1. Market Indices and Market Efficiency

2. Significance of security market indices
Investors gather and analyze vast amounts of information about security markets on a continual basis.
Because this work can be both time consuming and data intensive, investors often use a single measure that consolidates this information and reflects the performance of an entire security market.
Security market indices are simply used to measure.
The performance of various security markets.
Estimate risk.
And evaluate the performance of the investment managers.

4. Security Market Indices
A security market index is used to represent the performance of an asset class, security market, or segment of a market.
They are usually created as portfolios of individual securities, which are referred to as the constituent securities of the index.
An index has a numerical value that is calculated from the market prices (actual when available, or estimated) of its constituent securities at a point in time.
An index return is the percentage change in the index's value over a period of time.

5. Calculate and interpret the value, price return, and total return of an index.
An index return may be calculated using a price index or a return index.
A price index uses only the prices of the constituent securities in the return calculation.
A rate of return that is calculated based on a price index is referred to as a price return.
A return index includes both prices and income from the constituent securities.
A rate of return that is calculated based on a return index is called a total return.
If the assets in an index produce interim cash flows such as dividends or interest payments, the total return will be greater than the price return.

6. Calculate and interpret the value, price return, and total return of an index.
Once returns are calculated for each period, they then can be compounded together to arrive at the return for the measurement period:

7. Rp = Portfolio return during the measurement period
Calculate and interpret the value, price return, and total return of an index.
where:
Rp = Portfolio return during the measurement period
k = Total number of sub periods
Rsk = portfolio return during the sub period k
For example, if the returns for the first two periods were 0.50% and 1 .04%, they would be geometrically linked to produce 1.55%:
Rp = (1 + R51 )(1 + R52) -1 = (1.005)( ) -1 = or %
If the starting index value is 1 00, its value after two periods would be 100 x =

8. Compare the different weighting methods used in index construction.
Weighting schemes for stock indexes include
Price weighting.
Equal weighting
Market capitalization weighting
Float-adjusted market capitalization weighting,
And fundamental weighting.

9. Price weighting
A price-weighted index is simply an arithmetic average of the prices of the securities included in the index.
The divisor of a price-weighted index is adjusted for stock splits and changes in the composition of the index when securities are added or deleted, such that the index value is unaffected by such changes.

10. Price weighting

13. Eop weight= value at end / Total value e.g 55/105

15. Price weighting
The advantage of a price-weighted index is that its computation is simple.
One disadvantage is that a given percentage change in the price of a higher priced stock has a greater impact on the index's value than does an equal percentage change in the price of a lower priced stock.
Put another way, higher priced stocks have more weight in the calculation of a price-weighted index.
Additionally, a stock split in any one security causes arbitrary changes in the weights of all the constituents’ securities.

16. Equal Weighting
Another simple index weighting method is equal weighting.
This method assigns an equal weight to each constituent security at inception.
The weights are calculated as:

17. No of shares in an index = value of each security/BOP price e
No of shares in an index = value of each security/BOP price e.g 2000/50
Bop=2000/10000=20% Eop=2200/11040=19.93

18. Equal Weighting
To construct an equal-weighted index from the five securities in Exhibit 1, the index provider allocates one-fifth (20 percent) of the value of the index (at the beginning of the period) to each security.
Dividing the value allocated to each security by each security’s individual share price determines the number of shares of each security to include in the index.
Unlike a price-weighted index, where the weights are arbitrarily determined by the market prices, the weights in an equal-weighted index are arbitrarily assigned by the index provider.

19. Price weighting
Exhibit 3 illustrates the values, weights, and single- period returns following inception of an equal- weighted index with the same constituent securities as those in Exhibit 1.
This example assumes a beginning index portfolio value of 10,000 (i.e., an investment of 2,000 in each security). To set the initial value of the index to 1,000, the divisor is set to 10 (10,000 ÷ 10 = 1,000).
Exhibits 1 and 3 demonstrate how different weighting methods result in different returns. The 10.4 percent price return of the equal-weighted index shown in Exhibit 3 differs significantly from the 3.45 percent price return of the price-weighted index in Exhibit 1.

20. Price weighting
Like price weighting, the primary advantage of equal weighting is its simplicity.
Equal weighting, however, has a number of disadvantages.
First, securities that constitute the largest fraction of the target market value are under represented, and securities that constitute a small fraction of the target market value are overrepresented.
Second, after the index is constructed and the prices of constituent securities change, the index is no longer equally weighted.
Therefore, maintaining equal weights requires frequent adjustments (rebalancing) to the index.

21. Market Capitalization Weighting
In market-capitalization weighting, or value weighting, the weight on each constituent security is determined by dividing its market capitalization by the total market capitalization (the sum of the market capitalization) of all the securities in the index.
Market capitalization or value is calculated by multiplying the number of shares outstanding by the market price per share.
The market-capitalization weight of security i is:

22. Market Capitalization Weighting
where
wi = fraction of the portfolio that is allocated to security i or weight of security i
Qi = number of shares outstanding of security i
Pi = share price of security i
N = number of securities in the index

23. Market Capitalization Weighting
Exhibit 4 illustrates the values, weights, and single-period returns following
inception of a market-capitalization-weighted index for the same five-security market.
Security A, with 3,000 shares outstanding and a price of 50 per share, has a market capitalization of 150,000 or percent (150,000/570,500) of the entire index portfolio.
The resulting index weights in the exhibit reflect the relative value of each security as measured by its market capitalization

25. Float adjusted Market capitalization weighting
In float-Aadjusted market-A capitalization weighting, the weight on each constituent security is determined by adjusting its market capitalization for its market float.
Typically, market float is the number of shares of the constituent security that are available to the investing public.
For companies that are closely held, only a portion of the shares outstanding are available to the investing public (the rest are held by a small group of controlling investors).

26. Float adjusted Market capitalization weighting
In addition to excluding shares held by controlling shareholders, most float-adjusted market capitalization-weighted indices also exclude shares held by other corporations and governments.
Some providers of indices that are designed to represent the investment opportunities of global investors further reduce the number of shares included in the index by excluding shares that are not available to foreigner investors.
The index providers may refer to these indices as “free-float-adjusted market-capitalization- weighted indices.”

28. Float adjusted Market capitalization weighting
Float-adjusted market-capitalization-weighted indices reflect the shares available for public trading by multiplying the market price per share by the number of shares available to the investing public (i.e., the float-adjusted market capitalization) rather than the total number of shares outstanding (total market capitalization).
Currently, most market-capitalization-weighted indices are float adjusted.
Therefore, unless otherwise indicated, for the remainder of this reading, “market-capitalization” weighting refers to float-adjusted market capitalization weighting.

29. Fundamental Weighting
Fundamental weighting attempts to address the disadvantages of market-capitalization weighting by using measures of a company’s size that are independent of its security price to determine the weight on each constituent security.
These measures include book value, cash flow, revenues, earnings, dividends, and number of employees.
Some fundamental indices use a single measure, such as total dividends, to weight the constituent securities, whereas others combine the weights from several measures to form a composite value that is used for weighting

30. Fundamental Weighting
Relative to a market-capitalization-weighted index, a fundamental index with weights based on such an item as earnings will result in greater weights on constituent securities with earnings yields (earnings divided by price) that are higher than the earnings yield of the overall market- weighted portfolio.
Similarly, stocks with earnings yields less than the yield on the overall market-weighted portfolio will have lower weights.

31. fundamental Weighting
For example, suppose there are two stocks in an index. Stock A has a market capitalization of €200 million, Stock B has a market capitalization of €800 million, and their aggregate market capitalization is €1 billion (€1,000 million).
Both companies have earnings of €20 million and aggregate earnings of €40 million.
Thus, Stock A has an earnings yield of 10 percent (20/200) and Stock B has an earnings yield of 2.5 percent (20/800).

32. fundamental Weighting
The earnings weight of Stock A is 50 percent (20/40), which is higher than its market- capitalization weight of 20 percent (200/1,000).
The earnings weight of Stock B is 50 percent (20/40), which is less than its market- capitalization weight of 80 percent (800/1,000). Relative to the market-cap-weighted index, the earnings-weighted index over-weights the high- yield Stock A and under-weights the low-yield Stock B.

33. Market Efficiency

34. Market Efficiency
An information ally efficient capital market is one in which the current price of a security fully, quickly, and rationally reflects all available information about that security.
This is really a statistical concept. An academic might say, "Given all available information, current securities prices are unbiased estimates of their values, so that the expected return on any security is just the equilibrium return necessary to compensate investors for the risk (uncertainty) regarding its future cash flows."
This concept is often put more intuitively as, "You can't beat the market."

35. Market Efficiency
In a perfectly efficient market, investors should use a passive investment strategy (i.e., buying a broad market index of stocks and holding it) because active investment strategies will underperform due to transactions costs and management fees.
However, to the extent that market prices are inefficient, active investment strategies can generate positive risk-adjusted returns.

36. Market Efficiency
One method of measuring a market's efficiency is to determine the time it takes for trading activity to cause information to be reflected in security prices (i.e., the lag from the time information is disseminated to the time prices reflect the value implications of that information).
In some very efficient markets, such as foreign currency markets, this lag can be as short as a minute.
If there is a significant lag, informed traders can use the information to potentially generate positive risk-adjusted returns.

37. Market Efficiency
Note that market prices should not be affected by the release of information that is well anticipated. Only new information (information that is unexpected and changes expectations) should move prices.
The announcement that a firm's earnings were up 45% over the last quarter may be good news if the expected increase was 20%.
On the otherhand, this may be bad news if a 70% increase was anticipated or no news at all if market participants correctly anticipated quarterly earnings.

38. Forms of market efficiency
Professor Eugene Fama originally developed the concept of market efficiency and identified three forms of market efficiency.
The difference among them is that each is based on a different set of information.
Weak-form market efficiency.
The weak form o f the efficient markets hypothesis (EMH) states that current security prices fully reflect all currently available security market data.
Thus, past price and volume (market) information will have no predictive power about the future direction of security prices because price changes
will be independent from one period to the next

39. Forms of market efficiency
In a weak-form efficient market, an investor cannot achieve positive risk-adjusted returns on average by using technical analysis.
Semi-strong form market efficiency.
The semi-strong form of the EMH holds that security prices rapidly adjust without bias to the arrival of all new public information.
As such, current security prices fully reflect all publicly available information.
The semi-strong form says security prices include all past security market information and nonmarket information available to the public.

40. Forms of market efficiency
The implication is that an investor cannot achieve positive risk-adjusted returns on average by using fundamental analysis.
Strong-form market efficiency.
The strong form of the EMH states that security prices fully reflect all information from both public and private sources.
The strong form includes all types of information: past security market information, public, and private (inside) information.
This means that no group of investors has monopolistic access to information relevant to the formation of prices, and none should be able to consistently achieve positive abnormal returns.