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Expected utility and the non-normal returns of common portfolio rebalancing strategies

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Abstract

This study compares three common strategies: buy-hold, constant mix and constant proportion rebalancing separately for bull, bear and trendless markets using Monte Carlo simulation. These strategies are compared in terms of terminal wealth, risk and expected utility. Our results indicate that rankings of the strategies by general expected utility functions, defined across all moments of the distribution of terminal wealth, often differ from rankings by mean-variance statistics. As rebalancing can produce non-normal payoffs, relying purely on traditional mean-variance analysis may cause investors to select inappropriate rebalancing strategies.

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Notes

  1. Cesari and Cremonini (2003) used mean return, standard deviation of return, Sharpe ratio, Sortino ratio and a mean-variance utility function to analyze the performance of each rebalancing strategy.

  2. For each rebalancing strategy we assume that the investor allocates wealth across two assets: A risk-free bond and a risky stock index. Although simple, this is consistent with the concepts of two-fund separation and capital asset pricing theory.

  3. Equations (5) and (6) for rebalancing the risky and risk-free assets are from Do (2002).

  4. The multiplier, m, determines the rate at which wealth is transferred between the risky and risk-free assets in the portfolio.

  5. The margin or equity balance for the portfolio=1/b. Thus, b=2 implies 50 per cent margin trading, which is common with stock accounts. b>2 implies less than 50 per cent margin, which is typical with derivatives accounts.

  6. When m=b we have the case where mF/(m−b)=+∞. This implies that ΔS=m(ΔW−ΔF)∀W, so that the stock and bond allocations change at a constant rate.

  7. We conducted our simulations using a range of values for the risk aversion coefficients in equations (16), (18) and (19) and found that the rankings were mostly insensitive to changes in the value of these parameters. Only for unrealistically large and small values for the risk aversion coefficient in equation (19) did the rankings change.

  8. Although not reported, simulations were run assuming annual rebalancing as well as for alternative investment horizons of 2, 6 and 20 years. The results were qualitatively similar and the rankings of the strategies by the various measures were preserved. Simulations were also run without including a transaction fee without any change in the rankings.

  9. With m=2, b=1 and W 0=$100, a $70 floor initializes the CPPI strategy with the same 60/40 stock/bond mix used with the BH and CM strategies.

  10. The literature provides many definitions of market impact. A simple definition is to specify market impact as the difference between the actual transaction price and the price prevailing just before the transaction. A widely used proxy for the pre-transaction price is the mid-point of the bid-ask spread.

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Authors and Affiliations

  1. Department of Economics and Finance, Stephen F. Austin State University, Box 13009 SFA Station, Nacogdoches, 75962-3009, TX, USA

    Samuel Kyle Jones

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  1. Samuel Kyle Jones
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  2. Joe Bert Stine
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Correspondence to Samuel Kyle Jones.

Additional information

1received his PhD in finance from the University of Mississippi in 1998. He briefly worked for Ernst & Young, LLP as a consultant before joining the Department of Economics and Finance at Stephen F. Austin State University as an associate professor of Finance. Dr Jones regularly teaches courses in international, corporate and investment finance and his current research interests include corporate hedging analysis, and the analysis of open and closed-end mutual funds.

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Jones, S., Stine, J. Expected utility and the non-normal returns of common portfolio rebalancing strategies. J Asset Manag 10, 406–419 (2010). https://doi.org/10.1057/jam.2009.22

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