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Since it is a stock price index weighted by market value, TOPIX indicates the price trend of the entire First Section through changes in market value. Market value equals stock price multiplied by number of shares, and is more commonly referred to as market capitalization. The aggregate market value of the First Section of the TSE is simply the sum of market values for all individual stocks in that section.
Since market value is derived by multiplying stock price by number of shares, it is affected by changes to stock price and number of shares. Such changes are not important to investors focusing on the asset value of their investments. However, for investors focused on portfolio performance during a certain period of time, stock prices are an important consideration. In which case, the effect changes to the number of shares have upon portfolio value must be eliminated using the following mathematical formula.
2. Measuring Performance
If an investor bought 1,000 shares of stock at 1,000 yen per share on a certain day in the past (base date), this would provide 1,000,000 yen of asset value (= market value) on the base date. If the price of that stock today is 3,000 yen, the holding is now worth 3,000,000 yen in market value. In order to express the investment's appreciation in value in the form of an index, a base number for the index on the base date is necessary. Economic indicators frequently fix this base number at 100. The current index is obtained by the following formula:
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current market value / market value on
base date x base number |
Thus, the current index for the portfolio is 300. What happens to this index if an investor now subscribes for 100 shares of the stock through a public offering at 3,000 yen?
The current market value of the portfolio has increased by 300,000 yen to a total of 3,300,000 yen. However, it should be noted that the increment (300,000 yen) is not because of an increase in the stock price, but because of an additional investment. As we have been trying to single out the price change effects upon the portfolio only, the increment does not play any part in the index. So the index remains the same at 300. What changes should be made to the formula above? Current market value is 3,300,000 yen and the index is at 300. Thus, we need to change the market value on the base date as below:
|
3,300,000 yen / new market value on
base date x 100 = 300 |
The new market value on the base date is 1,100,000 yen. For the purpose of this index, the additional investment of 300,000 yen was made on the base date at 100,000 yen. Also, this adjustment was made on the assumption that the additional investment (of 300,000 yen today) was made on the base date at a cost of 100,000 yen and has grown to 300,000 yen in value, due to the rise in the stock price index from 100 to 300. The following equation clarifies the above explanation.
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V1 / V0 =
(V1 + Z) / Y |
This equation shows that the increment of 300,000 yen (Z) is modified by a reciprocal of the index value of the previous day {V0/V1}, i.e. 100/300. For the purpose of establishing the new market value on the base date, the actual increment of 300,000 yen was made at the price of 100,000 yen on the base date.
3. Now about TOPIX
TOPIX is computed in a similar way to the formulae explained above. The fraction includes aggregate market value on the base date (base market value) as denominator and current aggregate market value as numerator. This fraction is multiplied by 100 (base value on base date - January 4, 1968) and reduced to a decimal figure to the nearest one-hundredth. The formula is given below:
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current TOPIX = current market value /
base market value x 100 |
An adjustment in base market value of TOPIX is made as explained above. Hence, any corporate activity which affects current market value requires an adjustment to the base market value. New listings and delistings and other activities given below also impact market value and necessitate adjustments.
(a) new listings
(b) stock transfers between First and Second Sections
(c) delistings
(d) rights offerings
(e) public offerings
(f) private placements
(g) mergers
(h) exercise of stock subscription warrant
(i) conversion of convertible bond or preferred stock into common stock
(j) purchase and retirement of company's own stock
Corporate decisions/activities which do not entail changes in the market value of shares do not result in a basic market value adjustment. Furthermore, no adjustment is made in the case of stock split-ups, split-downs, or decreases in paid-in capital, as the new stock price multiplied by the increased (or decreased) number of shares is theoretically the same as the old stock price multiplied by the old number of shares.
The formula for the adjustment is as follows.
|
new base market value = old base
market value x new market value / old market value |
4. Example of Adjustment
On January 10, 19--, if base value and market value were 30 trillion yen and 300 trillion yen respectively, TOPIX on that day stood at 1,000.00.
|
{300 trillion yen / 30 trillion yen x
100} |
|
new base value = 30 trillion x 300.003
trillion / 300 trillion = 30.0003 trillion |
5. Prices Adopted for Computation of TOPIX
Prices are adopted in the following order when computing TOPIX.
a. Special quote1 at the time of computation
b. Traded price at the time of computation
c. Standard price2
1. Special quote
A special quote is a special bid/ask quote which is adopted in order to maintain the continuity of a trade price, and notify traders of a bid/ask price which exceeds the reasonable range of price variations. The special quote may be renewed every five minutes, or more frequently, with the approval of TSE.
2. Standard price
A standard price is adopted if there is neither a special quote nor traded price on the day TOPIX is computed. Standard prices are given in the following order.
a. Theoretical price of ex-rights to new shares
b. Latest special quote
c. Latest traded price
