Euan Sinclair - Positional Option Trading

Using sampling with replacement, generate a series of 100 returns from the historical data.

Apply the strategies (A and B) to this ahistorical data to get the pseudo-strategies A' and B'.

Subtract the mean return of A from A' and B from B'.

Calculate the average return of the return-adjusted strategies, A” and B”.

The larger of the returns of A” and B” is the first data point of our sample distribution.

Repeat the process N times to generate a complete distribution. This is the sampling distribution of the statistic, maximum average return of the two rules with an expected return of zero.

The p-value (probability of our best rule being truly the better of the two) is the proportion of the sampling distribution whose values exceed the returns of A, that is, 2%.

A realistic situation would involve comparing many rules. It is probably worth paying for the software.

There is also a totally different and complementary way to avoid overfitting. Forget about the time series of the data and study the underlying phenomenon. A hunter doesn't much care about the biochemistry of a duck, but she will know a lot about their actual behavior. In this regard a trader is a hunter, rather than a scientist. Forget about whether volatility follows a GARCH(1,1) or a T-GARCH(1,2) process; the important observation is that it clusters in the short term and mean reverts in the long term. If the phenomenon is strong enough to trade, it shouldn't be crucial what exact model is used. Some will always be better in a sample, but that is no guarantee that they will work best out of a sample.

As an example, this is the correct way to find a trading strategy.

There is overwhelming evidence that stocks have momentum. Stocks that have outperformed tend to continue outperforming. This has been observed for as long as we have data (see Geczy and Samnov [2016], Lempérière et al. [2014], and Chabot et al. [2009]) and in many countries (for example, Fama and French, 2010). The observation is robust with respect to how momentum is defined and the time scales over which it is measured. In the trading world, the evidence for stock momentum is overwhelming. Starting from this fact, design a simple model to measure momentum (e.g., 6-month return). Then sort stocks by this metric and buy the ones that score well.

The worst thing to do is take a predefined model and see if it works. Has a 30-day, 200-day moving average crossover been predictive of VIX futures? What if we change the first period to 50 days? I don't know or care.

Fundamental analysis aims to predict returns by looking at financial, economic, and political variables. For example, a fundamental stock analyst might look at earnings, yield, sales, and leverage. A global macro trader might consider GDP, currency levels, trade deficit, and political stability.

Fundamental analysis, particularly global macro, is particularly susceptible to subjectivity. It also tempts otherwise intelligent people to make investment decisions based on what they read in the Wall Street Journal or The Economist . It is exceedingly unlikely that someone can consistently profit from these public analyses, no matter how well the story is sourced or how smart the reader is.

Consider these statements from “experts”:

“Financial storm definitely passed.”

—Bernard Baruch, economic advisor to presidents Woodrow Wilson and Franklin Roosevelt in a cable to Winston Churchill, November 1929

Stocks dropped for the next 3 years, with the Dow losing 33% in 1930, 52% in 1931, and 23% in 1932.

“The message of October 1987 should not be taken lightly. The great bull market is over.”

—Robert Prechter, prominent Elliot wave theorist and pundit, in November 1987. The Dow rallied for 11 of the next 12 years, giving a return (excluding dividends) of over 490%.

“A bear market is likely… It could go down 30% or 40%.”

—Barton Biggs, chief strategist for Morgan Stanley, October 27, 1997

The Dow had its largest one-day gain on October 28 and continued to rally hard for the next 6 months.

In most situations it is just mean to make fun of people's mistakes. We all make mistakes. But the people I have quoted have proclaimed themselves experts in a field where real expertise is very, very rare.

And evidence of this is more than anecdotal.

The poor prediction skill of experts is a general phenomenon. Gray (2014) summarizes the results of many studies that show that simple, systematic models outperform experts in fields as diverse as military tactics, felon recidivism, and disease diagnosis. Expertise is needed to build the models, but experts should not make case-by-case decisions.

Koijen et al. (2015) show that surveys of economic experts (working for corporations, think tanks, chambers of commerce, and NGOs) have a negative correlation to future stock returns. They were also contraindicative for the returns of currencies and bonds. This effect applies across 13 equity markets, 19 currencies, and 10 fixed income markets. A simple “fade the experts” strategy would have given a Sharpe ratio of 0.78 from 1989 to 2012.

Financial advisors are equally bad. Jenkinson et al. (2015) look at the performance of advisors in picking mutual funds. They conclude with, “We find no evidence that these recommendations add value, suggesting that the search for winners, encouraged and guided by investment consultants, is fruitless.” And fund managers themselves can't consistently beat the averages. Due to costs, most managers underperform and there is no correlation between performances from one year to the next. So, managers can't pick stocks and it is pointless to try to pick good managers.

It is also likely that much of the alpha generated by fundamental analysis is smart beta, compensation for exposure to a certain risk factor. There is absolutely nothing wrong with this. Trading profits are profits, no matter whether they are due to smart beta or alpha. But before we ascribe a trader's results to skill, we should know what is causing the profits. Beta should cost a lot less than alpha.

It is difficult to make money in financial markets. The EMH isn't completely true, but it is closer to being correct than to being wrong. If a trader can't accept this, she will see edges in noise and consequently overtrade. Behavioral finance, technical analysis, and fundamental analysis can all be used as high-level organizing principles for finding profitable trades, but each of these needs to be believed only tentatively, and the most robust approach is to look for phenomena that are independently clear. For example, momentum can be discovered through technical analysis but also understood as a behavioral anomaly. The observable phenomenon must come before any particular method.

Exceptions to the EMH exist but they are rare.

Exceptions will either be inefficiencies, temporary phenomena that last only until enough people notice them, or poorly priced risk premia.

Risk premia will persist and can form the core of a trader's operations but the profits due to inefficiencies will decay quickly and need to be aggressively exploited as soon as they are found.

A promising trading strategy is one whose basis is independent of the specific methods used to measure it. Start with observation, then move to quantification and justification.

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