Solutions for End-of-Chapter Questions and Problems: Chapter Seven
Assets Liabilities and Equity
Cash $2,000 Certificate of Deposit $10,000
Bond $10,000 Equity $2,000
Total Assets $12,000 Total Liabilities and Equity $12,000
The bond has a ten-year maturity and a fixed-rate coupon of 10 percent. The certificate of deposit has a one-year maturity and a 6 percent fixed rate of interest. The FI expects no additional asset growth.
Interest income $1,000 $10,000 x 0.10
Interest expense 600 $10,000 x 0.06
Net interest income (NII) $400
Interest income $1,000 $10,000 x 0.10
Interest expense 700 $10,000 x 0.07
Net interest income (NII) $300
The decrease in net interest income is caused by the increase in financing cost without a corresponding increase in the earnings rate. Thus, the change in NII is caused by refinancing risk. The increase in market interest rates does not affect the interest income because the bond has a fixed-rate coupon for ten years. Note: this answer makes no assumption about reinvesting the first year’s interest income at the new higher rate.
Cash $2,000 Certificate of deposit $10,000
Bond $9,446 Equity $ 1,446
Total assets $11,446 Total liabilities and equity $11,446
Note: market value of equity falls to $1,446 due to lower market value of the bond
How do we know that bond price will be $9,446? If the coupon rate is 10%, yield to maturity = 11%, then using our financial calculator, N = 18 (only 9 years left), PMT = 50, I = 5.5%, FV = 10,000. Compute PV; find PV = -9437.70
The market value of the equity would be higher ($2,600) because the value of the bond would be higher ($10,600) and the value of the CD would remain unchanged.
(Note: if you rounded to the nearest cent, instead of to the nearest dollar, the new market value of equity would be $599.52; that answer also is considered correct.)
(By operating performance I mean what caused the change in net interest income, look at parts a. and b.; by market value, I mean what caused the change in market value in parts c. and d.)
For descriptions of refinancing and reinvestment risk, look at practice discussion problems 2 and 3.
The operating performance has been affected by the changes in the market interest rates that have caused the corresponding changes in interest income, interest expense, and net interest income. These specific changes have occurred because of the unique maturities of the fixed-rate assets and fixed-rate liabilities. Similarly, the economic market value of the firm has changed because of the effect of the changing rates on the market value of the bond.
Question #2 was not assigned; it is just being shown here to contrast with #3.
The zero-coupon bond would have more interest rate risk. Because the entire cash flow is not received until the bond matures, the entire cash flow is exposed to interest rate changes over the entire life of the bond. The cash flows of the coupon-paying bond are returned with periodic regularity, thus allowing less exposure to interest rate changes. In effect, some of the cash flows may be received before interest rates change.
In this situation the coupon-paying bond has more interest rate risk. The zero-coupon bond will generate exactly the expected return at the time of purchase because no interim cash flows will be realized. Thus the zero has no reinvestment risk. The coupon-paying bond faces reinvestment risk each time a coupon payment is received. The results of reinvestment will be beneficial if interest rates rise, but decreases in interest rate will cause the realized return to be less than the expected return.
Below are answers to some text book problems that were not assigned:
Today's principal value on the Euromark CD is DM173.82 and $125m (173.82/1.3905).
Today's principal value on the loan is DM104.292 ($60MM x 1.7382) and $75 (104.292/1.3905).
Today's principal value on the U.S. Treasury bill is $40m and DM55.62 (40 x 1.3905), although for a U.S. bank this does not change in value.
Qualitybank's loss is $10m or DM13.908.
Solution matrix for problem 27:
At Issue Date:
Dollar Transaction Values (in millions) D-Marks Transaction Values (in millions)
German Euromark German Euromark
Loan $60 CD $100 Loan DM104.292 CD DM173.82
U.S T-bill $40 U.S. T-bill DM69.528
$100 $100 DM173.82 DM173.82
Dollar Transaction Values (in millions) DM Transaction Values (in millions)
German Euromark German Euromark
Loan $75 CD $125 Loan DM104.292 CD DM173.82
U.S. T-bill $40 U.S. T-bill DM55.620
$115 $125 DM159.912 DM173.82
Beginning of the Year
End of the Year
The loss to the Swiss investor (SF884.82 + SF80 - SF1,000)/$1,000 = -3.52 percent. The entire amount of the loss is due to interest rate risk.
Price at beginning of year = SF1,000/SF1.50 = $666.67
Price at end of year = SF884.82/SF1.35 = $655.42
Interest received at end of year = SF80/SF1.35 = $59.26
Gain to U.S. investor = ($655.42 + $59.26 - $666.67)/$666.67 = +7.20%.
The U.S. investor had an equivalent loss of 3.52 percent from interest rate risk, but he had a gain of 10.72 percent (7.20 - (-3.52)) from foreign exchange risk. If the Swiss franc had depreciated, the loss to the U.S. investor would have been larger than 3.52 percent.
(1) A bank finances a $10 million, six-year fixed-rate commercial loan by selling one-year certificates of deposit. a, b
(2) An insurance company invests its policy premiums in a long-term municipal bond portfolio. a, b
(3) A French bank sells two-year fixed-rate notes to finance a two-year fixed-rate loan to a British entrepreneur. b, e, f
(4) A Japanese bank acquires an Austrian bank to facilitate clearing operations.
a, b, c, d, e, f
(5) A mutual fund completely hedges its interest rate risk exposure using forward contingent contracts. b, c
(6) A bond dealer uses his own equity to buy Mexican debt on the less-developed country (LDC) bond market. a, b, e, f
(7) A securities firm sells a package of mortgage loans as mortgage backed securities.
A, b, c
Liquidity risk is the uncertainty that an FI may need to obtain large amounts of cash to meet the withdrawals of depositors or other liability claimants. In times of normal economic activity, depository FIs meet cash withdrawals by accepting new deposits and borrowing funds in the short-term money markets. However, in times of harsh liquidity crises, the FI may need to sell assets at significant losses in order to generate cash quickly.
Insolvency risk involves the shortfall of capital in times when the operating performance of the institution generates accounting losses. These losses may be the result of one or more of interest rate, market, credit, liquidity, sovereign, foreign exchange, technological, and off-balance-sheet risks.
Measuring each source of bank risk exposure individually creates the false impression that they are independent of each other. For example, the interest rate risk exposure of a bank could be reduced by requiring bank customers to take on more interest rate risk exposure through the use of floating rate products. However, this reduction in bank risk may be obtained only at the possible expense of increased credit risk. That is, customers experiencing losses resulting from unanticipated interest rate changes may be forced into insolvency, thereby increasing bank default risk. Similarly, off-balance sheet risk encompasses several risks since off-balance sheet contingent contracts typically have credit risk and interest rate risk as well as currency risk. Moreover, the failure of collection and payment systems may lead corporate customers into bankruptcy. Thus, technology risk may influence the credit risk of FIs.
As a result of these interdependencies, FIs have focused on developing sophisticated models that attempt to measure all of the risks faced by the FI at any point in time.
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