Question 1: Expected return of the bonds
Face value = $1,000
Time to maturity = 1 year
Since the bonds have no coupon interests the price is the present value of the face value.
P = F(1+r)n
n = 1
Therefore, r = FP – 1
P = $800
r = 1,000800 – 1 = 1.25 – 1 = 25%
P = $950
r = 1,000950 – 1 = 1.0526 – 1 = 5.26%
P = $1000
r = 1,0001000 – 1 = 1 – 1 = 0
Question 2
r = FP – 1
0.2 = 1000P – 1
1000P = 1.2
P = 10001.2 = $833.30
The above price reflects the intrinsic value of the bond. The bond does not pay coupon interest hence it is selling at a discount. If investors require a return of 20%, the bond must be selling at a price of $833.30 for the market to clear (quantity supplied equals quantity demanded). Any price above or below this leads to a shortage or surplus. If it is selling at a price lower than $833.30, the return will be more hence the quantity demanded will increase leading to shortages. If the price is higher than $833.30, demand will fall hence there will be a surplus.
Question 3
Factors causing shift in demand and supply of bonds
Shifts in the demand and supply curves for bonds are caused by factors other than the price of bonds. Changes in the prices of bonds only cause movements along the demand and supply curves.
Shifts in demand curve for bonds
A shift in the demand curve for bonds is caused by factors affecting the quantity demanded of bonds other the price (Arnold, 2007, p. 305). They include the amount of wealth, interest rates, and expected rates of return, inflation expectations, relative liquidity and relative risk.
Amount of wealth
Investors purchase bonds using funds from their wealth. Bonds are an example of investments in which investors store their wealth and expect returns. Such investments come from savings, that is, income remaining after deducting the investor’s consumption. An increase in wealth increases the amount of funds available to investors (Johnson, 2010). Therefore, the quantity demanded of bonds increases when there is an increase of wealth. This causes an outward shift in the demand curve for bonds as shown in the diagram below. On the other hand, a decline of wreath causes a reduction in funds available for investment (Johnson, 2010). Consequently, the quantity demand of bonds declines thus causing an inward and leftward shift in the demand for bonds.
Interest rates
Market interest rates affect the demand for bonds in the bond market. Interest rates influence the price of bonds since bond coupon interests, and face values are discounted at the market interest rate (Johnson, 2013). The price of a bond increases if the market interest rate falls. Therefore, a fall in interest rates would reduce the quantity demanded of bonds since it reduces the real income or real wealth of investors. When bond prices rise as a result of a fall in interest rate, an investor can only purchase fewer bonds with the same amount of money than before the change in interest rate (Johnson, 2013). Thus, a fall in interest rate causes a leftward shift in the demand curve for bonds from D0 to D1 as shown in the diagram below. An increase in interest rates reduces the price of bonds thus making them more affordable to investors. This causes an increase in quantity demanded thus leading to an outward shift in demand curve from D0 to D2.
Expectations of changes in interest rates
If investors expect interest rates to decrease, the demand for bonds will rise. A fall in interest rates would increase the price of bonds thus investors would be buying more bonds now to resell at higher prices when interest rates fall (Brigham, 2010). Thus, the demand curve for bonds will shift rightwards from D0 to D2 as shown in the graph below. If investors in the bond market expect the interest rate to increase, the demand for bonds will fall since investors would want to wait until the rate increases so as to purchase the bonds at a lower price. Thus, the demand curve for bonds will shift inwards from D0 to D1.
The interest rate also affects the return on bonds. A fall in interest increases the price of bonds thus increasing the expected return on bonds (Brigham, 2010). Therefore, an expected fall in interest rates would cause an outward shift in demand curve from D0 to D2 as shown in the diagram below. This is because more investors will want to buy bonds at lower prices and sell them at a higher return when interest rate fall.
Inflation rates
An increase in inflation reduces funds available for investment in bonds and other securities. Inflation erodes the purchasing power of individuals leaving them with fewer funds for savings and investments. Thus, a rise in inflation rate will cause an inward shift in the demand curve for bonds. The demand curve will shift from D0 to D2 as illustrated in the diagram below. A fall in inflation rate will cause an increase in the demand for bonds hence the demand curve shifts to the right.
Liquidity in the bond market
Investors prefer liquid securities hence an increase in liquidity in the bond markets will lead to a rise in the demand for bonds. Thus, the demand curve for bonds will shift outwards if there is an improvement in the bond market’s liquidity. A fall in liquidity in the market will cause an inward shift in the demand curve for bonds.
Risk
Most investors are risk-averse hence a reduction in the risk of bonds will result in an increase in the demand for bonds. Thus, the demand curve for bonds will shift outwards from D0 to D2 as shown in the graph below. An increase in bond risk will cause a fall in the demand for bonds thus shifting the demand curve inwards from D0 to D1.
Price
Supply curve
D2
D1 D0
Quantity
Shifts in supply curves for bonds
a) Fiscal policy
Government fiscal policy, taxation and government expenditure, influences the supply of bonds in the market. If the government operates a deficit budget, its borrowing will increase. Thus, it will issue bonds to get funds to balance the deficit budget (O'Hara and Wesalo Temel, 2012). In this case, the supply of bonds will increase hence the supply curve shifts outwards from S0 to S2 as shown in the diagram below. A decrease in government expenditure reduces borrowing thus causing a fall in the supply of bonds in the bond market. Therefore, the supply curve will shift inwards from S0 to S1.
Government taxation also affects the supply of bonds. When the government increases taxation without a change in the total budget, its borrowing will fall. This will reduce the supply of bonds in the market (O'Hara and Wesalo Temel, 2012). Besides, the high taxation erodes corporations’ funds thus they will reduce capital expenditures and will be less likely to issue bonds. Therefore, the supply curve will shift inwards as shown below.
If the government operates a surplus budget, it may decide to use the surplus funds to redeem bonds and reduce its debt (O'Hara and Wesalo Temel, 2012). This will cause a fall in the supply of bonds in the bonds market thus causing an inward shift in the supply curve of bonds as shown in the figure below.
b) Inflation rates
High inflation rates erode funds from corporations thus making them less likely to undertake capital projects. This leads to a fall in the supply of bonds hence the supply curve will shift inwards from S0 to S1 as shown below.
Price S1
S0
S2
Demand curve
Quantity
Bibliography
Arnold, R. (2007). Economics. Cincinnati, Ohio: South-Western College Pub.
Brigham, E. (2010). Financial management. New York: Cengage Learning.
Johnson, R. (2010). Bond evaluation, selection, and management. Hoboken, N.J.: John Wiley & Sons.
Johnson, R. (2013). Debt markets and analysis. Hoboken, N.J.: Bloomberg Press.
O'Hara, N. and Wesalo Temel, J. (2012). The fundamentals of municipal bonds. Hoboken, N.J.: Wiley.
