Download Financial Time Series Analysis Course outline Overview Lunar

19/05/2014
Course outline
Financial Time Series Analysis
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
Patrick McSharry
[email protected]
www.mcsharry.net
Trinity Term 2014
Mathematical Institute
University of Oxford
1. Data analysis, probability, correlations, visualisation techniques
2. Time series analysis, random walk, autoregression, moving average
3. Technical analysis, trend following, mean reversion
4. Nonlinear time series analysis
5. Nonlinear modelling, regime switching, neural networks
6. Parameter estimation, model selection, forecast evaluation
7. Volatility forecasting, GARCH, leverage effect
8. Risk analysis, value at risk, quantile regression
9. Energy consumption, demand forecasting
10. Ensemble prediction, wind power generation
11. Weather derivatives, index-based insurance
12. Quantitative trading strategies, algorithmic trading
Copyright © 2014 Patrick McSharry
Lecture 3
Overview
•  Moving averages
•  Exponentially weighted moving averages
•  Technical analysis
–  Head and shoulders
–  Relative Strength Index
–  Moving Average Convergence / Divergence
–  Oscillators
–  Bollinger bands
–  Japanese candlesticks
–  Elliott waves
•  Fundamental analysis
Major stock market crashes
• 
“Black Tuesday,” October 29, 1929,
and “Black Monday,” October 19,
1987 occurred on the same annual
lunar calendar date, 7-28.
• 
Additionally, the other similar points in
the comparisons of those two years,
the spring lows, summer highs and
autumn failure highs all occurred
within one day on the lunar calendar.
• 
The figure shows those years in a
chart aligned with the lunar calendar,
where similar lunar dates are
juxtaposed above each other. The
panics are marked with arrows. The
other similar features are denoted
with dashed lines.
• 
The chart also includes Hong Kong’s
Hang Seng index for the panic year
1997
Lunar panics
•  Christopher Carolan (1998), demonstrated the
correlation between the lunar calendar and the stock
market panics of 1929 and1987.
•  “The annual lunar model for panics points to the 27th
and 28th days of the lunar month as the dark days, yet
that is only true in the autumn season, the 6th or 7th
lunar month.”
•  “When there is no full moon between October 3 and 19
inclusive, the Dow has been up 1.5% in October since
1915. In those years with a full moon between those
dates, the Dow’s average change is a loss of 1.9%.”
Largest daily crashes
A scan of daily data of the Dow Jones Industrial Average from 1915, the Hang Seng index
from 1980, The Japanese Nikkei index from 1950, and the German DAX index from 1960 for
the 10 largest, single-day percentage drops is shown.
Seven of those ten declines were days associated with one of the three panics. Two of the
others, the Spring 1989 declines in the Hong Kong market, were tied to a fundamental news
event, the Tiananmen crisis in China. The final entry is from the German market during the
“mini-crash” of October 1989, an October event similar to the others, but smaller in
magnitude
1
19/05/2014
Moving averages
Exponentially weighted moving
averages
•  A moving average may be viewed as a
convolution or a low-pass filter.
•  A simple moving average of the last n
observations is given by:
n
•  EWMA employs exponentially decreasing weights
to discount the influence of old observations:
•  By smoothing the time series, it can remove the
effects of seasonality.
•  Note that it gives equal weight to both new and
old observations
•  The EWMA may also be expressed via the
number of time periods n using the smoothing
factor, α=1/n, giving:
⎛ 1 ⎞
⎛ n − 1 ⎞
st = ⎜ ⎟ xt + ⎜
⎟ st −1
⎝ n ⎠
⎝ n ⎠
1
st = ∑ xt −i +1
n i =1
EWMA weights
st = αxt + (1 − α )st −1
•  The smoothing factor, 0<α<1,determines the rate
of decay of old information
Technical analysis
•  Technical analysts attempt to identify patterns in
historical financial market data (both price and
volume) that can be exploited to generate positive
returns
•  Using transformations of financial time series it may
be possible to forecast price movements
•  The idea is that large gains from successful trades
exceed more numerous but smaller losing trades
•  By controlling for risk, it should be possible
generate positive average returns in the long-term
Head and shoulders
The “head-and-shoulders" pattern is believed to be one of the most reliable trend-reversal
patterns.
Double bottoms
The “double bottom” looks like the letter "W". The twice touched low is considered a support
level.
Most technical analysts believe that the advance off of the first bottom should be 10-20%. The
second bottom should form within 3-4% of the previous low, and volume on the ensuing
advance should increase.
2
19/05/2014
Evidence for technical analysis
• 
Neftci (1991) showed that some of the rules employed in technical analysis
generate well-defined techniques of forecasting, but even well-defined rules
were shown to be useless in prediction if the economic time series is
Gaussian. However, if the processes under consideration are nonlinear,
then the rules might capture some information. Tests showed that this may
indeed be the case for the moving average rule.
• 
Brock et al. (1992) analysed numerous technical trading rules using 90
years of daily stock prices from the Dow Jones Industrial Average up to
1987 and found that they all outperformed the market.
• 
Lo et al. (2000) took a systematic and automatic approach to technical
pattern recognition, applying nonparametric kernel regression to a large
number of US stocks from 1962 to 1996. By comparing the unconditional
empirical distribution of daily stock returns to the conditional distribution
(conditioned on specific technical indicators) they found that several
technical indicators provided “incremental information and may have some
practical value”.
RSI example
Relative strength index
•  Wilder (1978) proposed the relative strength index (RSI) to measure
price strength by comparing upward and downward price changes:
⎛ s u
RSIt = 100⎜⎜ u t d
⎝ st + st
⎞
⎟⎟
⎠
where su and sd are EWMA estimates of ut = max(pt-pt-1,0) and
dt = max(pt-1-pt,0)
•  Wilder recommended a smoothing factor of α=1/14 and considered a
security to be overbought when RSI>70 and oversold when RSI<30
•  Cutler’s RSI uses a simple moving average instead of EWMA
Moving Average Convergence /
Divergence (MACD)
•  MACD is a trend-following indicator and measures
the difference between a fast and slow
exponential moving average (EWMA) of prices:
MACDt = EWMAt12(p) – EWMAt26(p)
st = EWMAt9(MACD)
•  MACD can be traded in a number of ways:
–  Buy (sell) when MACDt moves above (below) st
–  Buy (sell) when MACDt moves above (below) zero
–  Divergence between price and MACD levels
Source: Wikipedia
MACD example
Trix
•  Trix (Triple Exponential) is an oscillator
constructed by applying EWMA three times to
price time series
•  Positive values indicate and upwards trend and
negative values suggest a downward trend
•  The application of EWMA three times has the
effect of spreading out the weights and
decreasing the weight on the most recent
observations
Source: Wikipedia
3
19/05/2014
Stochastic oscillators
•  Lane (1950) introduced the stochastic oscillator to
measure momentum by comparing the closing price to the
price range over a specific period (usually n=14 days):
p −p 
low
s fast = 100 close

 phigh − plow 
•  The rational is that prices tend to close near their past
highs in bull markets, and near their lows in bear markets.
•  Trading signals can be generated when the fast stochastic
oscillator crosses its moving average, the slow stochastic
oscillator
€
•  A pair of fast and slow oscillators may be formed; the slow
oscillator can be derived from the fast one using a simple
moving average with n=3 days
Trading stochastic oscillators
•  Buy when sfast crosses up through sslow and sell
when sfast crosses down through sslow
•  An alternative trading strategy is to use the
oscillators directly based on their level as was the
case of RSI; s > 80 implies overbought and s < 20
implies oversold
•  Oscillators may be slowed down further during
periods of high volatility by taking additional moving
averages (or averages with longer periods)
•  This reduces fluctuations, the number of crossovers and hence transaction costs
Stochastic oscillators
Bollinger bands
• 
Bollinger bands provide a conditional measure of the highness or lowness
of the price relative to previous trades
• 
The bands are defined using an n-period simple moving average, µt for the
centre and ±kσt for the bands where σt is the n-period standard deviation
(typical values are n=20 and k=2)
• 
While we should not expect 95% of an equity's closing prices, on average,
to lie within the Bollinger bands (as for normal distributions), from
Chebyshev's inequality we can expect around 75% of the closing prices
• 
Trading strategies:
–  Buy when the price touches the lower band and exit when price reaches the
centre
–  Buy when the price moves above the upper band or sell when the price goes
below the lower band
–  Sell options when bands are historically far apart or buy options when the bands
are historically close together
Source: Wikipedia
Bollinger bands example
Japanese candlesticks
•  A candlestick chart, reflects the
open, high, low and close prices for
each time period
•  The filled part of the candlestick is
known as the body and reflects the
change between the open and close
•  Long thin lines above and below the
body represent the high/low range
•  A hollow candlestick implies that the
close was higher than the open
whereas a filled candlestick implies
the opposite
Source: Wikipedia
4
19/05/2014
Elliott waves
• 
Elliott argued that because humans are
themselves rhythmical, their activities and
decisions could be predicted in rhythms
• 
The wave principle posits that collective
investor psychology moves from optimism to
pessimism and back again
• 
Elliott's approach states that market prices
alternate between five point bullish waves and
three-point bearish waves
• 
As these waves develop, the larger price
patterns unfold in a self-similar fractal
geometry. Within the dominant trend, waves 1,
3, and 5 are "motive" waves, and each motive
wave itself subdivides in five waves. Waves 2
and 4 are "corrective" waves, and subdivide in
three waves.
• 
The Fibonacci sequence appears repeatedly in
Elliott wave structures, including motive waves
(1, 3, 5), a single full cycle (5 up, 3 down = 8
waves), and the completed motive (89 waves)
and corrective (55 waves) patterns
• 
The ratio of the second peak to the first is
1.618 (approximately the golden ratio)
€
Volume
•  Volume provides a measure of the number of contracts
or transactions occurring during a particular time period
•  Volume acts as an additional source of information as it
represents the level of activity in the market
•  Strong upward trends are usually associated with
increasing prices and high volume. In contrast
increasing prices and low volume could signal a
precursor to a reversal
•  Ying (1966) found a contemporaneous correlation
between volume and returns and conclude that (i) low
(high) volume is associated with decreasing (increasing)
prices and (ii) a large increase in volume is usually
accompanied by a large absolute change in price
From R.N. Elliott's essay, "The Basis of the
Wave Principle," October 1940.
Fundamental analysis
Fundamental ratios
•  Fundamental analysis attempts to identify securities that
have been mispriced by the market. By taking a position
now it should be possible to take profits once the market
corrects the price.
•  Key information includes prices, dividends, earnings and cash flows
•  The P/E ratio (price-to-earnings ratio) of a security is a measure of
the share price relative to the annual income or profit earned by the
firm per share. A higher P/E ratio means that investors are paying
more for each unit of income
•  The PEG ratio, Price/Earnings To Growth, is a valuation metric for
determining the relative trade-off between the price of a stock, the
earnings generated per share (EPS), and the company's expected
growth.
•  PEG is a widely employed indicator of a stock's possible true value.
The PEG ratio of 1 represents a fair trade-off between the values of
cost and the values of growth, indicating that a stock is reasonably
valued given the expected growth.
•  The lower the PEG ratio the more undervalued the stock. The PEG
ratio may be better able to discriminate between stocks because
unlike the P/E ratio it also accounts for growth.
•  The objective is to find good companies using
information from the analysis of income and financial
statements, management, competitive advantages of the
business and potential competitors and markets
•  Value investors specifically attempt to detect
undervalued securities
P/E ratio and S&P returns
• 
Shiller (2005) demonstrated that P/E ratios are
a predictor of twenty-year returns.
• 
The horizontal axis shows the real P/E ratio of
the S&P Composite Stock Price Index (inflation
adjusted price divided by the prior ten-year
mean of inflation-adjusted earnings).
• 
The vertical axis shows the geometric average
real annual return on investing in the S&P
Composite Stock Price Index, reinvesting
dividends, and selling twenty years later.
• 
Data from different twenty year periods is colorcoded as shown in the key.
• 
Shiller states that this "confirms that long-term
investors—investors who commit their money to
an investment for ten full years—did do well
when prices were low relative to earnings at the
beginning of the ten years.
• 
Long-term investors would be well advised,
individually, to lower their exposure to the stock
market when it is high, as it has been recently,
and get into the market when it is low."
5