Study Guide for Money and Banking - Chapter 9
Capital adequacy management
Reinvestment rate (income) risk
Capital (price risk)
Federal funds market/rate
Interest rate risk (for banks)
1. The discount rate is almost always lower than the Fed Funds rate. Why do banks not borrow at the discount rate very much?
2. Explain the tradeoff between holding too many reserves and holding too few reserves.
3. Why aren't banks allowed to own stock?
4. A bank has deficient reserves. What four options are available to meet reserve requirements. Which options are least desirable and which are most desirable.
5. In 1981, there was a downward sloping yield curve. Why was this a problem for the S&Ls?
T-F-U, Explain with a Short Essay
1. Duration is always less than maturity.
2. The higher the coupon rate the higher the duration.
3. If a financial firm's assets have a shorter duration than its liabilities, an increase in interest rates will increase the value of the firm.
4. If a firm needs to make a $1m payment in four years, a four year coupon bond can immunize the company against interest rate risk.
5. The optimal amount of excess reserves is zero.
6. The optimal amount of loan defaults is zero.
1. Calculate the duration of the following securities, assuming an interest rate of 10%. (Assume a face value of $1000)
a) two year 10% coupon bond
b) three year 10% coupon bond
c) three year 8% coupon bond
d) four year zero coupon bond
e) four year 12% coupon bond
f) four year 6% coupon bond
g) mortgage bond with $1000 annual payments and fours years to maturity
h) security with the following CFs: YR 2 - $500, YR 3 - $1000, YR 4 - $2000.
2. "The higher the coupon rate, the lower the duration." Prove this statement with the following example. Bonds A and B both sell at par, have four years to maturity and have face values of $1000. Bond A has a coupon rate of 4% and Bond B has a coupon rate of 8%. Current yields are 6%. Calculate duration for both bonds and prove the above statement.
3. The original studies of duration were instigated by the observation that investors seem to prefer high-coupon bonds to otherwise identical bonds with low coupons. Does this preference suggest that investors are more concerned with reinvestment rate (income) risk or price (capital) risk? Explain.
4. A bank has the following financial assets and
in PV dollars:
Cash Reserves $5m 10 years
Auto loans $15m 4 years
Business loans $25m 2 years
Credit Card debt $20m 3 years
Mortgages(fixed) $30m 8 years
Mortgages(variable) $5m 1.5 years
Checking accounts $60 1 year
Savings accounts $20 2 years
a) what is the duration of the asset portfolio?
b) what is the duration of the liabilities?
c) what is the current value of the bank?
d) what is the new value of the bank if interest rates increase by 5%?
e) what is the new value of the bank if interest rates decrease by 3%?
5. Interest Rate Risk and Immunization for a
A company has the following CFs as its only assets: $10m in YR 9 and $15m in YR 10. The company's only debt are 5 year zero coupon bonds with a face value of $8m. Interest rates are initially at 10%.
a) What is the PV of the firm's assets?
b) What is the PV of the firm's liabilities?
c) What is the current value of the firm? (V = PVA - PVL)
d) Calculate the duration of the firms assets and liabilities.
e) Assume that interest rates go to 15%. Calculate the new value of the firm using the formula:
%PV = -D x i.
f) Assume interest rates go to 6%. Calculate the new value of the firm using the formula in part e.
g) What duration of liabilities would be required to immunize the company's value, assuming that the company wants to maintain the PV of its debt? (use the formula: PVA x DA = PVL x DL)
h) If the company can issue some 20 year zero coupon bonds and retire some of the 5 year bonds. What combination of 5 year and 20 year bonds would the company need to achieve the desired duration of its liabilities? (Hint: x = 20 year bonds, y = 5 year bonds, x + y =1)
i) How much money would the company want to raise by issuing 20 year zero coupon bonds?
j) Assuming an interest rate of 10% and face value of $1000, what would the price per bond be?
k) How many bonds would the company sell?
6. Savings and Loan - Borrowing Short and
A savings and loan has cash reserves of $5m, $95m of outstanding
rate mortgages and deposits (checking and savings) of $96m. The
of the cash reserves is 10 years, the duration of the loan
5 years and the duration of the deposits is one year. (All dollar
a) what is the current net worth of the bank (V = PVA - PVL)?
b) what is duration of the loan portfolio?
c) if interest rates rise by 1%, what is the net worth of the bank?
d) if interest rates rise by 2%, what is the net worth of the bank?
e) if interest rates rise by 10%, what is the net worth of the bank?
f) what strategies could the bank take to reduce interest rate risk?