Course outline. Financial Time Series Analysis. Lunar panics. Overview. Largest daily crashes. Major stock market crashes 01/09/2014

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1 Financial Time Series Analysis Patrick McSharry Advanced Modelling Techniques September 204 University of Oxford Course outline. Data analysis, probability, correlations, visualisation techniques, random walk, autoregression, moving average 2. Technical analysis, trend following, mean reversion 3. Nonlinear time series analysis, nonlinear modelling, regime switching, neural networks 4. Parameter eimation, model selection, model evaluation, volatility forecaing, GARCH, leverage effect 5. Quantitative trading rategies, algorithmic trading Lecture 2 Copyright 204 Patrick McSharry Overview Moving averages Exponentially weighted moving averages Technical analysis Head and shoulders Relative Strength Index Moving Average Convergence / Divergence Oscillators Bollinger bands Japanese candleicks Elliott waves Fundamental analysis Lunar panics Chriopher Carolan (998), demonrated the correlation between the lunar calendar and the ock market panics of 929 and987. 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 9 inclusive, the Dow has been up.5% in October since 95. In those years with a full moon between those dates, the Dow s average change is a loss of.9%. Major ock market crashes Large daily crashes Black Tuesday, October 29, 929, and Black Monday, October 9, 987 occurred on the same annual lunar calendar date, 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 997 A scan of daily data of the Dow Jones Indurial Average from 95, the Hang Seng index from 980, The Japanese Nikkei index from 950, and the German DAX index from 960 for the 0 large, 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 989 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 989, an October event similar to the others, but smaller in magnitude

2 Moving averages A moving average may be viewed as a convolution or a low-pass filter. A simple moving average of the la n observations is given by: n = x t i+ n i= By smoothing the time series, it can remove the effects of seasonality. Note that it gives equal weight to both new and old observations Exponentially weighted moving averages EWMA employs exponentially decreasing weights to discount the influence of old observations: = αxt + ( α) The smoothing factor, 0<α<,determines the rate of decay of old information The EWMA may also be expressed via the number of time periods n using the smoothing factor, α=/n, giving: n = xt + n n EWMA weights Technical analysis Technical analys attempt to identify patterns in hiorical 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 foreca 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 Double bottoms The head-and-shoulders" pattern is believed to be one of the mo reliable trend-reversal patterns. The double bottom looks like the letter "W". The twice touched low is considered a support level. Mo technical analys believe that the advance off of the fir bottom should be 0-20%. The second bottom should form within 3-4% of the previous low, and volume on the ensuing advance should increase. 2

3 Evidence for technical analysis Neftci (99) showed that some of the rules employed in technical analysis generate well-defined techniques of forecaing, 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. Tes showed that this may indeed be the case for the moving average rule. Brock et al. (992) analysed numerous technical trading rules using 90 years of daily ock prices from the Dow Jones Indurial Average up to 987 and found that they all outperformed the market. Lo et al. (2000) took a syematic and automatic approach to technical pattern recognition, applying nonparametric kernel regression to a large number of US ocks from 962 to 996. By comparing the unconditional empirical diribution of daily ock returns to the conditional diribution (conditioned on specific technical indicators) they found that several technical indicators provided incremental information and may have some practical value. Relative rength index Wilder (978) proposed the relative rength index (RSI) to measure price rength by comparing upward and downward price changes: where s u and s d are EWMA eimates of u t = max(p t -p t-,0) and d t = max(p t- -p t,0) u RSI = t 00 u d + Wilder recommended a smoothing factor of α=/4 and considered a security to be overbought when RSI>70 and oversold when RSI<30 Cutler s RSI uses a simple moving average inead of EWMA RSI example Moving Average Convergence / Divergence (MACD) MACD is a trend-following indicator and measures the difference between a fa and slow exponential moving average (EWMA) of prices: MACD t = EWMA t 2 (p) EWMA t 26 (p) s t = EWMA t9 (MACD) MACD can be traded in a number of ways: Buy (sell) when MACD t moves above (below) s t Buy (sell) when MACD t moves above (below) zero Divergence between price and MACD levels MACD example Trix Trix (Triple Exponential) is an oscillator conructed by applying EWMA three times to price time series Positive values indicate and upwards trend and negative values sugge a downward trend The application of EWMA three times has the effect of spreading out the weights and decreasing the weight on the mo recent observations 3

4 Stochaic oscillators Lane (950) introduced the ochaic oscillator to measure momentum by comparing the closing price to the price range over a specific period (usually n=4 days): s fa =00 p close p low p high p low The rational is that prices tend to close near their pa highs in bull markets, and near their lows in bear markets. Trading signals can be generated when the fa ochaic oscillator crosses its moving average, the slow ochaic oscillator A pair of fa and slow oscillators may be formed; the slow oscillator can be derived from the fa one using a simple moving average with n=3 days Trading ochaic oscillators Buy when s fa crosses up through s slow and sell when s fa crosses down through s slow An alternative trading rategy 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 cos Stochaic 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, µ t for the centre and ±kσ t for the bands where σ t is the n-period andard 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 diributions), from Chebyshev's inequality we can expect around 75% of the closing prices Trading rategies: 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 hiorically far apart or buy options when the bands are hiorically close together Bollinger bands example Japanese candleicks A candleick chart, reflects the open, high, low and close prices for each time period The filled part of the candleick 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 candleick implies that the close was higher than the open whereas a filled candleick implies the opposite 4

5 Elliott argued that because humans are themselves rhythmical, their activities and decisions could be predicted in rhythms The wave principle posits that collective inveor psychology moves from optimism to pessimism and back again Elliott waves Elliott's approach ates 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, 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 ructures, including motive waves (, 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 fir is.68 (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 contra increasing prices and low volume could signal a precursor to a reversal Ying (966) 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 940. Fundamental analysis 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. The objective is to find good companies using information from the analysis of income and financial atements, management, competitive advantages of the business and potential competitors and markets Value inveors specifically attempt to detect undervalued securities Fundamental ratios 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 inveors 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 ock, the earnings generated per share (EPS), and the company's expected growth. PEG is a widely employed indicator of a ock's possible true value. The PEG ratio of represents a fair trade-off between the values of co and the values of growth, indicating that a ock is reasonably valued given the expected growth. The lower the PEG ratio the more undervalued the ock. The PEG ratio may be better able to discriminate between ocks because unlike the P/E ratio it also accounts for growth. P/E ratio and S&P returns Shiller (2005) demonrated 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 adjued price divided by the prior ten-year mean of inflation-adjued earnings). The vertical axis shows the geometric average real annual return on inveing in the S&P Composite Stock Price Index, reinveing dividends, and selling twenty years later. Data from different twenty year periods is colorcoded as shown in the key. Shiller ates that this "confirms that long-term inveors inveors who commit their money to an invement for ten full years did do well when prices were low relative to earnings at the beginning of the ten years. Long-term inveors would be well advised, individually, to lower their exposure to the ock market when it is high, as it has been recently, and get into the market when it is low." 5