**Mathematics in Trading & Analysis of the market**

**Golden**** ****Ratio **(Golden Mean), The golden ratio *(symbol is the Greek letter “phi” )* is a special number approximately equal to 1.618. It appears in geometry, art, architecture and other areas. The negative root is 0.618. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement. See definition fully described in WikipediA.

**π** (sometimes written **pi**) is a mathematical constant whose value is the ratio of any circle‘s circumference to its diameter; this is the same value as the ratio of a circle’s area to the square of its radius. π is approximately equal to 3.14159 in the usual decimal positional notation. Many formulae from mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants. See definition fully described in WikipediA.

However, according to mathematician Bob Palais of the University of Utah two times pi, not pi itself, is the truly sacred number of the circle, Palais contended. We should be celebrating and symbolizing the value that is equal to approximately 6.28 — the ratio of a circle’s circumference to its radius — and not to the 3.14’ish ratio of its circumference to its diameter (a largely irrelevant property in geometry). Palais’ followers gave the new constant, 2pi, a name: tau. The mathematicians aren’t saying that pi has been wrongly calculated. Its value is still approximately 3.14, as it always was. Rather they argue that 3.14 isn’t the value that matters most when it comes to circles. Palais originally argued that pi should be changed to equal 6.28 while others prefer giving that number a new name altogether. See this described in more detail here.

**Fibonacci Retracements****,** is method for determining support and resistance levels. They are named after their use of the Fibonacci sequence. Fibonacci retracement is based on the idea that markets will retrace a predictable portion of a move, after which they will continue to move in the original direction. In finance the most common Fibonacci retracements are 23.6%, 38.2%, 61.8% which are typically retracements in stock and commodity prices. See definition fully described at Wikipedia.

**Fibonacci Ratios**, Fibonacci ratios are mathematical relationships, expressed as ratios, derived from the Fibonacci sequence. The key Fibonacci ratios are 0%, 23.6%, 38.2%, and 100%. Two more important numbers we are going to use are the number .5 – or 50% , since we will see it demonstrated in patterns in financial markets. Remember .5. It is not the Golden Ratio, but it is related to Fibonacci numbers. Another number we want to keep in mind is .786, which represents the square root of .618. These are all numbers that we will use to analyze wave patterns in various markets.

See definition fully described at Wikipedia.

**Charting and analysis methods:**

**Point and figure** (from WikipediA) is a charting technique used in technical analysis, used to attempt to predict financial market prices. Point and figure charting is unique in that it does not plot price against time as all other techniques do. Instead it plots price against changes in direction by plotting a column of Xs as the price rises and a column of Os as the price falls. See full description in WikipediA.

**Here is a short explanation of some of the technical indicators we frequently use:**

**RSI:** The RSI (Relative Strength Indicator) is an oscillator that ranges from zero to 100. A low number reading suggests a stock is oversold and ready to bounce. A typical “buy” level for this indicator is when it turns up from 30 combined with positive divergence (on the indicator), and a typical “sell” level would be when it turns down from over 70 combined with negative divergence (on the indicator).

**MACD:** The MACD (Moving Average Convergence/Divergence) is calculated using the difference between two moving averages for a stock. A moving average of that difference is then used, and called the *signal line*. A common “buy” signal is generated when the MACD crosses above that signal line.

**MACD Histogram** works like headlights in a car – it gives traders a glimpse of the road ahead. If the indicator falls to a new low, it shows that the bears are strong and prices are likely to retest or exceed their latest low. Divergences between MACD Historgram and price only occur a few times a year, but they are some of the most powerful messages in technical analysis.

**Golden Cross: **A golden cross occurs when a shorter-term moving average crosses above a longer-term moving average. In analysis 50-day and 80-day moving averages are the most commonly used.

**Moving Average Crossover:** Here, we’re simply looking at the stock price crossing above a certain moving average. I compared returns after the stock’s price crossed above its 20-, 50-, and 200-day moving averages.

**Sentiment Indicators**

**CBOE Volatility Index (VIX): ** The VIX gauges expected market volatility over the next 30 calendar days by calculating a weighted average of S&P 500 Index (SPX) options with a constant maturity of 30 days to expiration. Extreme high and low VIX readings can provide good contrarian signals, though it actually doesn’t matter where the reading lies on an absolute basis if it is at an extreme relative to its recent readings. Buy signals often occur as the VIX reverses lower after an extreme peak, while sell signals occur as the VIX moves higher off an extreme bottom.

**The Put/Call ratio **(considered to be the dumb money is a contrarian indicator). We use a 10 and 20 moving average ( ma) to smooth out the data and avoid noise. Low readings under 0.7 on the ma indicate that investors are complacent and the market due for a correction. High readings over 1 on the ma indicate that investors are fearful and the market in due for a rally.

**Tick Index**compares the number of stocks on the New York Stock Exchange that are rising to the number of stocks that are falling. The calculation is very simple. You take the up ticking (or rising) stocks and subtract the down ticking (or falling stocks). If the number is positive, that means more stocks are rising than falling. If the number is negative, that means more stocks are falling than rising.

When the TICK approaches +1,000 or -1,000, watch out. These extremes indicate a severely overbought or oversold condition. In either case, expect the market to abruptly reverse itself. Understanding the TICK can help you decide when to buy or sell.

When the TICK is approaching +750 or more, it may be time to sell since conditions are ripe for the market to reverse itself and begin falling.

Using Tick reading to interpret Elliott Waves: In a rising market the top of the 5th wave has weaker Tick reading than the top of the 3rd wave. If not it’s likely that the 3rd wave is extending then that it is a 5th wave. In a declining market the bottom of the 5th wave have improved Tick reading compared to the bottom of the 3rd wave. If not it’s likely that the 3rd wave is extending then that it is a 5th wave.

**Market Breadth**

**The McClellan Oscillator** is a market-breadth indicator based on the moving average of the number of rising and falling stocks. Look for divergence on oversold or overbought readings to anticipate a turning point in the market.

**The NYSE Summation Index** a technical analysis indicator which uses NYSE market breadth to judge the strength of a market move in the near term. Calculated by subtracting a 39-day exponential moving average of the difference between advancing issues and declining issues on the NYSE from a 19-day exponential moving average of the same difference.

**Bollinger Band and related indicators**

**Bollinger Band **A band overlay that shows the upper and lower limits of ‘normal’ price movements based on the Standard Deviation of prices.

**b% **Shows where you are in relation to the Bollinger Band.

**Band Widths** Shows how wide the Bollinger Band is, used to identify low volatility (tight Bollinger Band) and high volatility (Expanding Bollinger Band). Band Widths is used to identify the beginning of a new trend or the end of a trend.

**Volume Indicators**

The third and the fourth category under are the most interesting and useful in todays trading environment. This is the ones we use and will describe here.

**1. Periodic price change, **On Balance Volume, Volume Price Trend

**2. Periodic volume change**, Negative and Positive Volume Indices

**3. Intraperiod structure**, Intraday Intensity, Accumulation Distribution

**4. volume weighting**, Money Flow Index, Volume weighted MACD

Money Flow Index A volume-weighted version of RSI that shows shifts is buying and selling pressure. Gives you the answer if the volume differential between up days and down days confirm the momentum of the trend.

**Volume analysis**

TRIN The definition in the book “The ARMS Index” by the inventor Richard Arms: It asks if buying pressure or selling pressure is really controlling the market an any given time. By comparing advances and declines to the volume of trading occurring on those advances and declines it recognizes underling pressures which are not apparent in just a price study. Reading higher than 1.00 is a bearish reading and means declining stocks are receiving more than their share of the volume. Readings under 1.00 is bullish and means advancing shares are receiving more than their fair share of the volume. See Investorpedia for further definition and formula of TRIN.

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