Please can you help me to solve and get the solution for these problems.
how to get the solution please help me
for my homework.
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 can help you solve these problems step by step. Let's start with the first 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%
To calculate the price of a bond, we can use the present value formula. The formula is:
PV = C * (1 - (1+r)^-n)/r + M/(1+r)^n
Where PV is the present value, C is the coupon payment, r is the interest rate, n is the number of years, and M is the face value of the bond.
Let's calculate the solution for part A, where interest rates increase by 1%.
PV = 0.1 * (1 - (1+0.11)^-10)/0.11 + 1000/(1+0.11)^10
Simplifying this equation will give us the price of the bond.
Now you can follow this same process to calculate the bond price for parts B, C, and D, where interest rates change accordingly.
Moving on to the next question.
2. A share is valued at present at $80. 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.
To calculate the forward price, we need to use the formula:
Forward Price = Spot Price * (1 + Interest Rate)^(Time until Delivery)
Forward Price = $80 * (1 + 0.05)^(1)
Simplifying this equation will give us the forward price for delivery in one year.
Now, let's move to the final question.
3. Calculate approximately the duration of a portfolio containing a coupon bearing-bond, which matures in two years with a face value of 100,000 SEK and pays a 6% coupon, plus a short position of a futures contract with maturity in two years on a three-year 6% coupon-bearing bond with a face value of 50,000 SEK. Interest rates are currently 5.5% annually with continuous compounding.
The duration of a portfolio is the weighted average maturity of the cash flows. We can calculate it using the following formula:
Duration = (PV1 * D1 + PV2 * D2) / Portfolio Value
Where PV1 and PV2 are the present values of the bond and futures contract, and D1 and D2 are the durations of the bond and futures contract, respectively.
The duration of a bond is given by the formula:
Duration = (1 + r) * (1 - (1 + r)^-n) / r
Where r is the interest rate and n is the number of years until maturity.
You can now apply this formula to calculate the duration of the bond and futures position. Then use the weighted average formula to find the duration of the portfolio.
I hope this helps you solve the problems for your homework. Let me know if you have any further questions!
Sure, I'd be happy to help you solve these problems!
1. To find the price of a bond with changing interest rates, you can use the formula for the present value of a bond. The formula is:
PV = C * (1 - (1 + r)^(-n)) / r + F / (1 + r)^n
Where PV is the present value, C is the coupon payment, r is the interest rate, n is the number of periods, and F is the face value of the bond.
For each interest rate change, you will need to plug in the new interest rate into the formula and calculate the price of the bond accordingly.
2. To determine the forward price of a share, you can use the formula:
Forward Price = Spot Price * (1 + Dividend Rate) / (1 + Interest Rate)
In this case, the spot price is $80, the dividend rate is 4% (0.04), and the interest rate is 5% (0.05). Plug in these values into the formula to calculate the forward price.
3. To calculate the duration of a portfolio containing a bond and a futures contract, you can use the formula:
Duration = (Duration of Bond * Market Value of Bond + Duration of Futures * Market Value of Futures) / Total Portfolio Value
To find the duration of each component, you can use the formula:
Duration = (1/r) * (1 - (1 + r)^(-n))
Where r is the interest rate and n is the number of periods. Calculate the duration for the bond and the futures contract separately, then plug in the values along with the market values into the portfolio duration formula to get the total duration.
These formulas should help you solve the problems step by step. Let me know if you have any further questions!