Please show your work A). A bond has a face value of $1000 and coupon payments o
ID: 2817925 • Letter: P
Question
Please show your work
A). A bond has a face value of $1000 and coupon payments of $120 annually. Market interest rates are 6%. This bond matures in three years and is selling in the market for (1) $____________. (2) What is this bond's duration? _________
B.) A bank has an average asset duration of 4.7 years and an average liability duration of 3.3 years. This bank has $750 million in total assets and $500 million in total liabilities. This bank’s leverage-adjusted duration gap is a _____ gap of ____ years.
C.) A bank has an average asset duration of 5 years and an average liability duration of 3 years. This bank has total assets of $500 million and total liabilities of $250 million. Currently, market interest rates are 10 percent. If interest rates fall by 2 percent (to 8 percent), what is this bank's change in net worth? Net worth will ____ by $____ million.
D.) A treasury bill currently sells for $9,876, has a face value of $10,000 and has 66 days to maturity. What is the bank discount rate on this security?
E.) A treasury bill currently selling for $9,765, has a face value of $10,000 and has 63 days to maturity. What is the yield to maturity equivalent on this security?
F.) A bond has a duration of 5.8 years. Its current market price is $1,152. Interest rates in the market are 2 percent today. It has been forecasted that interest rates will rise to 3 percent over the next couple of weeks. How will the bond's price change in percentage terms? The bond's price will ______________ by ______ percent.
Explanation / Answer
A) FV = 1000, Coupon = 120, Rate = 6%, Maturity= 3 years
Present value or market value = C1/(1+r)n
= 120/(1+6%)1 +120/(1+6%)2 + 120/(1+6%)3 + 1000/(1+6%)3
= 1160.38
Duration = ~3 years
B) It is a negative gap and is calculated as
LADG = Duration Assets Total Liabilities / Total Assets * Duration Liabilities
= 4.7 - (750/500 * 3.3) = -0.25 years
C) LADG = 5 - (500/250 * 3) = -1
A bank with a positive gap will experience a decrease in the market value of its net worth (equity) at times interest rates move up. Net worth increases for a bank with a negative gap
Therefore, if interest rates fall with a negative gap networth will increase by=
-{-1 * 250 * 2%/(1+2%)} = $4.9
D) Using the formula in section A and reverse calculating for rate,
PV = 9876 FV = 10,000 N=66
Rate = 6.9%