# VIDYA

## Introduction

Although the credit of introducing variable length moving average goes to Tushar S. Chande yet he wasn’t the first to introduce the idea of using variable average. George R. Arrignton, formulated a Variable Simple Moving Average dependent on Standard Deviation in June, 1991 edition of the Magazine “Technical Analysis of Stocks & Commodities”.

Tushar S. Chande later developed the Volatility Index Dynamic Average Indicator for Technical Analysis and published in March, 1992 Edition of the Magazine “Technical Analysis of Stock & Commodities”. This method was used for determining Dynamic Exponential Moving Average commonly known as “DEMA”. The ever dynamic period of changing prices demanded a different method of averaging. Chande introduced Volatility Index Dynamic Average to enhance the predictability of Technical Indicators because it used variable period of averaging rather than a fixed number of days like 9 or 14 days used in most other indicators. The basic difference between VLMA & VIDYA was the spread of Smoothing Time Period. VIDYA allowed much larger spread for the sake of smoothing.

The length of period in VIDYA depends on the Market Volatility. A number of options can be used to determine market volatility like Chande Momentum Oscillator. CMO (Chande Momentum Oscillator) requires two inputs to run. The first thing to determine CMO is “Period of VIDYA”. Secondly, CMO requires “Momentum Volatility Length”. VIDYA is directly affected by the short-term volatility. Due to the use of CMO, VIDYA speeds up as the short-term volatility speeds up and reduces speed when volatility loses its speed. Ultimately, 9 periods value of abs CMO (Absolute Chande Momentum Oscillator) determines Volatility Index.

## Calculation

In March 1992, When Tushar S. Chande presented the idea of VIDYA for the very first time, he used Standard Deviation to determine Volatility Index. Later on, Chande developed the Chande Momentum Oscillator. In 1995, he used value of CMO as Volatility Index.

The Formula for Determining VIDYA using CMO is as under:

Smoothing Constant = 2/N+1

Where,
N= Number of Days,
Volatility Index = CMO (Price).

Volatility Index Dynamic Average = Smoothing Constant * Volatility Index * Price + (1-Smoothing Constant * Volatility Index) * Price [-1]

Chande Momentum Oscillator is usually determined for Nine Periods. In order to Determine Exponential Moving Average, the formula is:

Exponential Moving Average [TODAY] = Alpha * Closing Price [TODAY] + (1-Alpha) * Exponential Moving Average [PREVIOUS]

Standard Exponential Moving Average can be calculated by the formula mentioned below:

Exponential Moving Average (i) = Price (i) * F + EMA (i-1) * (1-F)

Where,
F = 2/ (EMA Averaging Period +1) – Smoothing Factor,
Price (i) = Current Price,
EMA (i-1) = Previous Value of EMA.

In order to determine the Value of VIDYA using Chande Momentum Oscillator, use:

VIDYA (i) = Price (i) * F * ABS (CMO (i)) + VIDYA (i-1) * (1 – F * ABS(CMO (i)))

Where,
ABS (CMO (i)) = Absolute Value of Chande Momentum Oscillator,
VIDYA (i-1) = Previous value of VIDYA.

In this formula the value of Chande Momentum Oscillator is determined using this formula:

CMO (i) = (Up Sum (i) – Down Sum (i)) / (Up Sum (i) + Down Sum (i))

Where,
Up Sum (i) = Sum of Positive Price Increments during the Current Period,
Down Sum (i) = Sum of Negative Price Increments during the Current Period.

Note:

The Value of Alpha/Smoothing Constant is determined by the formula above. Alpha can also be determined by the formula:

Alpha = 0.2 * Volatility of Last 9 Days/Volatility of Last 30 Days

## Specifications

VIDYA is normally not used for trading purposes. The major output of VIDYA is its upper and lower borders which give traders an indication of the Upper Band ad Lower Band that are N% above or below VIDYA. In order to interpret trade signals using this indicator, the method followed is quite similar to the one used in Bollinger Bands. VIDYA is characterized of altering its smoothing period according to the Volatility Index and has no upper or lower limit of Smoothing Period either.

The VIDYA Smoothing Period can go immeasurably high when Volatility Index nears to 0. At this point, the Moving Average will hold a constant value and will be close to Previous Value of VIDYA. The Smoothing Period becomes equal to the value of User Choice of N (Number of Days) only when the Volatility Index is equal to 1. Evidence is provided in the graphical picture provided below with N on the Y Axis and Volatility Index on the X Axis.

Similarly when the Volatility Index rises above the value of 1, Smoothing Period immediately drops below the Number of Day (N) selected by the user. Smoothing Period will be equal to 1 when the Value of Volatility Index is equal to N/2 + 0.5. This means that the price will be equal to Volatility Index. So, one should make sure that the value of Volatility Index is controlled under N/2 + 0.5.

Here a question arises that which Volatility Index is better to use? In order to answer this question, a number of considerations must be taken into account. Chande originally used the Standard Deviation as his Volatility Index but later on in 1995, introduced his own Chande Momentum Oscillator.

The Basic Superiority of CMO over Standard Deviation is that it can range from -100 to 100 which is divided by 100 to obtain Absolute Value. The outcome of this division is quite similar to the results of Efficiency Ratio. That’s why CMO is the most commonly used Volatility Index. Strength of Trend can be determined easily with the help of CMO. If the readings which may range from 0 to N/2 + 0.5 are on the higher side then there is a strong trend indication.

## Role of Co-Efficient of Determination (r2)

The main role of Co-Efficient of Determination is to determine the strength of a Trend. It is a lagging indicator that acts as a confirming indicator. The value of r2 is dependent upon on the Number of Days (N) taken into consideration. For a fixed number of days there is a suggested critical value like for 10, 20 and 30 days the critical values are 0.4, 0.2 and 0.1 respectively. Whenever the values of r2 are greater the suggested critical values for a given number of days, the trend is said to be statistically significant. In order to determine the direction of a trend, the slope of regression is used. This can help anyone put positions according to their wish.

It is better to deploy both slope and r2 when making any trading decision. Reason behind it is that, even with a strong trend if the slope is small it may not attract as much of the interest of a Short-Term Trader as it should normally with a strong trend. Similarly, a weak trend with a reasonable slope indicates that the trend is about to change. So, we can conclude that when the values of slope and r2 are close to 0, it signifies that the trend is weak and vice versa.

In order to benefit from a significant trend, first of all determine the position of slope i.e. whether it is positive or negative. A Long Position is favorable when the Slope is extremely positive. On the other hand, if the Slope is extremely negative, one should open a short position. After making a peak (either positive or negative) the Slope will head towards the value of 0. This point indicates profit collection, Stop tightening and taking an anti-trend position. To conclude, there are a variety of strategies available while using Regression Analysis.

1. The Majority of Moving Averages deployed fixed number of days to determine the Volatility Index. Unlike other Moving Averages, VIDYA adjusts its length according to the Market Volatility.
2. VIDYA speeds up when the prices are moving rapidly and slows down when the prices are showing slight or marginal difference from their previous positions.
3. VIDYA allows its users to adjust instruct their trading style while determining future trends. The Range of VIDYA is highly dynamic, this allows the traders to adjust the number of days to be included and which days to be excluded.
4. The Change Momentum Oscillator can be utilized along with VIDYA to form an active average specifically designed to determine market momentum.
5. Co-Efficient of Determination helps in determining the Overbought and Oversold Conditions. The Slope can also be used for the same purpose. Thus, the direction of next trading day can be determined well in advance to develop an action plan for your future trading decisions.
6. VIDYA helps its users plan for more accurate contingencies. One can initiate new positions, set stops, or close old ones on the basis of a range of outcomes chalked out by the trading plan.
7. The Responsiveness of VIDYA is far better then other Indicators during times of High Volatility and Price Movements.

1. VIDYA doesn’t predict precise change from the actual. The Purpose of VIDYA is to give an estimated trend direction on the basis of past days.
2. A disadvantage or rather threat of using VIDYA is that in majority of the cases, the majority of technical indicator including VIDAY have failed to predict future trends in some specific markets. The use of VIDYA in such markets is not only useless but it can be costly as well.
3. Using VIDYA or any other moving average may not be as much fruitful as a weighted average would be. The only evidence for it is that it considers more situations then a single moving average.
4. VIDYA doesn’t consider any scenario other then the one provided to it within the Number of days in consideration.