We consider introducing a market >Remind me, please, of the difference.
Okay. We start with a bunch of money, namely $A, and consider an N-stock
- We divide our money into N equal piles and buy
of each stock in the*equal dollar amounts***Index**. Now A/N dollars divided by the stock price, P_{k}, gives (for the k^{th}stock purchase) (1) ....**S**_{k}= A/(NP_{k})**EQUAL**weighted shares of each stock in the**Index**(where the Price, P_{k}, varies from stock to stock, of course, so we buy a variable number of shares). We now have equal dollars invested in each stock. - A different tack is to buy, with our $A, a number of shares which is proportional to the total number of outstanding
shares of each stock in the
**Index**. That is, if stock #1 has n_{1}outstanding shares and stock #2 has n_{2}outstanding shares*etc.*then we buy C n_{1}shares of stock #1 and C n_{2}shares of stock #2*etc.*where "C" is a constant (which we'll determine momentarily). Our total cost is thenC n so the constant can be determined as:_{1}P_{1}+C n_{2}P_{2}+...+C n_{N}P_{N}= $A and the number of shares of each stock is:**C = A/Σn**_{i}P_{i} (2) .....**S**_{k}= An_{k}/Σn_{i}P_{i}**MARKET CAP**weighted, like the**TSE**or**S&P** where the number of shares, n_{k}, varies from stock to stock, of course, so we buy a variable number of shares.
For sanitary reasons, we'll write simply
ΣnP to mean
n >Wait! You call C a constant, yet it depends upon the stock prices which change ....
C nwhere, for example, C n _{1}P_{1} is invested in stock #1 and
n_{1}P_{1} is the market cap of that stock, and
C n_{2}P_{2} is invested in stock #2 and ..
>... and you rebalance the >Okay, I get it. Please continue. For scenario (1), the EQUAL-WEIGHT Index, our Index
begins with shares in each of N stocks according to:
Stock-Shares:where P _{1}(0), P_{2}(0), ..., P_{N}(0), denote the N stock
prices at time = 0.
If the prices of the N stocks change from month to month
(meaning time = Stock-Value:and the total Index-Value changes to: Index-Value:
The GainFactor (LossFactor?) in our
See? It's the Index.
>zzzZZZ
Our Stock-Shares:At the next time period, time = 1, we have: Stock-Value:and the total Index-Value changes to: Index-Value:
The GainFactor (LossFactor?) in our
It's the Gain (or Loss) in the Index.
>Don't you have a
>Okay, that's for something volatile. How about the S&P 500? >Try some DOW stocks.
>Fictitious, eh? You're assuming no change in number of shares.
Note the sensitivity of an If the price of stock#1 changes by ΔP_{1} it generates a change
in the Index according to the number of shares of that stock, namely:
Note (again!) that S_{1}P
is the fraction of the _{1}/VIndex represented by stock#1 and
a fractional change ΔP
in the price of stock#1 produces this fractional change in the _{1}/P_{1}Index:
ΔV/V, as given above.
- For an
**EQUAL WEIGHT****Index**each stock is equally represented in the**Index**. A 1% change in the price of stock #1 has exactly the same effect on the**Index**as a 1% change in stock#2 or stock#3*etc.*. The little companies have just as much weight as the big guys. - For a
**MARKET-CAP WEIGHTED****Index**the stocks are represented in proportion to their market capitalization. The largest companies produce the most dramatic changes in the**Index**(like the S&P or TSE). If the changes in stock prices of the largest companies are gradual (lethargic?), the**Index**will tend to change gradually.
Intel, for
example, has a small stock price so has little influence on the DOW ... in spite of the
fact that it's one of the largest companies on the DOW.
>So? What's your conclusion? >So? What's your conclusion? >zzzZZZ |