(a)
To calculate:
The implied one-year forward rates when yield to maturity for1st,2ndand 3rdyear is10%, 11% and 12%respectively.
Introduction:
The implied forward rate is the rate which helps in determining the movements of the interest rate.
The yield to maturity is the rate which provides the amount of expected return on a bond held till its maturity.
Answer to Problem 40PS
The implied one-year forward rate for2ndyear is12.01%and for3rdyear is14.03%
Given:
The yield to maturity for1styear is10%, for2ndyear is11%and for3rdyear is12%.
Explanation:
The formula for computing forward rate as follows:
Forward Rate=(1+YTM for current year)Corresponding year(1+YTM for previous year)Corresponding year−1
For computing forward rate of zero-coupon bond with11%yield to maturity and maturity of2years:
Forward Rate=(1+YTM for current year)Corresponding year(1+YTM for previous year)Corresponding year−1=(1+0.11)2(1+0.10)−1=12.01%
For computing forward rate of zero-coupon bond with12%yield to maturity and maturity of3years:
Forward Rate=(1+YTM for current year)Corresponding year(1+YTM for previous year)Corresponding year−1=(1+0.12)3(1+0.11)2−1=14.03%
Thus, the implied one-year forward rate for2ndyear is12.01%and for3rdyear is14.03%
Explanation of Solution
Given:
The yield to maturity for1styear is10%, for2ndyear is11%and for3rdyear is12%.
The formula for computing forward rate as follows:
Forward Rate=(1+YTM for current year)Corresponding year(1+YTM for previous year)Corresponding year−1
For computing forward rate of zero-coupon bond with11%yield to maturity and maturity of2years:
Forward Rate=(1+YTM for current year)Corresponding year(1+YTM for previous year)Corresponding year−1=(1+0.11)2(1+0.10)−1=12.01%
For computing forward rate of zero-coupon bond with12%yield to maturity and maturity of3years:
Forward Rate=(1+YTM for current year)Corresponding year(1+YTM for previous year)Corresponding year−1=(1+0.12)3(1+0.11)2−1=14.03%
Thus, the implied one-year forward rate for2ndyear is12.01%and for3rdyear is14.03%
(b)
To calculate:
The yield to maturity of a zero-coupon bond having maturity of one year for the next year i.e.2ndyear if the expectations hypothesis is assumed to be correct and expectation of market is accurate.
Introduction:
The implied forward rate is the rate which helps in determining the movements of the interest rate.
The yield to maturity is the rate which provides the amount of expected return on a bond held till its maturity.
Answer to Problem 40PS
The yield to maturity of zero-coupon bond for2ndyear is12.01%
Explanation:
The formula for computing yield to maturity as follows:
PV=n∑t=1PMT(1+r)1+FV(1+r)n
Here,
PV is Current price of the bond
FV is Face value of the bond
ris yield to maturity
nis no. of periods
For computing Price of the bond
Price of the Bond=FV(1+Forward rate)1(1+Forward rate)2=$1,000(1+0.1201)=$892.78
For computing yield to maturity:
PV=n∑t=1PMT(1+r)1+FV(1+r)n$892.78=1∑t=1$0(1+r)1+$1,000(1+r)1
Using function in excel, effective yield is calculated.
Enter the data as shown below:
Thus, the yield to maturity of zero-coupon bond for2ndyear is12.01%
Explanation of Solution
The formula for computing yield to maturity as follows:
PV=n∑t=1PMT(1+r)1+FV(1+r)n
Here,
PV is Current price of the bond
FV is Face value of the bond
ris yield to maturity
nis no. of periods
For computing Price of the bond
Price of the Bond=FV(1+Forward rate)1(1+Forward rate)2=$1,000(1+0.1201)=$892.78
For computing yield to maturity:
PV=n∑t=1PMT(1+r)1+FV(1+r)n$892.78=1∑t=1$0(1+r)1+$1,000(1+r)1
Using function in excel, effective yield is calculated.
Enter the data as shown below:
Thus, the yield to maturity of zero-coupon bond for2ndyear is12.01%
(c)
To calculate:
The yield to maturity of a zero-coupon bond having maturity of two year for the next year i.e.3rdyear if the expectations hypothesis is assumed to be correct and expectation of market is accurate.
Introduction:
The implied forward rate is the rate which helps in determining the movements of the interest rate.
The yield to maturity is the rate which provides the amount of expected return on a bond held till its maturity.
Answer to Problem 40PS
The yield to maturity of zero-coupon bond for3rdyear is13.02%
Explanation:
The formula for computing yield to maturity as follows:
PV=n∑t=1PMT(1+r)1+FV(1+r)n
Here,
PV is Current price of the bond
FV is Face value of the bond
ris yield to maturity
nis no. of periods
For computing Price of the bond
Price of the Bond=FV(1+Forward rate)1(1+Forward rate)2=$1,000(1+0.1201)(1+0.1403)=$1,0001.28=$782.93
For computing yield to maturity:
PV=n∑t=1PMT(1+r)1+FV(1+r)n$782.93=2∑t=1$0(1+r)1+$1,000(1+r)2
Using function in excel, effective yield is calculated.
Enter the data as shown below:
Thus, the yield to maturity of zero-coupon bond for3rdyear is13.02%
Explanation of Solution
The formula for computing yield to maturity as follows:
PV=n∑t=1PMT(1+r)1+FV(1+r)n
Here,
PV is Current price of the bond
FV is Face value of the bond
ris yield to maturity
nis no. of periods
For computing Price of the bond
Price of the Bond=FV(1+Forward rate)1(1+Forward rate)2=$1,000(1+0.1201)(1+0.1403)=$1,0001.28=$782.93
For computing yield to maturity:
PV=n∑t=1PMT(1+r)1+FV(1+r)n$782.93=2∑t=1$0(1+r)1+$1,000(1+r)2
Using function in excel, effective yield is calculated.
Enter the data as shown below:
Thus, the yield to maturity of zero-coupon bond for3rdyear is13.02%
(d)
To calculate:
The expected total
Introduction:
The expected rate of return is used to determine the total expected return on the bond for the holding period.
The yield to maturity is the rate which provides the amount of expected return on a bond held till its maturity.
Answer to Problem 40PS
The expected rate of return for two year bond is10%.
Explanation:
The formula for computing price of the bond as follows:
Price of the Bond=FV(1+r)n
For computing price of the bond with10%yield to maturity:
Price of the Bond=FV(1+r)n=$1,000(1+0.10)1=$909.09
For computing price of the bond with11%yield to maturity:
Price of the Bond=FV(1+r)n=$1,000(1+0.11)2=$811.62
Price at which the bond will sell in the next year:
Price=FV(1+Forward rate)1=$1,000(1+0.1201)=$892.78
The expected rate of return for two-year bond is as follows:
Rate of Return=$892.78$811.62−1=10%
Thus, the expected rate of return for two-year bond is10%.
Explanation of Solution
The formula for computing price of the bond as follows:
Price of the Bond=FV(1+r)n
For computing price of the bond with10%yield to maturity:
Price of the Bond=FV(1+r)n=$1,000(1+0.10)1=$909.09
For computing price of the bond with11%yield to maturity:
Price of the Bond=FV(1+r)n=$1,000(1+0.11)2=$811.62
Price at which the bond will sell in the next year:
Price=FV(1+Forward rate)1=$1,000(1+0.1201)=$892.78
The expected rate of return for two-year bond is as follows:
Rate of Return=$892.78$811.62−1=10%
Thus, the expected rate of return for two-year bond is10%.
(e)
To calculate:
The expected total rate of return over the next year when purchase of a three-year zero-coupon bond on current day.
Introduction:
The expected rate of return is used to determine the total expected return on the bond for the holding period.
The yield to maturity is the rate which provides the amount of expected return on a bond held till its maturity.
Answer to Problem 40PS
The expected rate of return for three-year bond is10%.
Explanation:
The formula for computing price of the bond as follows:
Price of the Bond=FV(1+r)n
For computing price of the bond with12%yield to maturity:
Price of the Bond=FV(1+r)n=$1,000(1+0.12)3=$711.78
Price at which the bond will sell in the next year:
Price=FV(1+Forward rate)1(1+Forward rate)2=$1,000(1+0.1201)(1+0.1403)=$1,0001.28=$782.93
The expected rate of return for two-year bond is as follows:
Rate of Return=$782.93$711.78−1=10%
Thus, the expected rate of return for three-year bond is10%.
Explanation of Solution
The formula for computing price of the bond as follows:
Price of the Bond=FV(1+r)n
For computing price of the bond with12%yield to maturity:
Price of the Bond=FV(1+r)n=$1,000(1+0.12)3=$711.78
Price at which the bond will sell in the next year:
Price=FV(1+Forward rate)1(1+Forward rate)2=$1,000(1+0.1201)(1+0.1403)=$1,0001.28=$782.93
The expected rate of return for two-year bond is as follows:
Rate of Return=$782.93$711.78−1=10%
Thus, the expected rate of return for three-year bond is10%.
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Chapter 10 Solutions
Essentials Of Investments
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