Please can you help me to solve and get the solution for these problems.
how to get the solution please help me
question:
1.Find the price of a 10% coupon bond with 10 years to maturity if interest rates:
A) increase by 1%
B) decrease by 1%
C) increase by 1.5%
D) decrease by 1.5%
Find the price of an 8% coupon bond with 30 years to maturity if interest rates:
A) increase by 3/4%
B) decrease by 3/4%
C) increase by 1 1/4%
D) decrease by 1 1/4%
2.A share is valued at present at 80 dollars. In nine months it will give a dividend of 4% of its value at that time.Determine the forward price for delivery in one year given that the rate of interest is 5% a year. my answer is 80.74
3.Calculate approximately the duration of a portfolio containing a cupon bearing-bond which matures in two years with face value 100'000
SEK and pays a 6%-coupon (this means that the coupon is paid every six month at 3% of the face value,) plus a short position of a futures contract with maturity in two years on a three year (at the time of maturity of the futures) 6% coupon-bearing bond (the¯rst coupon payment is six months after the maturity of the futures)
with face value 50'000 SEK. Interest rates are today 5.5% a year with
continuous compounding for any length of duration. my answers.(0.514 years)
Sure! I'd be happy to help you solve these problems step-by-step.
Question 1:
To find the price of a coupon bond with changing interest rates, we need to use the bond pricing formula. The formula is:
Bond Price = (Coupon Payment / (1 + Interest Rate))^Time + (Face Value / (1 + Interest Rate))^Time
For the first part of the question, where the interest rates increase by 1%, we can use the following values:
Coupon Payment = 10% * Face Value
Interest Rate = Current Rate + 1%
Time = Number of years to maturity
Similarly, we can perform the calculations for the other scenarios given in the question.
For the second part of the question, where an 8% coupon bond is given with changing interest rates, we can follow the same approach using the values given in each scenario.
Question 2:
To determine the forward price for delivery in one year, we need to calculate the future value of the share after one year, including the dividend.
The formula for future value is:
Future Value = Present Value * (1 + Interest Rate)^(Time) + Dividend
In this case, we are given:
Present Value = $80
Interest Rate = 5% per year
Time = 1 year
Dividend = 4% of the share value after 9 months
By plugging in these values, we can calculate the future value, which will give us the forward price for delivery in one year.
Question 3:
To calculate the duration of a portfolio containing a coupon-bearing bond and a short position in a futures contract, we need to calculate the weighted average duration of the two investments.
The formula for duration is:
Duration = ∑(Present Value of Cash Flow * Time of Cash Flow) / Total Portfolio Value
In this case, we have two investments - the coupon-bearing bond and the futures contract. We calculate the durations of each investment and then take their weighted average based on the portfolio values.
The duration of a coupon-bearing bond can be calculated using the following formula:
Duration = (1/2) * (Number of Coupon Payments + Maturity Time)
The duration of a futures contract can be calculated using the following formula:
Duration = (1/2) * (Time of Maturity - Time of Maturity of Futures Contract)
By plugging in the given values and performing the calculations, we can determine the approximate duration of the portfolio.
I hope this helps you to solve the problems step-by-step. If you have any further questions or need any clarification, feel free to ask!
Sure, I can help you solve these problems. Let's break them down one by one.
Question 1:
To find the price of a coupon bond, you need to use the present value formula. The formula is:
PV = C * (1 - (1 + r)^-n) / r + F / (1 + r)^n
Where:
PV = Present Value (price of the bond)
C = Coupon payment per period (annual coupon rate times face value)
r = Yield to maturity (as a decimal)
n = Number of periods (years to maturity)
F = Face value of the bond
For each scenario, you need to plug in the given values and compute the price of the bond using the formula.
A) For interest rates increasing by 1%:
Use the same values except for r, which will increase by 1%. Compute the price using the formula.
B) For interest rates decreasing by 1%:
Use the same values except for r, which will decrease by 1%. Compute the price using the formula.
C) For interest rates increasing by 1.5%:
Use the same values except for r, which will increase by 1.5%. Compute the price using the formula.
D) For interest rates decreasing by 1.5%:
Use the same values except for r, which will decrease by 1.5%. Compute the price using the formula.
Repeat the above steps for the second part of the question with different values.
Question 2:
To determine the forward price for delivery in one year, you need to use the formula for a future value of a single investment. The formula is:
FV = PV * (1 + r)^n
Where:
FV = Future Value (forward price)
PV = Present Value (current share price)
r = Rate of interest (as a decimal)
n = Number of periods (in years)
Use the given values and compute the forward price using the formula.
Question 3:
To calculate the duration of a portfolio, you need to use the weighted average duration formula. The formula is:
Duration = (n1*D1 + n2*D2) / (n1 + n2)
Where:
Duration = Weighted average duration of the portfolio
D1 = Duration of the first investment (bond)
D2 = Duration of the second investment (futures contract)
n1 = Weight of the first investment in the portfolio (usually the market value of the investment)
n2 = Weight of the second investment in the portfolio (usually the market value of the investment)
Use the given values and compute the duration of the portfolio using the formula.
I hope this explanation helps you solve the problems. If you have any further questions, feel free to ask.