A pension plan is obligated to make disbursements of $1 million, $2 million, $5 million, and $1 million at the end of each of the next four years, respectively. If the plan wants to fully fund and immunise its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? Assume the interest rate is 10% annually. Group of answer choicesDuration is 2.6019Duration is 2.7329Duration is 2.6873Duration is 2.5871

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $ 1 million per annum. The interest rate is 10%. You plan to fully fund the obligation using five-year and 20-year maturity zero-coupon bonds. a. how much market value of each of the zeros will be necessary to fund the plan if you desire an immunised position?

You are managing a portfolio of $1 million. Your target duration is 10 years and you can choose from two bonds: a zero-coupon bond with maturity of seven years and a perpetuity, each currently yielding 5%.a. how much of each bond will you hold in your portfolio?

Suppose we are in 2022. An insurer has to make a guaranteed payment to a policyholder in five years (2027) of $1,469, a lump-sum policy payout on retirement, equivalent to investing $1,000 at an annually compounded rate of 8 percent over five years. To protect itself, the insurer has bought a six-year maturity bond paying 8% annual coupons with an 8% YTM that has a duration of 4.993 or approximately 5 years. The face value of this bond is $1000. If the interest rates fall to 7%. At the end of fifth year, which of the following statements is FALSE?A.The insurer receives the proceeds from selling the bond at the end of fifth year of $1,009B.The insurer receives an reinvestment income of $60.C.The insurer has matched the maturity of its liabilties with that of its assets. D.The insurer receives coupons of $400.E.The insurer is immunized from interest rate risk.

A company starts a defined benefit pension plan on Jan 1 2020. The service cost is $300,000 each year while funding $200,000 per year (with payments made each Dec 31). Interest on the PBO is 12 percent while the actual and expected income on plan assets is 10 percent per year. What amount of pension expense should the company report for 2021

Suppose that a life insurance company sells a five-year guaranteed investment contract that guarantees an interest rate of 7.5% per year on a bond-equivalent yield basis (or equivalently, 3.75% every six months for the next 10 six-month periods). Also suppose that the payment made by the policyholder is $9,642,899. Consider the following three investments that can be made by the portfolio manager: Bond X: Buy $9,642,899 par value of an option-free bond selling at par with a 7.5% yield to maturity that matures in five years. Bond Y: Buy $9,642,899 par value of an option-free bond selling at par with a 7.5% yield to maturity that matures in 12 years. Bond Z: Buy $10,000,000 par value of a six-year 6.75% coupon option-free bond selling at 96.42899 to yield 7.5%. Answer the below questions. (a) Holding aside the spread that the insurance company seeks to make on the invested funds, demonstrate that the target accumulated value to meet the GIC obligation five years from now is $13,934,413.