Question

An insurance company is obligated to pay a policyholder $500 in one year and $2,000 in 3 years. The insurance company has decided to employ the dedication strategy. The following assets are available: 1 year zero coupon bond with annual effective yield of 7%. 3 year zero coupon bond with annual effective yield of 8%. Determine the cost of establishing the asset portfolio.

Answer 1

Answer:

The total cost of establishing the portfolio is $2054.95.

Explanation:

The present value of a bond is given as

$PV=FV\times\dfrac{1}{(1+r)^n}$

For 1 year zero-coupon bond is

• FV is 500
• r is 7% or 0.07
• n is 1

So the value is

$PV=FV\times\dfrac{1}{(1+r)^n}\\PV=500\times\dfrac{1}{(1+0.07)^1}\\PV=500\times\dfrac{1}{(1.07)}\\PV=500\times0.9346\\PV=\ 467.29$

Similarly, for 3 years zero-coupon bond is

• FV is 2000
• r is 8% or 0.07
• n is 3

So the value is

$PV=FV\times\dfrac{1}{(1+r)^n}\\PV=2000\times\dfrac{1}{(1+0.08)^3}\\PV=2000\times\dfrac{1}{(1.08)^3}\\PV=2000\times0.7938\\PV=\ 1587.66$

So the total cost is

Total Cost=Cost of  1-year zero-coupon bond+Cost of 3-years zero-coupon bond

Total Cost=$ 467.29+$ 1587.66

Total Cost= $ 2054.95

So the total cost of establishing the portfolio is $2054.95.