Academic journal article Atlantic Economic Journal

Defined Contribution Beta When Combined with a Defined Benefit Plan

Academic journal article Atlantic Economic Journal

Defined Contribution Beta When Combined with a Defined Benefit Plan

Article excerpt

JEL G11 * G23

This research is prompted by an analysis of the retirement allocations of civilian employees of the United States Navy. These employees have the option of participating in a Defined Benefit (DB) plan, a Defined Contribution (DC) plan, or both. Since the DB plan is an obligation of the United States government, it is essentially a risk free asset equivalent to United States Treasury bonds.

For any individual, the desired beta of their total retirement portfolio should be the same regardless of the spectrum of plans or assets in plans held:

[beta](D[C.sub.B], DB) = [beta](DC). (1)

That is, the desired beta of any individual's total portfolio is a constant. The beta of the portfolio that the individual holds must be the same whether the person has two assets in their portfolio (both the DB and DC assets), or only one asset (the DC plan asset) in their portfolio. The beta of any portfolio is the weighted average of the asset's beta or:

[beta](D[C.sub.B] DB) = a x [beta](DB) + (1 - a) x [beta](D[C.sub.B]) (2)

where D[C.sub.B] represents the defined contribution assets of a participant in both plans. If we consider the defined benefit plan to be an obligation of the United States government and essentially a risk-free asset composed of United States Treasury securities, then the DB plan will be uncorrelated with the market portfolio:

[beta](DB) = 0 (3)

substituting Eqs. …

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