One of the Deficiencies of the Bootstrap Method Is That $d ( t )$

question 16

Multiple Choice

One of the deficiencies of the bootstrap method is that it only returns discount functions that are on discrete dates. One approach to address this problem for cashflows that do not fall on these dates is to split them into allocations to near dates for which discount functions are available. Suppose we have discount functions $d ( t )$ , where $d ( 1 ) = 0.95$ and $d ( 2 ) = 0.90$ . Assuming continuous compounding, how will a cashflow at $t = 1.5$ years of $100 be allocated to $t = 1$ and $t = 2$ years such that the present value and duration of cashflow remains the same? Assume that the forward rate between 1 and 2 years is constant. The allocation of cashflows is:

• A) $48.63 at one year and $51.33 at two years.
• B) $47.33 at one year and $52.63 at two years.
• C) $46.19 at one year and $53.87 at two years.
• D) $50 at one year and $50 at two years.

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Definitions:

Marginal Tax Rate

The rate at which the last dollar of a taxpayer's income is taxed, indicating the percentage of additional income that is paid in tax.

Efficiency

The optimal use of resources to achieve the best possible outcome or output with minimal waste.

Equity

Equity refers to fairness or justice in the way people are treated and involves ensuring equal opportunities and rights for all individuals.

Benefits Principle

A theory in taxation where taxes are apportioned according to the benefits received by taxpayers; those who benefit more from government services, pay more taxes.