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. 2018 Jul 18;13(7):e0200561.
doi: 10.1371/journal.pone.0200561. eCollection 2018.

The mathematics of market timing

Guy Metcalfe  1
Affiliations

The mathematics of market timing

Guy Metcalfe. PLoS One. .

Abstract

Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns. What is the likelihood of having a successful market timing strategy? With an emphasis on modeling simplicity, I calculate the feasible set of market timing portfolios using index mutual fund data for perfectly timed (by hindsight) all or nothing quarterly switching between two asset classes, US stocks and bonds over the time period 1993-2017. The historical optimal timing path of switches is shown to be indistinguishable from a random sequence. The key result is that the probability distribution function of market timing returns is asymmetric, that the highest probability outcome for market timing is a below median return. Put another way, simple math says market timing is more likely to lose than to win-even before accounting for costs. The median of the market timing return probability distribution can be directly calculated as a weighted average of the returns of the model assets with the weights given by the fraction of time each asset has a higher return than the other. For the time period of the data the median return was close to, but not identical with, the return of a static 60:40 stock:bond portfolio. These results are illustrated through Monte Carlo sampling of timing paths within the feasible set and by the observed return paths of several market timing mutual funds.

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Conflict of interest statement

The author has declared that no competing interests exist.

Figures

Fig 1
Fig 1. Quarterly returns data.
Quarterly return time series for stock and bond total market index funds, 1993–2017. Returns are in multiplicative form.
Fig 2
Fig 2. Two asset, all or nothing market timing model.
Two asset, all or nothing market timing model switches to whichever of the two assets classes will have the better return that quarter. (a) Quarterly returns of the best and worst market timing portfolios as a function of time in multiplicative form. (b) Histograms of returns for the indicated data sets. (c) Feasibility envelope plotted on semi-log axes. Thick red lines are the best and worst possible return paths over this time period. Blue lines are the three data sets: stocks (f = 1), bonds (f = 0), and balanced (f = 0.6). The fixed portfolio lines order as expected from f = 0 to f = 1.
Fig 3
Fig 3. Optimal timing path.
Optimal timing path fb that would have produced the highest possible return path ρb over the time period. Black regions have fi = 1 (stocks > bonds). White regions have fi = 0 (bonds > stocks).
Fig 4
Fig 4. Return paths for random timing paths.
Return paths (gray) for M = 105 randomly generated timing paths. Red lines are the best and worst market timing return paths. The black line is the observed f = 0.6 balanced fund returns.
Fig 5
Fig 5. Probability distribution functions.
Probability distribution function of (a) log-return and (b) return estimated from M = 105 trials with p = pb ≈ 0.64. Green and purple vertical bars are respectively the worst and best timing portfolios. The orange bar is the median of the PDF and the observed return of the f = 0.6 balanced index fund, which so closely approximates the median as to be indistinguishable at this scale. Inset of (b) is the full data range, showing the extreme low probability position of the optimum timing portfolio (purple bar) in the tail of the distribution.
Fig 6
Fig 6. Market timing funds in the feasible set.
Reprise of Fig 4 with the addition of two market timing funds with publicly available data of comparable length (yellow lines). Red lines are the best and worst timing portfolio return paths. The black line is the observed f = 0.6 balanced index fund.
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References

    1. Henriksson RD. Market Timing and Mutual Fund Performance: An Empirical Investigation. The Journal of Business. 1984;57(1):73–96. 10.1086/296225 - DOI
    1. Bello ZY, Janjigian V. A Reexamination of the Market-Timing and Security-Selection Performance of Mutual Funds. Financial Analysts Journal. 1997;53(5). 10.2469/faj.v53.n5.2114 - DOI
    1. Becker C, Ferson W, Myers DH, Schill MJ. Conditional Market Timing with Benchmark Investors. Journal of Financial Economics. 1999;52(1):119–148. 10.1016/S0304-405X(99)00006-9 - DOI
    1. Goetzmann WN, Ingersoll J, Ivković Z. Monthly Measurement of Daily Timers. Journal of Financial and Quantitative Analysis. 2000;35(3):257–290. 10.2307/2676204 - DOI
    1. Chance DM, Hemler ML. The Performance of Professional Market Timers: Daily Evidence from Executed Strategies. Journal of Financial Economics. 2001;62(2):377–411. 10.1016/S0304-405X(01)00081-2 - DOI

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