UNIVERSITY OF ILLINOIS

UNIVERSITY OF ILLINOIS College of Business Finance 461 Financial Intermediaries Final Examination Answers Instructions: Total Time is 120 minutes. This is a closed-book examination except that one 8.5x11 inch page of double-sided notes is permitted. Part I. Circle the single best answer to the following 18 questions. (5 points each)  1. Bank of America advertises a two-year maturity Certificate of Deposit (CD) that has an annualized, quarterly-compounded yield of 8.00 %. This CD’s annual percentage yield (annual, annually-compounded yield) is (a) (b) (c) (d) (e) (f) 7.38 % 7.76 % 7.92 % 8.08 % 8.24 % 8.62 % 42 George Pennacchi December 14, 2004 Answer: (e) Note that PV  1  2  i4    FV  PV 1  i1  , so 4  4 4  i   0.08  i1   1  4   1   1    1  0.0824 4 4    2. The annualized, continuously-compounded yields to maturity on 3-month, 6-month, and 9month to maturity Treasury bills are 4.20 %, 4.25 %, and 4.30 %, respectively. (Treasury bills are like Treasury strips in that they are zero-coupon bonds.) What is the annualized, continuously-compounded 3-month forward rate starting six months from now? In other words, according to the Expectations Hypothesis, what annualized, continuouslycompounded rate do investors expect will be observed on a 3-month Treasury bill six months from now? (a) (b) (c) (d) (e) Answer: d 4.25 % 4.30 % 4.35 % 4.40 % 4.45 % 2 it  1   2 1 2 it  3   1 4 3 1 3 so i    E i i    E i  2i    E i t 1 4 t t 1 4 t t 1 2 t t1 4 t1 4  1   it   1    4 4   1   4  1 2  1   4  t1 2 3 Et it  1  1    3it  4   2it  1   3(4.30)  2(4.25)  4.40% 2  2 4  3. An “asset sensitive” bank (as described in the Banc One Case) is characterized as a bank whose earnings rise when market interest rates increase. This bank would have a duration of (a) (b) (c) (d) (e) liabilities that is smaller than its duration of its assets. liabilities that is positive. equity that is negative. assets that is greater than its duration of equity. assets that is positive. Answer: (c) Recall case discussion. Note that a bank’s net worth (equity) rises when interest rates increase if the duration of equity is negative (duration of liabilities > duration of assets). 4. A default-free floating-rate bond has a 20-year maturity and makes semi-annual payments tied to 6-month LIBOR. Currently, the annualized, semi-annually compounded yields on zero-coupon bonds that mature in 1.5, 2.0, and 2.5 years are 4.00 %, 4.20 %, and 4.40 %, respectively. Based on a principal value of $100, what would be the present value of this floating-rate bond’s coupon to be paid exactly two years from today? (a) $100 1  0.04  2 (b) (c) (d) (e) (f) 1.5 2  1  0.042   2   3 4 $100 1  0.04   1  0.042   2 2   0.042 1.5 0.044 2  $100 1  2   1  2    3 4 $100 1  0.042   1  0.044   2 2   0.04 1.5 0.044 2  $100 1  2   1  2    3 4 $100 1  0.04   1  0.044   2 2   Answer: (b) This is equivalent to PVcoupon  FV  P 1.5  P  2.0    5. A bank securitizes $100 million of auto loans that have a duration of 3.5 years. The special purpose vehicle that owns these loans issues an $80 million, AAA-rated, four-year maturity, 3 floating-rate coupon bond that pays semi-annual coupons equal to six-month LIBOR. (This asset-backed bond’s principal is also $80 million.) The remaining $20 million of financing for the special purpose vehicle is in the form of a subordinated equity share owned by the originating bank and hedge fund investors. When this securitization is initiated (and the asset-backed bond is first issued), the duration of the equity share is (a) (b) (c) (d) (e) 1.5 years 2.0 years 3.0 years 10.0 years 15.5 years Answer: (e) Note that the asset-backed, floating-rate bond has a duration of 6-months when it is first issued. Therefore DE  A L 100 80 DA  DL  3.5  0.5  15.5 A L A L 20 20 6. A life insurance company agrees to be a floating-rate receiver (fixed-rate payer) in a plain vanilla interest rate swap with a three-year maturity and a notional principal of $100 million. The swap exchanges occur semi-annually with an annualized, semi-annually compounded fixed rate of 6.00 % being swapped for 6-month LIBOR. Two years after the swap is agreed to, market interest rates have declined so that the annualized, semi-annually compounded yield-to-maturity on a two-year maturity bond making semi-annual coupon payments and having an annual coupon rate of 6.00 % is 4.00 %. Therefore, two years after the swap was agreed to, the value of the insurance company’s swap position is (a) (b) (c) (d) (e) (f) $ 7.77 million $ 1.94 million $ 0.96 million $ -0.96 million $ -1.94 million $ -7.77 million Answer (e). PVswap  PV fl  PV fx . PV fl  FV  $100 million. PV fx  3 103   $101.94 million. 0.04 1  2  1  0.04 2 2 PVswap  PV fl  PV fx  100  101.94  $  1.94 million 7. A finance company has made a 10-year, floating-rate loan to a manufacturing firm. The loan requires the manufacturing firm to make semi-annual coupon payments tied to six-month LIBOR. To obtain the funds to make this loan, the finance company has issued a 10-year, fixed-rate bond. To hedge its interest rate risk from this transaction, the finance company could (a) (b) (c) (d) buy an interest rate cap. become a floating-rate payer in an interest rate swap. purchase a put option on a Treasury bond. take a short position in a forward contract on a Treasury bond. 4 (e) issue a floating-rate bond tied to six-month LIBOR and invest the proceeds in six-month commercial paper. Answer (b). The swap converts the finance company’s fixed-rate bond liability to a floating rate (swap) liability. 8. The yen per euro two-year forward exchange rate is ¥128/€ while the current spot exchange rate is ¥139/€. If a bank issues a two-year yen-denominated wholesale CD at the current annualized, annually-compounded yen market interest rate of 1%, what would be the effective annualized, annually-compounded euro interest rate that it would pay if it buys forward yen for euros under a two-year forward contract? (a) (b) (c) (d) (e) 5.25 % 5.39 % 5.56 % 5.82 % 6.00 % 1+i¥  Answer (a) F¥/ €  S ¥/ € 2 1+i€  2 so i€  S ¥/ € 139 1  i¥   1  1.01  1  5.25% F¥/ € 128 9. A hedge fund owns a yen-denominated bond that makes annual coupon payments and has a face value of ¥ 10,000 million. The bond’s annual coupon rate is 4 % and the bond matures in exactly two years. (The next coupon payment is exactly one year from now). The hedge fund manager is concerned about the future value of the yen and decides to use a currency swap to lock-in the dollar value of this bond’s cash flows. Currently, the one-year, yen per U.S. dollar forward exchange rate is ¥115/$ and the two-year forward exchange rate is ¥109/$. The annualized, annually-compounded yields on dollar-denominated zero coupon bonds maturing exactly one and two years from now are 4.00 % and 4.50 %, respectively. After selling forward the yen-denominated bond’s cashflows for dollars, what is their present value in U.S. dollars? (a) (b) (c) (d) (e) $ 64.57 million $ 87.37 million $ 90.72 million $ 96.02 million $ 103.62 million Answer: (c) PV  ¥400 /  ¥115 / $  ¥10400 /  ¥109 / $    $3.3445  $87.3724  $90.717 2 1.04 1.045 10. Altman’s Z-Score Model is (a) used to establish consumer credit scores. (b) based on option pricing methodology. 5 (c) used to predict consumer loan defaults. (d) used to predict sovereign country defaults. (e) used to predict business bankruptcies. Answer: (e) . See class notes on credit scoring models. 11. Moodys-KMV estimates that Delta Airlines’ expected default frequency (EDF) over the next two years is 40 %. To price a semi-annual pay credit default swap, an analyst needs to estimate Delta’s probability of default over each six-month period during the next two years. Assuming (as in the First American Bank Case) that the probability of default over a six month period, given no default in a previous period, is constant during these two years, what would be Delta’s expected default frequency over the next six months? (a) (b) (c) (d) (e) 10 % 12 % 14 % 15 % 16 % Answer: (b) Let p be the probability of defaulting over a six month period given no previous default. Then the probability of not defaulting over two years is (1-p)4 = 1 – 0.40 = 0.60. Therefore p  1   0.60 4  0.12 1 12. Small banks often buy pieces of commercial loans from large money-center banks because small banks are more likely to (a) (b) (c) (d) (e) be deposit rich. have lower capital requirements. have higher reserve requirements. monitor the loan efficiently. be loan rich. Answer: (a) See class notes on loan sales. 13. A bank that securitizes its consumer loans often retains a subordinated share of the loans’ cashflows because this (a) reduces the bank’s capital requirements. (b) reduces the bank’s risk from loan defaults. (c) increases the senior asset-backed securities default risk. (d) reduces the bank’s need to screen the loan’s credit risk. (e) increases the bank’s incentive to monitor the loans. Answer: (e) See class notes on asset securitizations. 6 14. The Federal Deposit Insurance Corporation (FDIC) insures the deposits of banks that fail (default). The value of the FDIC’s guarantee against a particular bank’s default can be estimated by calculating its value as a (a) put option on the bank’s assets with an exercise price equal to the bank’s promised payment on its insured deposits. (b) call option on the bank’s assets with an exercise price equal to the bank’s promised payment on its insured deposits. (c) put option on the bank’s shareholder’s equity with an exercise price equal to the bank’s promised payment on its insured deposits. (d) call option on the bank’s shareholder’s equity with an exercise price equal to the bank’s promised payment on its insured deposits. (e) standby letter of credit on the bank’s loans. Answer: (a) See the notes on option models of firm default risk. Deposit insurance is equivalent to a debt guarantee, in this case the debt being the bank’s insured deposits. 15. Recall that the Black-Scholes approach to valuing default-risky debt leads to the value of risky debt as D  AN  d1   Be  rT N  d 2  where N( ) is the standard, normal distribution function, d1  ln  A / B    r  1  2  T  /  T , d2  d1   T , A is the 2   borrower’s assets available to repay the loan,  is the volatility of the assets’ returns, B is the promised payment of the debt, T is the time until maturity of the debt, and r is the default-free interest rate. An estimate of the value of a guarantee against default on this debt is (a) AN  d1  (b) Be  rT N  d 2  (c) Be  rT  AN  d1   Be  rT N  d 2  (d) AN  d1   Be  rT N  d 2   Be  rT (e) AN  d1   Be  rT N  d 2    Answer: (c) Note that Be-rTis the value of default-free debt. Therefore, since the value of the guarantee equals the value of default-free debt minus the value of the defaultrisky debt, we get Be  rT  AN  d1   Be  rT N  d 2  . 16. If a firm’s commercial paper is backed by a line of credit from the firm’s bank, credit rating agencies (such as Moodys or Standard & Poors) assign a credit rating to the commercial paper based on the firm’s default risk. If, instead, the firm’s commercial paper is backed by a standby letter of credit from the firm’s bank, the credit rating agencies assign a credit rating to the commercial paper based on the bank’s (usually lower) default risk. The logic for this difference in assigning a credit rating is due to a (a) back-up line of credit being a stronger guarantee than a standby letter of credit. (b) standby letter of credit requiring the bank to issue a bankers’ acceptance. (c) materially adverse change clause in a back-up line of credit agreement. (d) standby letter of credit being cheaper to purchase than a back-up line of credit. 7 (e) bank needing to hold greater capital against a back-up line of credit. Answer: (c) See the notes on loan commitments. A BULC is not as solid default insurance as a SLC. 17. Given the movement in exchange rates over the past year, a hedge fund would have profited greatly if at the beginning of the year it had (a) (b) (c) (d) (e) invested in dollar denominated bonds and borrowed in yen-denominated bonds. entered into a one-year forward contract to deliver dollars for euros. sold call options on the euro with a strike price in yen. bought put options on the euro with a strike price in dollars. entered into a currency swap to pay British pounds for receiving dollars. Answer: (b) As discussed in current events presentations, the U.S. dollar has weakened over the past year. Only choice (b) would lead to a profit due to the dollar’s decline. 18. The main reason why it is more difficult for banks to sell loans made to small businesses compared to loans made to large businesses is because (a) (b) (c) (d) (e) asymmetric information is likely to be greater for small business loans. default risk is likely to be greater for small business loans. small business loans are backed by less collateral. banks provide fewer credit enhancements for small business loans. banks tend to sell small business loans without recourse. Answer: (a) Recall in-class discussion of the nature of liquidity risk on the last day of class. Part II. Give concise answers to the following three questions. (10 points each.) Show your work. 1. Both commercial banks and open-end mutual funds allow investors to withdrawal funds on demand. Explain carefully why open-end mutual funds are not subject to the same type of liquidity risk that can lead to runs (panics) at banks that have uninsured deposits. See Class Note 16 p.7. 2. Explain the potential incentive problems that can arise when a bank originates a loan and then buys credit protection against the loan’s default. For example, in the First American Bank Case, Charles Bank International (CBI) plans to make a loan to CapEx Unlimited (CEU) and then buy credit protection via a credit default swap from First American Bank (FAB). However, based on CEU’s particular financial characteristics, why might these potential incentive problems not be a big concern for investors who buy a credit-linked note tied to CEU’s default? See Class Note 15 p.11. This might not have been a great problem for CEU because CBI’s loan to CEU ($50 million) was a very small portion of CEU’s total debt ($4.15 billion). CEU was a relatively large company with publicly-traded stock, and there were most likely other banks, debt holders, and stock analysts monitoring CEU. 8 3. Many of the small banks acquired by Banc One specialize in making small business loans tied to the prime rate. They financed these loans with longer duration retail CDs and equity capital. Given that Banc One’s balance sheet contained these types of loans and deposits, explain carefully how it could use both plain vanilla interest rate swaps and basis swaps to create a situation where its capital/asset ratio was hedged against changes in market interest rates. Without any derivative hedging, Banc One would have had a duration of assets less than its duration of liabilities. (It would be “asset-sensitive.”) To create a situation where its capital/asset ratio was hedged against changes in market interest rates, Banc One would want to use derivatives so that its on- and off-balance sheet assets had a duration equal to its on- and off-balance sheet liabilities. (See Class Note 11 p.38.) The ideal hedge would be for Banc One to swap its Prime-rate floating rate loan payments for fixed interest rate payments, that is, be a Prime-rate payer and a fixed-rate receiver. However, such a swap does not exist. Therefore, as discussed in the case, Banc One could replicate this swap by agreeing to a plain vanilla interest rate swap where it pays LIBOR and receives fixed interest and also agreeing to a basis swap where it receives LIBOR and pays Prime. These two swaps (plain vanilla and basis) should have an equivalent notional value that would be sufficient to make Banc One’s assets and liabilities have an equal duration.