Expected Return on Zero Coupon Bonds

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Economics
Answer - 1
Often bonds are an issue so as to provide a discount on the face value of the bond however no
interest is visible on the same. The interest here refers to the coupon. Hence such bonds are
termed as zero coupon bonds. The bonds are offered at a price which is the market price and at
maturity, they are repaid at face value. The difference between the face value and market value is
referred to as the coupon. In the given assignment, there are four bonds that need analysis and
computation (Arnold, 2010). Let us discuss them one at a time. All the bonds are held for one
year and hence time is not a factor of comparison for all of these bonds. Expected return if the
market of the bond is $800.
a. The given face value of a zero coupon bond is $1000. The time to maturity is 1 year.
Computation of r, i.e. yield to maturity is = {(face value/current price of the bond)^(1/years to
maturity)} -1
If the market price is $800, the r component as asked for in the assignment, which is nothing but
yield to maturity is computed as= {(1000/800)^(1/1)}-1
= 1.25-1
= 0.25
= 25%
Thus the expected return of the bond is 25%.
There is no market risk here because the contingency and reactivity to market are negligible.
Once a bond has been issued at a price, it will for sure be repaid at par. It needs to be noted that
maturity happens in a year and there is no contingency related to maturity as well. Such bonds
are extremely popular amongst investors (Berk, DeMarzo & Stangeland, 2015). This provides a
high degree of reliability and such bonds ensure that the investor receives at least their
investment at the end of the period (Porter & Norton, 2014).
The coupon on zero coupon bonds also acts as market thresholds. The rates fluctuate based on
zero coupon bond rates as well. They are volatile as well because they do not offer any fixed rate
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Economics
of return for a given period. The yield on bonds is subjective to bind types and issuers (Bodie,
Kne & Marcus, 2014).
25% bond yield implies the yield will be greater than interest rates and there will be more
demand of bonds than the supply. The market will tend to increase the interest rate and there will
be inflationary tendencies in the economy (Brigham & Daves, 2012).
b. Expected return if the market of the bond is $950
The given face value of a zero coupon bond is $1000. The time to maturity is 1 year.
Computation of r, i.e. yield to maturity is = {(face value/current price of the bond)^(1/years to
maturity)} -1
If the market price is $800, the r component as asked for in the assignment, which is nothing but
yield to maturity is computed as= {(1000/950)^(1/1)}-1
= 1.053-1
= 0.053
= 5.3%
Thus the expected return of the bond is 5.3%.
There is no market risk here because the contingency and reactivity to market are negligible.
Once a bond has been issued at a price, it will for sure be repaid at par. Also, the maturity is in a
year and hence, there is no contingency related to maturity as well. Such bonds are extremely
popular amongst investors (Derris, Noronha & Unlu, 2010).
The coupon on zero coupon bonds also acts as market thresholds. The rates fluctuate based on
zero coupon bond rates as well. They are volatile as well because they do not offer any fixed rate
of return for a given period (Petty et. al, 2012). The yield on bonds is subjective to bind types
and issuers. 5.3% bond yield implies the yield wills almost that of interest rates (Damodaran,
2012). The market is almost at equilibrium.
Expected return if the market of the bond is $1000
The given face value of a zero coupon bond is $1000. The time to maturity is 1 year.
3

Economics
Computation of r, i.e. yield to maturity is = {(face value/current price of the bond)^(1/years to
maturity)} -1
If the market price is $800, the r component as asked for in the assignment, which is nothing but
yield to maturity is computed as= {(1000/1000)^(1/1)}-1
= 1-1
=0
Thus the expected return of the bond is 0%.
There is no market risk here because the contingency and reactivity to market are negligible.
Once a bond has been issued at a price, it will for sure be repaid at par. Also, the maturity is in a
year and hence, there is no contingency related to maturity as well. Such bonds are extremely
popular amongst investors (Graham & Smart, 2012). The coupon on zero coupon bonds also
acts as market thresholds. The rates fluctuate based on zero coupon bond rates as well. They are
volatile as well because they do not offer any fixed rate of return for a given period. The yield on
bonds is subjective to bind types and issuers (Guerard, 2013).
There is no return on the bonds. The bond is not attractive for investors since there is no return
on it. The market rate will tend to go down.
c. Expected return if the market of the bond is $1250
The given face value of a zero coupon bond is $1000. The time to maturity is 1 year.
Computation of r, i.e. yield to maturity is = {(face value/current price of the bond)^(1/years to
maturity)} -1
If the market price is $800, the r component as asked for in the assignment, which is nothing but
yield to maturity is computed as= {(1000/1250)^(1/1)}-1
=0.80-1
=(0.20)
=-20%
Thus the expected return of the bond is -20%, which means the return is negative.
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