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Optimal portfolios differ according to the length of time they are held without being rebalanced. For the case in which asset returns are identically and independently distributed, it has been shown that optimal portfolios become less diversified as the holding period lengthens.We show that the anti-diversification result does not obtain when asset returns are serially correlated, and examine properties of asymptotic portfolios for the case where the short term interest rate, although known at each moment of time, may change unpredictably over time. The theoretical results provide no presumption about the effects of the length of the holding period on the optimal portfolio. Using estimated processes for stock and bill returns, we show that calculated optimal portfolios are virtually invariant to the length of the holding period. The estimated processes for asset returns also imply very little difference between portfolios calculated ignoring changes in the investment opportunity set and those obtained when the investment opportunity set changes over time.

Investments --- Portfolio Management --- Mathematical models. --- Mathematical Models. --- Portfolio management

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This paper presents a dynamic model of a public pension fund's choice of portfolio risk. Optimal portfolio allocations are derived when pension fund management maximize the utility of wealth of a representative taxpayer or when pension fund management maximize their own utility of compensation. The model's implications are examined using annual data on the portfolio allocations and plan characteristics of 125 state pension funds over the 2000 to 2009 period. Consistent with agency behavior by public pension fund management, we find evidence that funds chose greater overall asset - liability portfolio risk following periods of relatively poor investment performance. In addition, pension plans that select a relatively high rate with which to discount their liabilities tend to choose riskier portfolios. Moreover, consistent with a desire to gamble for higher benefits, pension plans take more risk when they have greater representation by plan participants on their Boards of Trustees.

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We argue that the appropriate discount rate for pension liabilities depends on the objective. In particular, if the objective is to measure pension under- or over- funding, a default-free discount rate should always be used, even if the liabilities are themselves not default-free. If, instead, the objective is to determine the market value of pension benefits, then it is appropriate that discount rates incorporate default risk. We also discuss the choice of a default-free discount rate. Finally, we show how cost-of-living adjustments (COLAs) that are common in public pensions can be accounted for and valued in this framework.