variance basic

The discussion below may appear unrelated to stock markets, It helps you relate better to the term ‘Volatility’.

Consider 2 batsmen and the number of runs they have scored over 6 consecutive  IPL  matches –

Match	RAINA	RAYADU
1	20	45
2	23	13
3	21	18
4	24	12
5	19	26
6	23	19

You are the captain of the team, and you need to choose either RAINA or RAYADU for the 7^th match. The batsman should be dependable – in the sense that the batsman you choose should be in a position to score at least 20 runs. Whom would you choose?  that people approach this problem in one of the two ways –

1.     Calculate the total score (also called ‘Sigma’) of both the batsman – pick the batsman with the highest score for next game. Or..

2.     Calculate the average (also called ‘Mean’) number of scores per game – pick the batsman with better average.

Let us calculate the same and see what numbers we get –

o    RAINA’s Sigma = 20 + 23 + 21 + 24 + 19 + 23 = 130

o    RAYADU’s Sigma = 45 + 13 + 18 + 12 + 26 + 19 = 133

So based on the sigma you are likely to select RAYADU. Let us calculate the mean or average for both the players and figure out who stands better –

o    RAINA = 130/6 = 21.67

o    RAYADU = 133/6 = 22.16

So it seems from both the mean and sigma perspective, RAYADU deserves to be selected. But let us not conclude that yet. Remember the idea is to select a player who can score at least 20 runs and with the information that we have now (mean and sigma) there is no way we can conclude who can score at least 20 runs. Therefore, let’s do some further investigation.

To begin with, for each match played we will calculate the deviation from the mean. For example, we know RAINA’s mean is 21.67 and in his first match RAINA scored 20 runs. Therefore deviation from mean form the 1st match is 20 – 21.67 = – 1.67. In other words, he scored 1.67 runs lesser than his average score. For the 2^nd match it was 23 – 21.67 = +1.33, meaning he scored 1.33 runs more than his average score.

The middle black line represents the average score of RAINA, and the double arrowed vertical line represents the the deviation from mean, for each of the match played. We will now go ahead and calculate another variable called ‘Variance’.

Variance is simply the ‘sum of the squares of the deviation divided by the total number of observations’. This may sound scary, but its not. We know the total number of observations in this case happens to be equivalent to the total number of matches played, hence 6.

So variance can be calculated as –

Variance = [(-1.67) ^2 + (1.33) ^2 + (-0.67) ^2 + (+2.33) ^2 + (-2.67) ^2 + (1.33) ^2] / 6
= 19.33 / 6
= 3.22

Further we will define another variable called ‘Standard Deviation’ (SD) which is calculated as –

std deviation = √ variance 

So standard deviation for RAINA is –
= SQRT (3.22)
= 1.79

Likewise RAYADU’s standard deviation works out to be 11.18.

Lets stack up all the numbers (or statistics) here –

Statistics	RAINA	RAYADU
Sigma	130	133
Mean	21.6	22.16
SD	1.79	11.18

 

We know what ‘Mean’ and ‘Sigma’ signifies, but what about the SD? Standard Deviation simply generalizes and represents the deviation from the average.

Here is the text book definition of SD “In statistics, the standard deviation (SD, also represented by the Greek letter sigma, σ) is a measure that is used to quantify the amount of variation or dispersion of a set of data values”.

Please don’t get confused between the two sigma’s – the total is also called sigma represented by the Greek symbol ∑ and standard deviation is also sometimes referred to as sigma represented by the Greek symbol σ.

One way to use SD is to make a projection on how many runs RAINA and RAYADU are likely to score in the next match. To get this projected score, you simply need to add and subtract the SD from their average.

Player	Lower Estimate	Upper Estimate
RAINA	21.6 – 1.79 = 19.81	21.6 + 1.79 = 23.39
RAYADU	22.16 – 11.18 = 10.98	22.16 + 11.18 = 33.34

These numbers suggest that in the upcoming 7^th match RAINA is likely to get a score anywhere in between 19.81 and 23.39 while RAYADU stands to score anywhere between 10.98 and 33.34. Because RAYADU has a wide range, it is difficult to figure out if he is going to score at least 20 runs.  He can either score 10 or 34 or anything in between.

However RAINA seems to be more consistent. His range is smaller, which means he will neither be a big hitter nor a lousy player. He is expected to be a consistent and is likely to score anywhere between 19 and 23. In other words – selecting RAYADU over RAINA for the 7^th match can be risky.

Going back to our original question, which player do you think is more likely to score at least 20 runs? By now, the answer must be clear; it has to be RAINA. RAINA is consistent and less risky compared to RAYADU.

So in principal, we assessed the riskiness of these players by using “Standard Deviation”. Hence ‘Standard Deviation’ must represent ‘Risk’. In the stock market world, we define ‘Volatility’ as the riskiness of the stock or an index. Volatility is a % number as measured by standard deviation.

Going by the above definition,  if Infosys and TCS have volatility of 25% and 45% respectively, then clearly Infosys has less risky price movements when compared to TCS.

 

 

STOCK FUTURES - PRICING

We will calculate the futures price of RELIANCE INDUSTRIES through the pricing formula and compare it with the current futures price in the market. 

The spot price of RELIANCE is 2324 as of 9/8/2020(assumption) 

 The stock has not declared any dividend in the current August series. Sept series expiry is on 24th i.e last 

Thursday of the month. There are 16 days for expiry : 24/9 (taking both the days into consideration) 

What should RELIANCE INDUSTRIES’s current month futures contract be priced at? 

HERE assume In the month of August 2020  AS  on 9/8/2020

 FUTURES PRICE =(2324*(1+0.0338*((22/365))-0))

 FUTURE PRICE = 2328.73 

 Put the above formula in Excel sheet You other than the exact 365 days. 

Therefore a more generic formula would be – Futures Price = Spot price * [1+ rf*(x/365)]– d 

Where, x = number of days to expiry.

 One can take the RBI’s 91 day Treasury bill as a proxy for the short term risk-free rate.

SENSEX AND NIFTY 50 INDEX CALUCLATIONS

 Sensex Meaning - Know What is Sensex & How is it Calculated

For an investor it is very important to know the basic terminologies like Sensex meaning, what is Sensex, how the calculation are done.

Therefore, let us learn and understand about it here.

The term Sensex was named by a stock market analyst Mr. Deepak Mohoni, the word is a portmanteau of Sensitive and Index. The Sensex is primarily an index which reflects the Bombay Stock Exchange (BSE) which got established in 1875. Till Jan1, 1986 the stock exchange did not have any official index. This was the time when Sensex was opted for gauging the performance of the Indian market. The Sensex comprises of 30 prominent stocks which are derived from sectors and are traded actively in the exchange market. Sensex truly reflects the Indian stock market movement. If the Sensex value increases it means that there is a general increase in the prices of shares whereas, if the Sensex decreases it means there is a general decrease in the price of shares.

You can identify the booms and busts going in the stock market through S&P BSE Sensex. From Feb 19, 2013, BSE and S&P Dow Jones Indices entered into an alliance to calculate Sensex. Nifty is the other index calculated in India for the National Stock Exchange.

Sensex comprises of the 30 largest and most actively traded stocks on BSE, providing a gauge of India’s economy. The Sensex is one of the oldest stock indexes in India. Sensex is used to observe the overall growth, development of particular industries, ups and downs of the Indian economy by the investors.

Calculation Methodology for Sensex

Historically Sensex used the weighted market capitalization methodology, but from September 1, 2003, it shifted to Free Float Market Capitalization methodology. All the major indices in the world use the same methodology. The performance of the 30 selected key stocks directly reflects the level of the index.

Free-Float Market Capitalization = Market Capitalization * Free Float Factor

Now let’s see what is referred to as the Free Float Factor?

Free Float is referred to as that % of the total shares issued by the company that is readily available for trading in the market. It excludes the shares that are held by the promoters, government, etc.

To understand better let’s look at an example: If the company has 100 shares, in which 30 are held by the government or the promoters and the remaining 70 are available for trading to general public then, those 70 shares are the free-floating shares and thus the free float factor will be 70%. Whereas the word market capitalization represents the valuation of the company. Market capitalization is determined by multiplying the price of a stock with the number of shares issued by that company.

Hope till now you have learnt about what is Sensex meaning, its methodology; now let’s look how Sensex is calculated. The above two terminologies play a major role while calculating Sensex.

How Sensex is calculated?

·         The Sensex comprises of the 30 stocks which are selected according to the criteria set.

·         The Market Capitalizations of all the 30 companies are determined.

·         The Free Float Market Capitalization of all the 30 companies is determined.

·         Of all the 30 companies the Free Float Market Capitalization is summed up to get a total of all the Free Float Market Capitalization.

·         As the formula of Sensex= (total free float market capitalization/ Base market capitalization) * Base index value.

·         The base year to calculate Sensex is 1978-79, the base value is static but it has to be changed. According to BSE Rs. 2501.24 crore is to be used as the base market capitalization.

·         The base index value is 100.

Therefore,

Sensex= free float market capitalization of 30 selected companies /25041.24 crores* 100

(The free float market capitalization of 30 selected companies is added and which get divided by 2501.24 crores and multiplied by 100.)

How is NIFTY for Share Market Calculated?

The NIFTY share index is managed by a team of professionals at the NSE Indices Limited. It formed an Index Advisory Committee that offers its expertise and guidance on large-scale issues pertinent to equity indices.

NIFTY 50 indices are computed based on a float-adjusted and market capitalisation weighted method. In this method, the level of index demonstrates the aggregate market value of stocks present in the index in a specific base period. Such a base period for a NIFTY 50 index is 3rd November 1995 where the base value of the index is considered 1000 and its base capital stands at Rs. 2.06 Trillion.

The formula for calculating price index is listed below –

Index value = Current MV or market value / (Base Market Capital * 1000)

The methodology involved in the calculation of indices also considers changes in corporate actions, which for instance comprise of rights issuance, stock splits, etc.

The NIFTY share market index is standard against which all equity markets in India are measured. Therefore, NSE conducts regular index maintenance to ensure that it remains stable and persists as the benchmark in the Indian stock market context.

 

 

 

Monopolistic Competition

The Monopolistic Competition, there are a large number of firms that produce differentiated products which are close substitutes for each other. In other words, large sellers selling the products that are similar, but not identical and compete with each other on other factors besides price.

 Features of Monopolistic Competition

1.       Product Differentiation: This is one of the major features of the firms operating under the monopolistic competition, that produces the product which is not identical but is slightly different from each other. The products being slightly different from each other remain close substitutes of each other and hence cannot be priced very differently from each other.

2.       Large number of firms: A large number of firms operate under the monopolistic competition, and there is a stiff competition between the existing firms. Unlike the perfect competition, the firms produce the differentiated products which are substitutes for each other, thus make the competition among the firms a real and a tough one.

3.       Free Entry and Exit: With an intense competition among the firms, the entity incurring the loss can move out of the industry at any time it wants. Similarly, the new firms can enter into the industry freely, provided it comes up with the unique feature and different variety of products to out stand in the market and meet with the competition already existing in the industry.

4.       Some control over price: Since, the products are close substitutes for each other, if a firm lowers the price of its product, then the customers of other products will switch over to it. Conversely, with the increase in the price of the product, it will lose its customers to others. Thus, under the monopolistic competition, an individual firm is not a price taker but has some influence over the price of its product.

5.       Heavy expenditure on Advertisement and other Selling Costs: Under the monopolistic competition, the firms incur a huge cost on advertisements and other selling costs to promote the sale of their products. Since the products are different and are close substitutes for each other; the firms need to undertake the promotional activities to capture a larger market share.

6.       Product Variation: Under the monopolistic competition, there is a variation in the products offered by several firms. To meet the needs of the customers, each firm tries to adjust its product accordingly. The changes could be in the form of new design, better quality, new packages or container, better materials, etc. Thus, the amount of product a firm is selling in the market depends on the uniqueness of its product and the extent to which it differs from the other products.

The monopolistic competition is also called as imperfect competition because this market structure lies between the pure monopoly and the pure competition.

Oligopoly Market

Definition: The Oligopoly Market characterized by few sellers, selling the homogeneous or differentiated products. In other words, the Oligopoly market structure lies between the pure monopoly and monopolistic competition, where few sellers dominate the market and have control over the price of the product.

 Under the Oligopoly market, a firm either produces:

§  Homogeneous product: The firms producing the homogeneous products are called as Pure or Perfect Oligopoly. It is found in the producers of industrial products such as aluminum, copper, steel, zinc, iron, etc.

§  Heterogeneous Product: The firms producing the heterogeneous products are called as Imperfect or Differentiated Oligopoly. Such type of Oligopoly is found in the producers of consumer goods such as automobiles, soaps, detergents, television, refrigerators, etc.

Types of Oligopoly Market

Features of Oligopoly Market

1.       Few Sellers: Under the Oligopoly market, the sellers are few, and the customers are many. Few firms dominating the market enjoys a considerable control over the price of the product.

2.       Interdependence: it is one of the most important features of an Oligopoly market, wherein, the seller has to be cautious with respect to any action taken by the competing firms. Since there are few sellers in the market, if any firm makes the change in the price or promotional scheme, all other firms in the industry have to comply with it, to remain in the competition.

Thus, every firm remains alert to the actions of others and plan their counterattack beforehand, to escape the turmoil. Hence, there is a complete interdependence among the sellers with respect to their price-output policies.

3.       Advertising: Under Oligopoly market, every firm advertises their products on a frequent basis, with the intention to reach more and more customers and increase their customer base.This are due to the advertising that makes the competition intense.

If any firm does a lot of advertisement while the other remained silent, then he will observe that his customers are going to that firm who is continuously promoting its product. Thus, in order to be in the race, each firm spends lots of money on advertisement activities.

4.       Competition: It is genuine that with a few players in the market, there will be an intense competition among the sellers. Any move taken by the firm will have a considerable impact on its rivals. Thus, every seller keeps an eye over its rival and be ready with the counterattack.

5.       Entry and Exit Barriers: The firms can easily exit the industry whenever it wants, but has to face certain barriers to entering into it. These barriers could be Government license, Patent, large firm’s economies of scale, high capital requirement, complex technology, etc. Also, sometimes the government regulations favor the existing large firms, thereby acting as a barrier for the new entrants.

6.       Lack of Uniformity: There is a lack of uniformity among the firms in terms of their size, some are big, and some are small.

Since there are less number of firms, any action taken by one firm has a considerable effect on the other. Thus, every firm must keep a close eye on its counterpart and plan the promotional activities accordingly.

Duopoly

A duopoly is a market structure dominated by two firms.

A pure duopoly is a market where there are just two firms. But, in reality, most duopolies are markets where the two biggest firms control over 70% of the market share.

Characteristics of duopoly

• Strong barriers to entry in the market, e.g. brand loyalty (Coca-cola and Pepsi).
• Significant economies of scale which suit a small number of firms (e.g. Airbus and Boeing – airline manufacture)

 

I

• Firms may compete on price or they could seek to collude – either tactically or formal agreement. This will depend on the nature of the industry. For example, Coca-cola and Pepsi compete on brand image and spend a high share of revenue on advertising. Price competition is relatively muted. The creation of Airbus in 1970 helped to make airline manufacture more competitive, airlines could now choose a different company to Boeing forcing more price competition and greater choice of goods.
• Duopolies are usually quite profitable industries and are likely to have an outcome similar to monopoly – with price above marginal cost and a degree of allocative inefficiency. The drawbacks of higher prices may be offset by economies of scale and lower average costs.