# Market model timing-The mathematics of market timing

Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September Help Advanced Search. Donate to arXiv Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September We gratefully acknowledge support from the Simons Foundation and member institutions. Comments: 18 pages, 6 figures Subjects: Portfolio Management q-fin.

Fund data and objectives summaries scrapped from Yahoo Finance 6 November ; applicable terms of service were complied with. In the i Market model timing time Sex photo nude male t i the return of stocks is denoted r si and the return of bonds is denoted r bi. Good pseudo-random number generators Market model timing pass the NIST modrl but are produced by deterministic systems. Hence, the Treynor and Mazuy model is tested again for the up-market condition with a lagged dummy variable. Skip to primary navigation Skip to content Skip to footer Market Timing.

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Select asset 6. This result is consistent with financial research and conventional wisdom that higher return incurs higher risk. Waksman et al. The initial selection of an indicator is rooted in the scientific method : formulate a hypothesis, design Makret experiment, test the hypothesis, draw a conclusion. Proponents against market timing back their arguments with the efficient market hypothesis. Market model timing investing is an investment strategy to maximize returns by minimizing buying and selling. Period Weighting Weight rank orders Weight performance. Investing Markwt. Import Benchmark Period 2 Market model timing unit Days Months. By this definition of risk, a money market's risk based on T-Bills is zero.

Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns.

- This tool allows you to test different market timing and tactical asset allocation models based on moving averages, momentum, market valuation and target volatility.
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Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September Help Advanced Search. Donate to arXiv Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September We gratefully acknowledge support from the Simons Foundation and member institutions. Comments: 18 pages, 6 figures Subjects: Portfolio Management q-fin.

PM] for this version. Which authors of this paper are endorsers? Browse v0. Portfolio Management q-fin. Metcalfe G The mathematics of market timing.

Returns for the model are based on next-day trades at the close. Period 5 length. Each stock and portfolio has exposures or betas relating to the different types of systematic risks. Popular Courses. The answer would be no, given that the binary logistic regression used here and the great number of weeks would require about 68 indicators to represent an overfit, based on the Rule of Passive Investing: What's Best for You? It opened the door for me to sell within 24 hours for a modest profit, and the fund held its shares even longer for a bigger gain.

### Market model timing. Moving Averages - Single Asset

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### [] The Mathematics of Market Timing

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 — 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.

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 stock:bond portfolio.

Market timing is an investment technique whereby an investment manager professional or individual attempts to anticipate the price movement of asset classes of securities, such as stocks and bonds, and to switch investment money away from assets with lower anticipated returns into assets with higher anticipated returns. Market timing managers use economic or other data to calculate propitious times to switch.

The antithesis of market timing, and another broadly popular investing approach, is buy-and-hold, whereby investment managers allocate static fractions of their monies to the available asset classes and then ignore market price gyrations. Is market timing likely to be successful relative to investing in a static allocation to the available asset classes?

The literature in this area is focused on developing sophisticated statistical tools that can detect and measure the market timing ability of professional fund managers [ 1 ]. Some authors detect no market timing ability, while others report statistically significant evidence of market timing ability. These studies find unambiguously that market timing by the average investor is unsuccessful relative to a static allocation.

My goal here is both different and simpler than statistical tests to detect market timing. I want to create a simple model to ask the question, what is the likelihood of successful market timing? Is the PDF of market timing returns symmetric? If it is hard to obtain above average returns by market timing, is it also hard to obtain below average returns?

In the rest of the paper my approach will be to calculate the boundaries of the feasible set of market timing portfolios using fund data for perfectly timed by hindsight switching between two asset classes, stocks and bonds. Department of Commerce, www. The key elementary result is that the geometric mean of market timing returns has an asymmetric PDF. To begin, in the next section I describe the data. The data consists of time series of quarterly returns for three index funds starting in , the advent of the youngest of the three funds, and ending in Q3 Other information on these funds is in S1 Appendix.

Fig 1 shows the quarterly return time series for stocks and bonds. Because the data are from live funds, calculated return paths are net of management and trading costs; however, tax consequences are ignored. Note that because fund data are the basic building blocks of the model, all return paths calculated could have been obtained by an investor during the time period. Quarterly return time series for stock and bond total market index funds, — Returns are in multiplicative form.

Since the way to calculate total return is to multiply the sub-period returns together, I trivially transform the original data to multiplicative form, e. The differences between multiplicative and additive random processes will be important in the subsequent analysis. Here I define the simple two asset market timing model with all or nothing quarterly switches, emphasizing the deliberate choice to assume a simple model in order to gain insight into the fundamental mathematics. Using perfect hindsight, it is easy to identify the best and worst possible market timing portfolios, which form the boundaries of the feasible return paths for all market timing portfolios, i.

Technically it is all market timing portfolios that conform to the assumptions of the model; however, in the discussion section we will see that real, non-conforming market timing funds fall within the feasible set.

I reveal the optimal highest possible return timing sequence and test it for randomness. A later section focuses on deriving the return PDF for the model. The model consists of quarterly all or nothing switches between stocks and bonds. In the i th time period t i the return of stocks is denoted r si and the return of bonds is denoted r bi. A timing path is the binary sequence f i that is. The j th return path is given by. With perfect hindsight the best and worst performing return paths are easily found.

Two asset, all or nothing market timing model switches to whichever of the two assets classes will have the better return that quarter. Thick red lines are the best and worst possible return paths over this time period.

Fig 2 c plots several return paths on semi-log axes. The best and worst possible return paths for this period are thick red lines. Note, however, that the large difference in returns normally associated with stocks and bonds is dwarfed by the difference in returns between the best and worst market timing portfolios. The potential reward to successful market timing is clearly enormous; however, just as enormous is the potential penalty to unsuccessful market timing.

The best and worst possible return paths demark the feasible set of return paths for the two asset model. As the model has all or nothing switches, the number of possible paths of length N is 2 N. Is f b random? It is worth distinguishing random and unpredictable.

The historically optimal timing path is not a random bit sequence because ones occur about two-thirds of the time. Nonetheless, the important question is can I predict the next element in the sequence, given knowledge of the previous elements of the sequence? How can a sequence be not random but at the same time unpredictable?

Consider a 6-sided die, of which four sides have a one and two sides have a zero. For each fair roll of the die there is a two-thirds probability of a one and a one-third probability of a zero, i. Since each fair roll of the die is independent of all rolls that have come before, there is no way to predict from the past sequence of rolls what the next roll of the die will produce.

Although p b is not known a priori —in fact p b could be different over different time periods or markets—the unpredictable die analogy holds for all p b by changing the number of sides to the die. If we look at f b and randomly generated timing paths without knowing which is which , can we distinguish f b from the masses of possible timing paths? As the optimal timing path is indistinguishable from a random sequence, I review elementary properties of random multiplicative processes, from which it follows that the highest probability outcome of market timing is a return less than the median of the PDF of market timing returns.

The median of the return PDF can be directly calculated as the weighted average of the returns of the assets with the weights given by the fraction of time each asset has a higher return than the other. The distribution of typical returns of the model can be estimated by Monte Carlo methods. Generate M random timing paths of length N and calculate M return paths with Eq 2. In order to match the period data, set random timing paths to have the same fraction of ones and zeros as the data, i.

Before further examination of the return PDF it will be useful to review several facts about distributions from random multiplicative processes, such as that of Eq 2. Red lines are the best and worst market timing return paths. A sum of random numbers is guaranteed by the central limit theorem to converge to a Gaussian normal PDF in the limit of a large number of terms in the sum. A product of random numbers, such as that used in Eq 2 to calculate return, does not share this nice property.

On the contrary, the PDF for a random multiplicative process of positive numbers depends on rare sequences that generate an asymmetric PDF with a long tail. The average value of the PDF or of any moment depends sensitively on the sampling size M and, until M approaches the number of possible outcomes, becomes larger and larger compared to the mode [ 12 ]. Nonetheless, what can be done is to take the log of the geometric mean of Eq 2 to change the product of returns to a sum of the log returns:.

Eq 4 says that the log of the geometric mean is given by the average of the log return. In other words, the return PDF for market timing is log-normal, as a simple consequence of elementary properties of the logarithm. To illustrate, Fig 5 a plots the histogram of end of period log returns from the Monte Carlo data of Fig 4. Fig 5 b plots the histogram of the end of period return not log-return. The predicted log-normal form with a long tail is also evident.

The inset shows the entire data range to indicate how long the return tail is. The highest probability outcome is the mode maximum of the distribution, which is less than the median return marked by the orange bar.

Green and purple vertical bars are respectively the worst and best timing portfolios. 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.

Recall p b is the observed fraction of time periods that the stock return exceeds the bond return. It is important to note that Fig 5 shows the PDF for costless market timing.

In practice, market timing costs higher than the index fund costs would shift the PDF to the left, but the boundaries of the feasible set and the median of the PDF would not shift because they are calculated from fund data, which already includes the small index funds costs. Several critiques could be leveled at the analysis in this paper. For example, adherents of market timing would claim that their timing systems are not random, therefore they would be able to choose timing paths to have returns far out on the right tail of the PDF, i.

There are two answers to this. One is that the feasible set is well-defined and that it is simply a fact that all market timing paths, no matter how they are generated , are contained in the feasible set. As such, any sampling of the feasible set generates valid timing paths.

S4 Appendix has details about these two funds, which are rated by Morningstar as above average. While these market timing funds were neither limited to two asset classes, nor did they make all or nothing switches, yet their return paths are, as expected, contained inside the feasible set. The conclusion is that real-life market timers are correctly characterized—except for costs—by the PDF within the feasible set, and that random sampling of the PDF does properly characterize the return distribution expected from market timing schemes.

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. Fig 6 also illustrates the main result with live, not simulated, market timing data. Not only has the group of tactical allocation funds underperformed, but not a single one of them outperformed the simple, low-cost, passive fund. This is because of the possibility of hidden variables.

Hidden variables represent information, such as earnings, book value, anything, that a market timer could put into a function that produces a timing path. While the observed optimal timing path f b is random to the extent that it passes the NIST tests, it is possible that there was a set of hidden variables that could have been combined in a function that would have produced the optimal timing path f b.

Good pseudo-random number generators also pass the NIST tests but are produced by deterministic systems.

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