Unweighted index:
· Assigns an equal weight to all constituent securities.
· Equivalent to a portfolio with $1 invested in each security.
· Arithmetic averages or geometric averages can be used.
· Geometric has a downward bias so is always lower than arithmetic.
Arithmetic average = ΣX/ n, Geometric average =(X1…Xn)1/n
where X=(1+HPR)
Price-weighted index:
· Assign a weight proportional to the price of each security.
· Equivalent to a portfolio with one unit of each security.
· Higher priced stocks have a greater influence on the index.
· Price must be adjusted to reflect stock splits, causing a downward bias since successful firms split stocks and lose weight in index.
Price-weighted index value = Sum of Stock prices / Number of stocks after splits
Example of stock splitting:
If the index consists of two securities, A & B,
Initial price A $25 B$100, then
Price weighted index = (25+100)/2 = 62.50
If each security B split into 2 and the price after split price A $25 B$50, then calculate the value of divisor;
(25+50)/divisor= 62.5
=> divisor = 1.2
Then use the determined divisor for computation on the day end price.
Day end price A $30 B60
Price weighted index = (30+60)/divisor = 90/1.2 = 75
Example: DJIA( Dow Jones Industrial Ave) Nikkei
Value-weighted index:
· Assign a weight proportional to the market cap of each security.
· Uses geometric averaging.
· The index ends up controlled by a few large firms.
Value-weighted index value = [Sum of stock prices today x Number of stocks) / (Sum of stock prices in base year x Number of stocks)] x Index value in base year.
= sum of current market values x beginning value / sum of base market values
Example: S&P500, NYSE, NASDAQ, MSCI
Dow Jones (DJIA):
Price-weighted index of 30 stocks traded on NYSE. Criticized for being too limited and representing only large blue chips and downward bias due to price weighting. Studies show that DJIA tracks NSYE well on daily/monthly basis, but not in the long term.
Other Equity indexes:
· S&P 500 - value-weighted index of 500 US stocks
· Nikkei – price-weighted index of the 225 Japanese stocks
· FTSE 100 - value-weighted index of 100 UK stocks
· FT/S&P Actuaries value - weighted indexes of 2,500 international stocks
· MSCI Indexes- value-weighted indexes of over 1,400 stocks
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2 comments:
I found one exception for price weighted Index. Security A is 100 and security B is 25 will provide index 62.5. Now security A increased by 10 percent to 110 with Stock split 1:2 and Security B increase by 20 percent to 30. Without split index Level is 70 with the return of 12%. But if adjust the split with divisor 1.2, Index level comes 70.833 with return of 13.33%.
Kindly suggest
I found one exception for price weighted Index. Security A is 100 and security B is 25 will provide index 62.5. Now security A increased by 10 percent to 110 with Stock split 1:2 and Security B increase by 20 percent to 30. Without split index Level is 70 with the return of 12%. But if adjust the split with divisor 1.2, Index level comes 70.833 with return of 13.33%.
Kindly suggest
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