APR留学生代做、代写java/C++程序设计、代做CS/python、代写RV Insurance

日期：2018-11-16 10:40

Individual Project

Derivatives: Options and Futures, Hong Kee Sul

Instructions: You must hand in a printout with the answers, and send in the excel sheet

through email, before beginning of the class on Nov 28, 2018. For simplicity, let’s assume that

the APR convension is used throughout this project. Answers should be exact up to three

digits for full credit. If it is required that you use the answer from the previous question

to answer the followup questions, it is suggested to use formula from the previous answer,

and not the value itself. (To prevent from the rounding errors distorting the answers in the

followup questions.)

1. (50 points) You are the portfolio manager of the RV Insurance Company.

(a) (5 points) The insurance company has the following bonds available for investment. First, determine

the characteristics of these semiannual bonds.

Bond B1: Given Number of Periods to Maturity is 8, Face Value is $1,000.00, Discount Rate

per year is 4.54%, and the Bond Price is $880.00. What is the Coupon Payment in dollars?

Bond B2: Given Number of Periods to Maturity is 6, Face Value is $1,000.00, Coupon Payment

is $10.00, and the Bond Price is $955.00, what is the Discount Rate per year?

(b) (5 points) In addition to the bonds listed in the previous question, let’s assume that you can also

invest in the following two annual bonds. Bond T1: a 1-year bond with a face value of $1,000 and

an annual coupon rate of 1.50%, Bond T2: a 2-year bond with a face value of $1,000 and an annual

coupon rate of 2.70%. These bonds are both priced at $985. Let’s assume that the firm has sold a

series of GIC contracts, so that the firm has the following series of liability to be paid: 4.5, 5.1, 5.6,

6.3, 6.8, 7.2, 7.9, and 8.6. (Units are in millions, and each payment is due every 6 months so that

the last payment is due in 4 years). We assume that at the firm level, the 3% annual yield is used

to discount cashflows. What is the break-even point of these series of GIC contracts? That is, how

much should the Sales department of the RV Insurance Company charge for these contracts not to

loose money? (Here we exclude transaction costs.) If the Sales department asked for a $500,000

1

premium for these contracts, how much should the buyer pay? (Hint: Here the break-even point

refers to the present value of the liabilities, and Buyer pays break-even point + premium.)

(c) (5 points) The company wants to construct a portfolio to fulfill it’s liability agreement. How many

of each bonds should the insurance company buy in order to fully fund the liability and be immunized

against the interest rate risk now? How much would it cost to construct this portfolio? Likewise,

we use the 3% annual yield to discount cashflows. And for simplicity we assume that bonds can be

divisible.

(d) (5 points) In this case what would be the convexity of assets and the convexity of the liabilities?

(For the calculation of the Convexity, please refer to the method outlined in the tutorial)

(e) (5 points) Assume that the transaction fee for buying bonds is 0.2% of the bond value for orders

larger than 10M$, 0.5% of the bond value for orders larger than 1M$, and 1% of the bond value for

smaller orders. What is the total dollar amount of fees for constructing the portfolio? In this case,

what would be profit of this deal? (Hint: Profit = Break-even point - cost of constructing portfolio

- total transaction fee + premium)

(f) (5 points) Is there a portfolio that matches the same criteria, but maximizes the profit? What is

the Portfolio and the Profit in this case?

(g) (5 points) After constructing the portfolio, the RV Insurance Company suddenly found out that

they cannot sustatin a negative cash outflow exceeding 2 million dollars per period, during period

6 through 8, due to business reasons. That is, they want to make the net cash flow in periods

between 6 and 8(t =3, 3.5, and 4 years), larger than -0.2 M$. In this case how would the new profit

maximizng portolio be constructed? Is there anything strange about this portfolio?

(h) (5 points) Now suppose that the firm suddenly found out that they could invest in a 3 and a halfyear

semiannual bond with a face value of $1,000 and an annual coupon rate of 4.0%, selling at par

value. How would the answer to the previous question(Profit Maximizng Portfolio) change? If they

are any different, please explain why.

(i) (5 points) If the transaction fees for selling bonds are identical to transaction fees for buying bonds,

what is the total dollar amount of fees for adjusting your portfolio, from (c-e) to (h)? How about

adjusting your portfolio from (f) to (h)?

(j) (5 points) Are there any alternative methods to satisify their business neeeds rather than paying

for expensive transaction fees as in (i)? Be creative.