Expected Return on Zero Coupon Bonds

This article discusses the concept of expected return on zero coupon bonds and analyzes the expected returns for different market prices. It also explains the factors that can cause a shift in the demand curve for bonds.

PORTFOLIO MANAGEMENT
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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.
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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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Economics
This bind is highly unattractive because it is giving negative returns. This cannot be opted for by
any sane investor.
Answer 2
Expected return can be defined as a tool that helps in the determination if an investment contains
a positive or negative net income on an average basis. It is computed as the expected value of the
investment provided the major returns in various situations (Mankiw, Gregoryand & William,
2011).
Expected return is the anticipated rate of return or the budgeted gain expected on an investment
(here, zero coupon bonds). The face value of the bond is $1000 and the maturity period is one
year.
The expected return can be calculated using the below formula:
E= (F-M)/M
Where,
E is the expected return
F is the face value
M is the market value
Answer1
a) When M= $800
E= (1000-800)/800
= 25%
b) When M= $950
E= (1000-950)/950
=5.26%
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Economics
c) When M= $1000
E= (1000-1000)/1000
=0
d) When M= $1250
E= (1000-1250)/1250
= -20%
With the increase in market prices from $800 to $950 to $1000 to $1250, the expected return
falls from 25% to 5.26% to 0% to -20%. This clearly shows that the larger the price gap between
the market price and the face value, the greater is the expected return. Hence, the expected
return depends on the difference between the price gaps (Northington, 2011).
People use expected to return to estimate the profit from an investment. In the case of
government bonds, the estimates deviate less when compared with the actual. However, in the
case of high-risk bonds, the expected rate of return might not be actual (Parrino, Kidwell &
Bates, 2012). In short, the investors can utilize the expected return on bonds to ascertain the
amount on an optimal basis that is expected to receive on the bond. In some cases, like the
government bond, the expected return provides an accurate estimate of the return that the
investor will receive (Needles & Powers, 2013).
Apart from the expected rate of return model, other models that can be used to predict interest
rates in the future are the variance model, the portfolio variance model, and the standard
deviation model. I variance model, we first calculate the expected value of sale for the next year
(Chen, 2018). Then we subtract the potential sales outcomes from the expected value of the sale
and then square the difference and then calculate their weighted average to find the variance. The
same variance method, when used on a portfolio, becomes portfolio variance. Standard deviation
is found by taking the square root of the variance (Ross et. al, 2014). Then the standard deviation
model is made.
The given expected rate of return = 20%.
Face value = $1000
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Economics
We know,
E= (F-M)/M
Where,
E is the expected return
F is the face value
M is the market value
Therefore,
0.2= (1000-M)/M
0.2M + M = 1000
1.2M=1000
M= 833.33
As is reiterated from the above problem, we see that a greater expected rate of return means that
there will be a greater gap between face value and market price. Hence, the main point of
learning that can be gathered in this scenario is that the difference between the FV and MV
produces a higher degree of return. Also, market price lower than the face value means that the
investor is going to enjoy profits and the expected rate of return will be greater than zero
(positive). However, on the other hand, when the market price is higher than the face value, the
expected rate of return will be less than zero (negative). The negative expected rate of return
means that the investor is going to face losses with the investment at the given market price and
the given return (Melville, 2013). Hence, negative expected return leads to loses and such a
scenario erode the entire structure of the investment.
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Economics
Answer 3
Shifting Curves
There are various situations that leads to a shift in the demand curve because other factors
can undergo a major change. In this scenario the shift can be observed. It needs to be noted
that there can be more demand for bonds by the investors when the movement happens from
point A to point B. This can be cited as a change in the quantity demanded. The investors
enhance the quantity that is demanded as the bond price becomes cheaper (Mankiw &
Taylor, 2011). It is a common parlance that the investors are always looking for bonds that
are cheaper in nature and that have a major implication in the long run. When the outside
factors undergo change then the demand curve will shift (Mankiw, 2010). When the shift
happens to the right it is termed as the increase in demand while a shift towards the left is
seen as a decline in the demand.
Figure 1Shift in Demand of Bonds
There are various factors that lead to the shift of the demand curve. When investors are in need
of the bonds then the following phenomena happens in the bond market:
 There is a shift of the demand curve to the right. When more bonds are demanded there is
a strong surge among the investors to purchase more of bonds. This leads to an alteration
in the demand of the bonds.
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Economics
 The investors are prepared to purchase more bonds (increment in Q) This is another
factor where the investors have the appetite to purchase more bonds. This leads to a
major change in the quantity demanded.
 The bond’s market price increases that is increment in P. Once the price changes this
leads to an alteration in the overall demand of the bonds.
 On using the formula of Present value (PV), there is a decline of the bond’s interest rate.
Figure 2 Increase in demand for Bonds
Shift in demand
The increment in wealth – this factor leads to a shift of the demand towards the right. The
economy is able to earn wealth when it grows. In a similar fashion, the bond’s demand increases
as the investors, as well as people are having more wealth and can invest in the bond market.
Fall in the return that is expected – When the investment takes place, the demand curve will shift
to the right. If the investors are of the opinion that the interest rate will fall in the future then
more bonds will be purchased currently. For instance, if the interest rates are going to fall in the
future then the bond price will surge. More bonds will be purchased as it is available at a cheaper
price.
Fall in expected inflation – this will lead to a shift of the demand curve towards the right.
Inflation tends to destroy the household’s purchasing power together with a negative impact on
government and businesses. The investments even undergo a major fall. It needs to be noted that
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Economics
less investment will be done by the investors if it is perceived by them that the inflation rate will
surge specifically in terms of bonds. The opposite holds true. If the investors perceive that
stability will be seen then the investors will buy more bonds (Mankiw, Gregoryand & William,
2011)
The increment in liquidity – when more liquidity is witnessed there will be a shift f the demand
curve to the right. Investors are influenced by the bonds that are liquid in nature. The future is
exposed to uncertainty and investors want to sell an asset quickly and minimal transaction cost
(Mankiw, Gregoryand & William, 2011).
Shift in the supply curve
Figure 3Factors that would cause the supply curve for bonds to shift
Alterations in the spending of the government
The government is required to issue bonds that impact the bonds supply. Both changes in the
policy of tax and changes in the spending of fixed nature can impact the requirement of
government to borrow. Irrespective of the reason, any increment in the requirement of
government borrowing enhances the bond quantity that is outstanding thereby leading to the shift
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Economics
in the bond curve to the right. However, the increment in the supply leads to the lowering of the
price and enhances the rate of interest.
Changes in the condition of the general business
During the expansion phase when the scenario of the business is strong, there are opportunities in
terms of investment thereby leading to the increment in the borrowing. When the debt amount in
the economy raises then the bond quantity increases (Mankiw, 2010). Hence, when the business
conditions enhance, the supply curve of bond moves to the right forcing the bond prices to be
reduced and the interest rate rises.
Figure 4 Shift in the supply curve
Changes in the expected inflation rate
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Economics
When there is an increment in the expected inflation it reduces the borrowing real cost and
hence, enhances the bond supply. This leads to the increment in the interest rates while the prices
tend to fall. This leads to a shift in the supply curve (Mankiw, 2010).
Changes in the corporate tax
Bond supply tends to increase when there is an increment in the incentives of the government
tax. There is a sharp increment in the rate and the price undergoes a fall. This tends to shift the
supply curve.
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Economics
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