Econ 2210 Money and Banking No explanation = No credit Max points 30. 1) 3 points Explain the difference between smaller monetary aggregates like M1+ and broader monetary aggregates like M2++? Which of them is used as a forecasting tool for higher economic activity? 2) 3 points Describe the difference between the money market and the capital market. Classify the following as capital or money market instrument: a. 3-Month Government of Canada Bond b. Student Loan maturing in 10 years 3) 3 points How is current yield defined?
Calculate the Yield to Maturity for Bond X: a 20-year bond with FV of $1000, selling for $800 with a current yield of 15%. 4) 3 points Calculate the Fixed Monthly Payment if you were to borrow $900,000 today and the annual interest rate is 3%. Assume the amortization period is 30 years 5) 6 points Consider the following three bonds which you bought today at the listed purchase prices. Bond A: Purchase price $15,000 with Face Value of $20,000 in 1 years.
Bond B: a perpetuity has a price of $1250 and an annual coupon payment of $25 Bond C: Purchase price of $15000, Face Value of $20,000 in 10 years and pays annual coupon payments of $25 Assume 1 year from now you want to sell these bonds: For each of these bonds calculate price after 1 year and the Holding period Return if interest rate after 1 year is 5% 6) 4 points Demonstrate graphically and explain the effect of the following on bond prices and interest rates. a. an increase in the personal savings rate.
How would this change affect capital spending? b. increased profitability of investments and increased deficits 7) 3 points The spread between the interest rates on Baa corporate bonds and Canada bonds was very large during the Great Depression years 1930-1933. Explain with the help of graphs this difference using the bond supply and demand analysis. 8) 5 points When interest rates on a 1 year bonds is 2.0 percent and is expected to have a path of 2.5, 3, 3.5, and 4 percent over the next four years and the liquidity premium, is ln,t = (n-1)(0.05)% a. Calculate the yield today on 2 year, 3 year, 4 year and 5 year bonds respectively. Draw the yield curve. b. What information do we derive on future economic growth and inflation from this yield curve? c. If Bank of Canada increases the short term yield to 2.5%, and people expect it to be a temporary change, what will be the effect on the yield curve.
Money and Banking
1.
M1+, the smaller monetary aggregate, is a measure of physical paper and coin currency in an economy, the monetary base, demand deposits, and traveler’s checks. M2++ is the measure of M1+ variables, savings deposits, money market shares, and other types of time deposits. The primary difference between M1+ and M2++ monetary aggregates is the assets’ liquidity in the two categories. M1+ assets are more liquid while M2+ assets are less liquid, implying that their holders cannot easily convert them into ready cash. The federal government uses the M1+ as a forecasting tool for higher economic activity because it constitutes all liquid assets that can affect an economy.
The money and capital markets are part of the financial market in which financial investors and lenders trade in financial instruments. The difference between the two markets is the nature of financial instruments traded. On the one hand, the money market involves short-term debt instruments such as treasury bills, commercial papers, and certificates of deposit. On the other hand, the capital market consists of long-term assets such as stocks and bonds.
- A 3-month government of Canada bond is a money market instrument because it is a short-term debt instrument used by the Canadian government to borrow money.
- A student loan maturing in 10 years is a capital market instrument because it has a long maturity date.
3.
The current yield is the amount of return an investor would earn if a borrower held a bond for a year.
In the given scenario, bond X is a 20-year bond with a face value of $1,000, a current price of $800, and a current yield worth 15%.
Calculation of Yield to Maturity:
Formula= {Annual interest + (Face value-market price)/number of years to maturity}/ (Face value+ market price/2)
Step 1: Calculate the Annual Interest
If the current yield is 15%, we can also assume that the bond’s coupon rate is 15%. Therefore, the annual interest rate can be derived from multiplying the coupon rate by the bond’s face value.
Annual interest= 150 (15%*$1,000)
Step 1: Calculate the yield-to-maturity using the formula
Yield to maturity= {100+ ($1,000-$800)/20}/($1,000+$800)/2
Yield to maturity= 0.1222 or 12.22%
After solving the equation, the yield-to-maturity for the bond would be 12.22%
A fixed monthly payment is an amount that a borrower pays to a lender each month to settle a loan.
In this scenario, the loan is worth $900,000, has an interest rate of 3%, and an amortization period of 30 years.
Calculate the fixed monthly payment
Formula= Loan amount [i(1+i) n/((1+i) n)-1)]; where i is monthly interest rate and n represents the number of loan payments.
Step 1: Convert the annual interest rate into monthly interest and the number of payments to months.
If the annual interest rate is 3%, the monthly rate is 3% divided by 12 months. Therefore, the monthly interest rate is 0.005. Similarly, if the payment period is 30 years, the number of payments will be 360 (30 years*12 months).
Step 2: Substitute the information into the equation
Fixed monthly payment= 900,000[0.005(1+0.005)360/ ((1+0.005)360)-1
Fixed monthly payment= $5,396.4
After solving the equation, the fixed monthly payment would be $5,396.4
The current yield formula can be used to calculate the price of a bond after one year.
The formula for current yield is Annual interest/current price.
Bond A has a purchase price of $15,000 and a face value of 20,000. Therefore, the current yield is 1.33% ($20,000/$15,000). The yield in percentage can be used to calculate the amount of yield in dollars by multiplying the percentage by the purchase price.
Yield amount= 1.33%*$15,000
The yield amount is 199.5
Therefore, the price of the bond after one year is $15,199.5 (199.5+15,000)
Calculate the holding period return
Formula: [Income+ (End of period value-initial values)]/Initial value
Holding period return= 199.5 + (15,199.5- 15,000)/15000
Holding period return is 2.6%
Bond B is perpetuity worth $1250 and an annual coupon payment of $25
Step 1: Calculate the yield amount
$25/$1250= 0.02
The yield amount is 0.02*1250= $25
Therefore, the value after one year is $1,275 ($1250+$25)
Holding period return= $25+ ($1,275-$1,250)/$1,250
The holding return period is 4%
Bond C has a purchase price of $15,000, face value of $20,000, maturity period of 10 years and annual coupon payments of $25.
Step 1: Calculate the yield period amount
$20,000/$15,000= 1.333
The yield amount is 1.333%*15,000= $199.5
Add the yield amount to a coupon payment of $25 to get the total yield amount, which is $224.5
Therefore, the value after one year is $15,224.5
Holding period return= $224.5+ ($15,224.5-15,000)/$15,000
Therefore, the holding period return for this bond is 2.9%
An increase in the propensity to save among consumers increases the fund’s supply in the economy and reduces the interest rates. As the interest rates decline, from I0 to I1, the bond prices rise significantly from P0 to P1, as shown in figure 1. Increased savings also increases capital spending because more funds are available to finance long-term investment.
b.
When the profitability of investments increases, the money supply in the economy also increases significantly. The interest rates also lower, and it becomes less expensive for firms and individuals to loan money. Therefore, the bond prices also reduce, from P0 to P1, and the interest rates reduce from i0 to i1 to make them attractive. However, when deficits increase, the interest rises too, and it becomes more expensive to borrow. Therefore, the bond prices also increase in the market, as shown in figure 2.
During the great depression, a majority of the businesses failed. With the high risk of failure, firms were also prone to default loans, thus increasing corporate bonds’ default risk. The increased default risk led to a decrease in demand for corporate bonds as lenders feared to incur the bonds’ losses, as shown in figure 3. Conversely, Canada bonds became more attractive because the government was less likely to default, as shown in figure 4.
Figure 3.
As figure 3 shows, an increase in default risk for corporate bonds led to reduced demand for the bonds from D0 to D1.
As shown in figure 4, the spread between the interest rates made Canada bonds more attractive, increasing their demand from DO to D1.
The yield today of the 2,3,4 and 5-year bonds can be calculated using the liquidity premium formula: In,t= (n-1) (0.05)%
Therefore, the
2 year bond yield would be (2-1) (0.05)% = $5
The 3-year bond yield would be (3-1) (0.05)%= $10
The 4-year bond yield would be (4-1) (0.05)%= $15
The 5-year bond yield would be (5-1) (0.05)%= $20
Yield Curve
b.
This upward-sloping yield curve suggests an overall improvement in the economy and less likelihood of inflation.
c.
If the Bank of Canada increases the short-term yield to 2.5%, people will direct their funds to short-term securities in hopes of earning higher profits. Therefore, the yield curve would take a recession.
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