Summary Book 1 - Chapter 2 An Introduction to Statistics

Quantitative trading strategies harnessing the power of quantitative techniques to create a winning trading program:
Summary:

Descriptive statistics are tools that allow traders to better understand and comprehend
data in an easy and effective manner.

Instead of presenting the height measurements of 100 men, I could instead offer that
the average height of these 100 men is 5 feet 8 inches.

By providing one descriptive statistic, I have characterized a quality of the entire
sample of height measurements.

I can take this process further by revealing that the standard deviation of heights is 3 inches.

By calculating descriptive statistics on market prices, market returns, and market

volume, we can learn much about the nature of recent price movement.

These descriptive statistics will become the building blocks for our quantitative
trading systems.

The mean of a series, more commonly referred to as the average, is a measure of
central location. The mean is the sum of the values in a distribution divided by the
number of data points in the distribution.

We may wish to measure how widely values spreadacross a distribution. Do the values clump closely around a central point or are they distributed widely? The most popular methods used to measure the dispersion
of values are variance and standard deviation.

Variance, often represented by 2, measures how wide the spread of values
span from the mean.

if a company has a larger variance than another company it means the returns of that
company vary more widely and are more volatile.

Correlation is another important descriptive statistic. It measures the strength of a
relationship between two series.

The correlation statistic is calculated by multiplying the difference
of one series from its mean by the corresponding difference of another series
from its mean, taking the average product, and then dividing by the product of the
standard deviation of both series.

In Figure 2.5, y increases as x does. This indicates a positive correlation
between x and y. In Figure 2.6, a different relationship exists. As x increases, y
decreases, indicating negative correlation.

it is important to perform your analysis using returns rather than prices.

Standard deviation is a popular method of measuring dispersion, primarily due
to its properties under certain circumstances, specifically those associated with
a normal distribution.

normal distribution, For example, we know that roughly 68.26 percent of
the values in a normal distribution fall between ±1 standard deviation of the mean,
95.44 percent fall between ±2 standard deviations, and 99.74 percent between ±3
standard deviations

explain how volatility varies over time. These models are called GARCH, for Generalized Auto
Regressive Conditional Heteroskedasticity. A GARCH process exists when
volatility itself changes over time, wandering back and forth around a long-term
average.

We start by calculating the standard deviation of the first 20 returns. On the
next day, we drop the first return from our calculation, add the 21st return, and
recalculate the standard deviation of returns. The following day we drop the second
return and add the 22d return in our calculation of standard deviation. And so
on. Each value of the 20-day standard deviation will have 19 common return
points as the value before and value after. In this sense, the calculation “rolls” with
each day, hence the expression “rolling volatility.”

volatility scales with the square root of time, we multiply our daily standard deviation by the square root of trading days in a year (typically 252 for equity markets). The result of this adjustment is an annualized standard deviation, or volatility.

This property of volatility is common to almost all markets. Periods of
high volatility are often followed by further periods of high volatility, slowly
decreasing to more normal levels over time. Similarly, periods of low volatility are
often followed by further periods of low volatility, eventually returning to normal
levels over time.GARCH cannot or does not predict
market returns or prices, volatility has important implications
for generating trading signals as well as managing the risk of portfolios

If we know a market’s annualized volatility, we can calculate the daily risk of
being long or short.

The daily standard deviation of being long or short the S&P
500 is equal to the value of the portfolio multiplied by the annualized standard
deviation divided by the square root of 252 (trading days in year)

lognormal distribution. This is somewhat similar to the normal
distribution in its shape, except the left- and right-hand side of the distribution
is not symmetrical.The lognormal distribution
of prices is used commonly and is the basis for the Black-Scholes option pricing
formula.

Summary Book 1 - Prologue

Quantitative trading strategies harnessing the power of quantitative techniques to create a winning trading program:

SUMMARY

Quantitative trading strategies are a combination of technical and statistical analysis which, when applied, generate buy and sell signals.

Once these trading strategies are formed, their performance is tested historically to validate the trading ideas.

After the performance is tested, we select the markets to be traded.

By trading a widely diversified portfolio, we are able to minimize our risk while maintaining expected reward.

Developing the idea, testing historical performance, and picking markets to trade are a few of the many techniques required for efficient and profitable trading strategies.

While a few books have touched on various areas of the development process, I believe this book is the first to fully capture all the nuances of the trading process.

Studying these fundamental factors is the most common method of analyzing markets.

Technical analysis does not attempt to predict market movements based on fundamentals.

As a result, technical analysts believe that price action is the best source of information.

Catchy names such as "Head and shoulders top," "Symmetrical triangle," and "Trendline" are a large part of the technical analyst's toolbox.

Typically, the technical analyst relies on a good bit of discretion for his or her trading ideas.

While a pattern may look like a buy signal to one technical analyst, another may see a different pattern emerging and actually be preparing to sell the market.

Whenever we make statements about the market, we can perform mathematical and statistical tests to determine if we are correct in our beliefs.

Do changes in interest rates affect returns on the stock market? If corn prices have been rising, is it likely that they will continue to do so in the near future? Considering that historical data for market prices is available back to the turn of the twentieth century in many cases, we can study historical market prices and usually find answers to these questions once we quantify each of these questions.

The remainder of this book will attempt to answer questions aimed at understanding exactly how markets behave and how investors and traders can profit from this information.

Most of our study involves creating, testing, and applying trading strategies.

A trading strategy is a set of rules that signal the trader when to buy, when to sell, and when to sell short a market.

The signals can also be very complex and include statistical regression and relationships between many related markets.
The most vital part of trading system development is performance testing.

When we test historical performance, we first want to see if our strategies have been profitable in the past.

Because many strategies will be profitable historically, we need a methodology to compare the profitability among trading strategies.

Very often the most profitable system is not the best system for our trading.

I believe most traders use outdated and inconsistent performance measures to evaluate historical performance.

Finally, we need to develop a money management plan for trading our strategies.

Once we have designed and tested our trading strategy, the next choice is to decide which markets to trade.

Shares of companies trade on three major markets in the United States: the New York Stock Exchange , the American Stock Exchange, and the NASDAQ.

While the NYSE and AMEX are physical trading floors where buyers and sellers meet to trade shares, the NASDAQ is a linkage of market makers negotiating prices with customers and with each other.

Due to the high leverage and low transaction costs associated with the futures market, these markets have long been a popular trading vehicle for quantitative traders.

Most of these markets are actually combinations of other markets where one asset is bought and the other asset is sold short.

Once we design and test our quantitative trading strategies, we can implement them on these new markets to gain access to products outside the typical stock and futures markets.

Three forms of the EMH (Efficient Markets Hypothesis) exist: strong form EMH, semi-strong form EMH, and weak form EMH.

The strong form of EMH suggests that all information, both public and private, is always incorporated into current prices.

The semi-strong form of the EMH states that current prices reflect all information in the public domain, including annual company reports, USDA crop estimates, Wall Street research reports, and quality of corporate management.

The weak form EMH suggests that prices already reflect all information that can be derived from analyzing historical market data, such as closing prices, volume, and short interest.

All three forms of the EMH suggest that our attempts to make money by buying and selling based on prior price patterns are hopeless.

These cracks in the EMH hint that markets may not be as efficient as was once thought.