CHAPTER 4
Interest Rates
Practice Questions
Problem 4.1.
A bank quotes you an interest rate of 7% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?
(a)The rate with continuous compounding is
or 6.94% per annum.
(b)The rate with annual compounding is
or 7.19% per annum.
Problem 4.2.
Explain how LIBOR is determined
LIBOR is the London InterBank Offered Rate. It is calculated daily from borrowing rates estimated by a panel of banks
Problem 4.3.
The six-month and one-year zero rates are both 5% per annum. For a bond that has a life
of 18 months and pays a coupon of 4% per annum (with miannual payments and one having just been made), the yield is 5.2% per annum. What is the bond’s price? What is the 18-month zero rate? All rates are quoted with miannual compounding.
Suppo the bond has a face value of $100. Its price is obtained by discounting the cash flows at 5.2%. The price is
总则
If the 18-month zero rate is, we must have
which gives R=5.204%.
Problem 4.4.
An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with a) annual compounding, b) miannual compounding, c) monthly compounding and d) continuous compounding.
(a)With annual compounding the return is
or 10% per annum.
(b)With mi-annual compounding the return is where
i.e.,
so that. The percentage return is therefore 9.76% per annum.
(c)With monthly compounding the return is where
i.e.
so that . The percentage return is therefore 9.57% per annum.
紫薯芋圆
(d)With continuous compounding the return is where:
i.e.,
so that. The percentage return is therefore 9.53% per annum.
Problem 4.5.
Suppo that zero interest rates with continuous compounding are as follows:
Maturity (months) | Rate (% per annum) |
山东菜3 | 3.0 |
6 | 3.2 |
| 那双眼睛 9 | 3.4 |
12 | 3.5 |
15 | 3.6 |
18 | 丑陋近义词3.7 |
| |
Calculate forward interest rates for the cond, third, fourth, fifth, and sixth quarters.
The forward rates with continuous compounding are as follows to
Qtr 2 | 3.4% |
Qtr 3 | 3.8% |
Qtr 4 | 3.8% |
Qtr 5 | 4.0% |
Qtr 6 | 4.2% |
| |
Problem 4.6.
Assuming that risk-free rates are as in Problem 4.5, what is the value of an FRA where the holder will pay LIBOR and receive 4.5% (quarterly compounded) for a three-month period starting in one year on a principal of $1,000,000. The forward LIBOR rate for the three month period is 5% quarterly compounded. 大班下学期
From equation (4.9), the value of the FRA is therefore
or −$1,195
Problem 4.7.
The term structure of interest rates is upward sloping. Put the following in order of magnitude:
(a)The five-year zero rate
(b)The yield on a five-year coupon-bearing bond
(c)The forward rate corresponding to the period between 4.75 and years in the future
What is the answer to this question when the term structure of interest rates is downward sloping?
When the term structure is upward sloping, . When it is downward sloping, 兔子和老虎.
Problem 4.8.
What does duration tell you about the nsitivity of a bond portfolio to interest rates? What are the limitations of the duration measure?
Duration provides information about the effect of a small parallel shift in the yield curve on the value of a bond portfolio. The percentage decrea in the value of the portfolio equals the duration of the portfolio multiplied by the amount by which interest rates are incread in the small parallel shift. The duration measure has the following limitation. It applies only to parallel shifts in the yield curve that are small.
Problem 4.9.
What rate of interest with continuous compounding is equivalent to 8% per annum with monthly compounding?刺绣图案大全
The rate of interest is where:
i.e.,
The rate of interest is therefore 7.97% per annum.
Problem 4.10.
A deposit account pays 4% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
The equivalent rate of interest with quarterly compounding is where
or
The amount of interest paid each quarter is therefore:
or $100.50.
Problem 4.11.
Suppo that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are, respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pay a coupon of 4% per annum miannually.
