Question

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 floor portfolio. This difference is defined as the margin of error. In this regard, assume a $200 million portfolio with a time horizon of five years. The available market rate at the initiation of the portfolio is 12%, but the client 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 3 are as follows:

End of Year : 1, Market Value ($ Mil) $227.3, Market Yield 11 %
End of Year : 2, Market Value ($ Mil) $268.3, Market Yield 8 %
End of Year : 3, Market Value ($ Mil) $263.5, Market Yield 12 %
Assume that semiannual compounding is used. Do not round Intermediate calculations. Enter your answers in millons. 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

Answer 1

The required ending-wealth value of a $200 million fixed-income portfolio with a 10% floor interest rate over five years is $322.102 million. This involves compounded interest calculation using the formula: FV = PV * (1 + interest rate)^n.

Step-by-step explanation:

The question involves calculating the required ending-wealth value of a fixed-income portfolio managed using a contingent immunization strategy. Since the client is willing to accept a future value with an interest floor rate of 10%, we can calculate the wealth that needs to be reached in five years. The formula to calculate the future value (FV) is Present Value (PV) multiplied by the factor (1 + interest rate) to the power of number of years (n). In this case, the Present Value is $200 million, the interest rate (floor rate) is 10%, and the time horizon is 5 years.

Using the formula:

FV = PV * (1 + interest rate)^n

FV = $200 million * (1 + 0.10)^5

FV = $200 million * (1.10)^5

FV = $200 million * 1.61051

FV = $322.102 million

Therefore, the required ending-wealth value for this portfolio after five years, given a floor rate of 10%, is $322.102 million.