Canvas D Question 15 1 pts An insurance company must make a payment of $19,487 i
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Canvas D Question 15 1 pts An insurance company must make a payment of $19,487 in six years. The market interest rate manager wishes to fund the obligation using two-year zero coupon bonds and perpetuities paying annual coupons. In order to immunize the portfolio against interest rate fluctuations how much she should invest in zero-coupon bonds is 10%. The company's portfolio o $19,487 5/9 $6,111.11 O $111.11 D | Question 16 1 pts Question 16 & 17 are based on the following information: What would be the proceeds to an investor who purchases the September 2011 expiration 1BM calls with exercise price $165 it the stock price at option expiration is $150?Explanation / Answer
CONSTRUCTING AN IMMUNISED PORTFOLIO
STEP1: Calculate the duration of this liability. To get you started calculate the PV of the obligation. i.e. what is the PV of $19,487 needed in sIX years discounted at 10%?
present value factor of 10%, 6 years = 0.56447393004
amount=$19487
present value of liability= $10990.668 rounded off to 11000
The cash flow of this is identical to a zero-coupon bond. So the duration would be determined exactly the same.
STEP2: Calculate the duration of the asset portfolio. The portfolio duration is the weighted average of duration of each component asset, with weights proportional to the funds placed in each asset. So calculate the duration of the zero-coupon bond, and also the duration of the perpetuity.
the equation for calculating the duration of a perpetuity is (1+y)/y.
Where y = market interest rate.
What is the duration for each? The fraction of the portfolio invested in the zero coupon is called “w”, and the fraction invested in the perpetuity is (1-w), WHERE w=weighted proportion.
Duration of zero coupon bond= 2 years
Duration of perpetuity as per the above formula= 1.10/.10= 11 years
Asset Duration= w* 2 years + (1-w)* 11 years
Asset duration = Liability duration =6 years
6 = w* 2 years + (1-w)* 11 years
w=0.55
STEP3: The insurance company must invest 0.55, or 55% in zero coupon bond, and the rest in perpetuity that is 45%. This will result in an asset duration of 6 years.
investment in zero coupon bond= $11000*55% = $6050
( which is approximaely equal to option 3rd given = $6111 due to rounding off error ignored)
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