Assignment
Credit Risk
1. Sarah's gross salary is $200,000 per year. She is interested in purchasing a $600,000 house. She will make a down payment of 20% and take out a 15 year, 4.5% fixed rate mortgage. The taxes plus insurance is $8000. In addition, she has student debt and makes annual payments of $6000 per year. What is the Gross Debt Service and Total Debt Service ratio? If the bank requires that these ratios must be less than 30 and 35% respectively, can she obtain her mortgage?
2. Calculate the Altman's Z score using the following figures:
Net working capital/total assets =0.10
Retained earnings/total assets=0.20
EBIT/total assets=0.13
MV of equity/BV of debt=0.65
Sales/total assets=0.95
3. Metrobank offers one year loans with a 9% stated rate, charges a 0.50% origination fee, requires 8% compensating balances, and faces a 10% reserve requirement. What is the return to bank on these loans?
4. Using the information from 3 above, what is the true cost of this loan to the borrower?
5. Using the RAROC model: A bank is considering making a $10,000,000 loan to a steel company. The rate for these firms is 10%, and the risk premium is 0.20%. In addition, they expect to charge fees of 0.15%. The extreme loss rate for this company has historically been 4%, and if default occurs, the loss has historically been 85%. If the cost of funds (and benchmark is 10%) should the bank make the loan? Why or why not?
Liquidity Risk
6. Assets Liabilities
Cash 30 Deposits 100
Loans 150 Debt 40
TOTAL 180 Equity 40
TOTAL 180
Show how the bank can handle a 15 deposit drain using both stored and purchased liquidity management.
7. If the bank earns 5% on the loans, and the cost on debt is 4% and 2% on deposits, should the bank use stored or purchased liquidity management? Why?
8. Bank A has $10 in T-bills, a $5 line of credit to borrow in the repo market, and $5 in excess reserves. The DI has borrowed $6 in fed funds and $2 from the fed discount window. What is the total available liquidity? What is the current total use of liquidity?
9. An investment fund has $10 million in securities and 10 million shares outstanding. The fund experiences unanticipated withdrawals and 1 million shares are sold back to the fund; as a consequence the fund is forced to sell $1 million worth of securities at 10% below market value. What is the NAV after the sale of securities and redemption of fund shares?
Interest Rate Risk
10. Calculate the repricing gap and impact on net interest income of a 1 percent increase in rates for the following:
RSA=100 million RSL=50 million
RSA=75 million RSL=100 million
11. Consider the following balance sheet
ASSETS LIABILTIES
Floating-rate mortgages 75 6 month deposits 115
30 year fixed rate mtgs 125 5 year deposits 20
Equity 65
TOTAL 200 200
What is the expected net interest income over the next year?
Using the one year cumulative repricing gap model, what is expected net interest income for a 2% increase in rates?
12. What is the duration of a 2 year bond that pays a 5% annual coupon with a 9% YTM? Use $1000 as the face value of the bond. Using the duration, what is the expected change in the bond if rates are expected to drop by 25 basis points?
13. Consider the following balance sheet:
ASSETS LIABILTIES
Cash 30 Core Deposits 20
Fed funds 20 Fed funds 50
Loans (floating) 105 Euro CDs 130
Loans (fixed) 65 Equity 20
TOTAL 220 220
Fed funds rate is 8.5%
Floating loans are 15%
Fixed rate loans selling at par, 5 year maturities, 12% annual coupon.
Core deposits fixed rate for 2 years at 8%.
Euro CDs 9% yield.
a. What is duration of fixed-rate loan portfolio?
b. If duration of floating rate notes is 0.36, what is duration of bank's assets? (Cash and fed fund assets= 0)
c. What is the duration of the core deposits is they are priced at par?
d. If the duration of fed fund liabilities and Euro CDs is 0.401, what is the duration of the bank's liabilities?
e. What is the duration gap? If all rates increase by 1% (Dr/(1+r))=0.01), what is the impact on equity?
Off Balance Sheet
14. A bank has 200 million in floating-rate loans yielding T-bills plus 2%. The loans are financed with 200 million in fixed rate deposits costing 9%.
A savings association has 200 million of mortgages with a fixed rate of 13%. They are financed with 200 million of CDs with a variable rate of T-bill plus 3%.
What risks does the bank and savings association face?
Propose a swap that both parties would accept.
15. A bank buys a 6 month $1million Eurodollar deposit with a 6.5%. It invests the funds in a 6 month Swedish krona bond paying 7.5%. The spot rate is $0.18/krona.
The 6 month forward rate is 0.181/krona. What is the net spread earned on this investment if the bank hedges its exposure using the forward market?
16. A FI holds $10 million of a 15 year priced at 1040 and yields 7%. The FI plans to sell them in 2 months. The bond's duration is 9.4 years.
The FI's analyst is predicting the Fed will raise interest rates which will push the YTM on these bonds to 8%. The analyst's opinion is not held by most other analysts.
If the analyst is correct, what happens to the value of the bonds?
If the FI is able to hedge the position by using a two month forward contract priced at 1040, what would they do? If rates rise, what is the impact on the FI?
17. TR Bank has:
Assets of $150 million with a duration of 6.
Liabilities of $135 million with a duration of 4.
Market interest rates are 10$.
TR Bank wishes to hedge its exposure with T bond futures.
The futures have a price of $95 per $100 face value with a market yield of 8.5295% and duration of 10.37 years. (Face value is $100000 per future.)
How should the bank hedge its exposure?
Show that if rates increase by 50 bps your hedge will work.
18. An FI has a $100 million portfolio of 6 year Eurodollar bonds with an 8% coupon. The bonds are trading at par and have a duration of 5 years. The FI wishes to hedge the portfolio with T-bond options, which have a delta of -0.625. The underlying bonds on the option have a duration of 10.1 years and trade at $96157 per $100000 face value. Each put option has a premium of 3.25 (% of $100000).
How many put options are needed to hedge the portfolio?
If interest rates increase by 1%, what's the expected gain or loss on the puts?
If interest rates increase by 1%, what's the expected change in market value?
How far must interest rates move before the gain on the bond portfolio offsets the cost of the hedge?
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