First National Bank

  1. First National Bank
    Assets Liabilities
    Reserves $3 m Checkable deposits $22 m
    Treasury bonds $3 m Certificates of deposits $75 m
    Residential mortgages $50 m
    Commercial loans $50 m Bank capital $9 m
    Second National Bank
    Assets Liabilities
    Reserves $3 m Checkable deposits $22 m
    Treasury bonds $3 m Other Borrowings $75 m
    Real estate loans $45 m
    Commercial loans $55 m Bank capital $9 m
    Use the above balance sheets to answer the following questions. The questions are
    unrelated with each other.
    A. Calculate the banks’ reserve ratio. (1 point)
    B. If the required reserve is 10%, what is the maximum deposit outflow that each bank
    can handle before it has to change its asset holdings? (3 points)
    C. If the capital requirement is 8% of risk-adjusted assets, what is the minimum capital
    that each bank needs to maintain the current balance sheet? (2 points)
    D. If both banks suffer a loss of $3 m in the portfolio of commercial loans, which bank
    will be undercapitalized? And, by how much? (2 points)
    E. What can the bank do to meet the capital requirement? (No calculation needed)
    (2 points)
    A. A fund manager holds a bond which pays $10 in one year, $15 in two years, $15 in three
    years and $120 in four years from now. The current interest rate i for this bond is 5%.
    What is the duration of the bond? (2 points)

B. Assume that the interest rate i rises to 5.5%. What is the change of the equilibrium bond
price (in $) in that case if you use the bond’s duration to calculate the price change?
(2 points)
C. Assume you are the manager of a large pension fund. For some reason, you have private
information and know that the interest rate will increase in the (near) future. Would you
purchase a bond with short or long duration in this situation? Briefly explain your
answer. (2 points)

  1. Assume that the (expected) one-year interest rates over the next five years are 3%, 4%, 5%,
    6%, and 7%. The interest rates on one- to five-year bonds are 3%, 4%, 5%, 6%, and 8%.
    Determine the liquidity premium for a two-year, three-year, four-year, and five-year bond.
    (2 points)
  2. Suppose yield to maturities of discount bonds issued by China Mobile are shown as follows:
    1-year 2.5%
    2-year 3%
    3-year 3.2%
    Compute the price of the 3-year annual coupon bond with 4% coupon issued by China
    Mobile with $1000 face value. (2 points)

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