your answer as a percentage and do not use the % symbol.arrow_forwardSuppose that the interest rate on one-year bonds is currently 4 percent and is expected to be 5 percent in one year and 6 percent in two years. Using the expectations hypothesis, compute the yields on two- and three-year bonds and plot the yield curve.arrow_forwardConsider a 4-years bond with a 8% annual coupon rate and semi-annual payments. Let us suppose that the zero coupon curve rate today with annual compounding is given by the one in Table 1.(a) Calculate the discount factors for all the previous maturities and then the bond price.(b) Calculate the equivalent continuous compounding rates. What do you expect as result for the bond price with these rates? Should it be lower, higher or equal to the one in part (a)? Why? The equivalent continuous compounding rates should be lower than the annual rates. Why?arrow_forward
- In calculating the current price of a bond paying semiannual coupons, one needs to O use double the number of years for the number of payments made. O use the semiannual coupon. O use the semiannual rate as the discount rate. O All of the above needs to be done.arrow_forwardSuppose that y is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that y is expressed with simply com- pounding, that interest is paid annually on the bond, and that y follows the process dy = a(y0 −y)dt + oydWt, where a, y0, and o are positive constants and dWt is a Wiener process. (a) What is the process followed by the bond price? (b) What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?arrow_forwardSuppose the real risk-free rate of interest is r*=4%�*=4% and it is expected to remain constant over time. Inflation is expected to be 1.60% per year for the next two years and 3.90% per year for the next three years. The maturity risk premium is 0.1×(t−1)%0.1×�−1%, where t� is number of years to maturity, a liquidity premium is 0.45%, and the default risk premium for a corporate bond is 1.40%. The average inflation during the first 4 years is2.37% . What is the yield on a 4-year Treasury bond? 4.30% 8.90% 6.75% 7.05% What is the yield on a 4-year BBB-rated bond? 8.90% 7.50% 7.05% 8.45% If the yield on a 5–year Treasury bond is 7.38% and the yield on a 6–year Treasury bond is 7.83%, the expected inflation in 6 years is . (Hint: Do not round intermediate calculations.)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning
Intermediate Financial Management (MindTap Course...
Finance
ISBN:9781337395083
Author:Eugene F. Brigham, Phillip R. Daves
Publisher:Cengage Learning
Bond Valuation - A Quick Review; Author: Pat Obi;https://www.youtube.com/watch?v=xDWTPmqcWW4;License: Standard Youtube License