Question

Problem 13-11 A major requirement in managing a fixed-income portfolio using a contingent immunization policy is monitoring the relationship between the current market value of the portfolio and the required value of the Poor portfolio. This difference is defined as the margin of error. In this regard, assume a $300 million portfolio with a time horizon of five years. The available market rate at the initiation of the portfolio is 11, but the dient is willing to accept 10% as a floor rate to allow use of active management strategies. The current market values and current market rates at the end of Years 1, 2, and are as follows: End of Year Market Value (SMI) Market Yield 405.5 4012 Assume that semiannual compounding is used. Do not round intermediate calculations. Enter your answers in millions For example, an answer of $1.20 million should be entered as 1.20, not 1,200,000. Round your answers to two decimal places a. Calculate the required ending-wealth value for this portfolio million b. Calculate the required ending-wealth value for this portfolio at the end of Years 1, 2, and 3. End of Year 1:6 million End of Year 2: $ million End of Year mon Compute the margin of error at the end of Years 1.2 and 3. End of Year 1: 5 million End of Year 2:5 million End of Year 3: million d. Indicate the action that a portfolio manager utilizing a contingent immunization policy would take if the margin of error at the end of any year had been zero or negative select active management of the portfolio and immunize it. If the margin of error at the end of any year had been zero or negative, the portfolio manager would

Answer 1

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Answer:

a)

The required ending wealth for the portfolio can be computed using the formula below Required ending wealth value = Value of portfolio x PVAF for required period = Value of portfolio x PVAF (5% for 10 periods) = $300 million x 1.629 = $488.70 million.

b)

The required floor portfolio is the present value of the required ending value ($88.70 million) at the current market yield. The required portfolios for the years 1, 2 and 3 can be computed as below: For year one = Market Value x PVF (10% for 4 years) = Market Value x PVF (5% for 8 periods) = $488.70 million x 0.677 = $330.85 million.

For year two = Market Value x PVF (8% for 3 years) = Market Value x PVF (4% for 6 periods) = $488.70 million x 0.790 = $386.07 million.

For year three = Market Value x PVF (12% for 2 years) = Market Value x PVF (6% for 4 periods) = $488.70 million x 0.792 = $387.05 million.

c)

Margin of error is the difference between the expected market value and the required floor value of the portfolio computed above. The margin of error can be computed using the table as below:

Expected Required floor portfolio Safety margin of error (In $ million) ear (In $ million) Market value (In $ million) 337.9 405.5 401.2 330.85 386.07 367.05 7.05 19.43 34.15

d)

(d) Action that a portfolio manager utilizing a contingent immunization policy would have to take if the margin of error at the end of any year had been zero or negative: If the margin of error at the end of any year had been zero or negative, the portfolio manager would discontinue the management of the portfolio and immunize it. If the margin of error had been negative, the manager would immunize the portfolio and thereby minimize any further losses to the portfolio.