Analysing the Stock Market Using A Mathmatical ModelBy Ya-Gui Wei
I have warned about the danger of the current stock market (1, 2) and its imminent collapse (3, 4) since last December. Now the market collapse is in full swing (5, 6). Today's column should ballance things out a little and put it all in perspective.
[I do like to ballance things out. For example, a week after I predicted that Qualcomm would rise to 600 in a month -- it did finally rise to 800 in 36 days -- I began writing about the fraudulent nature of the market (1, 2). But after that I no longer feel comfortable recommending momentum stocks in this column.]
Simply put, the current phase of the market downturn, while ugly, and still not finished, is not going to go all the way down. Isn't that comforting?
A Model Stock MarketWhy does the market go up and down? It's because money flows in and out of the pool of funds that investors use to trade stocks. When this pool increases, the market goes up. When this pool of money declines, the market goes down. But by how much? (Some will say that the stock market goes up and down because of the underlying companies' businesses go up and down, but recent market history has proven that to be mostly fiction. The market is capable of detaching itself from reality by large measures.)
As we are about to see, every 1 dollar of change in the trading fund pool will be magnified into hundreds, if not thousands of dollars in the overall market capitalization.
Let's device a model of the market by hypothesing a market that is the simplest possible: a market that has only one stock, and two traders (it takes 2 to trade), and no fructuation in trading volume. Suppose the stock has ten million shares outstanding, with each trader holding 5 million shares. Each day, 10,000 shares change hands between the traders.
The first day, Trader A bought 10,000 shares from Trader B for $10 a share. $100,000 of funds is transferred from Trader A to Trader B, and this amount shall constitute the initial size of the trading fund pool. Suppose the next day, the value of the stock somehow rises, and Trader B decided to buy 10,000 shares back for $11/share. Now the amount of money he had in his trading account is not going to be enough, and he will need to put up an additional $10,000 to complete the trade.
Now between the first day and the second day, the size of the trading fund pool increased from $100,000 to $110,000, and the total market capitalization increased from $100,000,000 to $110,000,000. We are seeing a 1000-fold magnification in the additional money Trader B put up. How could that be? We put up $10,000 and got $10,000,000 in return. Where did the extra $9,990,000 come from?
Nowhere. The answer is the money comes from nowhere, except through magical imagination by the savvy accounting scheme that I have been denouncing -- when even a single share of the stock changes hand at $11, our accounting scheme assumes that every share of the stock is also instantly worth $11. (The extra money is really not there, but most people actually assume they are, and it is the way real world markets operate, so we'll have to work with it.) Through this accounting scheme, every dollar invested in our model stock market is instantly magnified 1000 times -- the ratio between the total shares outstanding and the number of shares traded each time. (Likewise, each dollar taken out of the trading pool will be amplified to be a much larger reduction in the overall market capitalization.)
What's the value of the magification ratio in the real world markets? I've heard that U.S. stocks turned over every 80 days to a year. So the magnification ratio for U.S. markets should be between 80 and 360.
Real world situations are a bit more complex. A lot of trades will cancel each other out without affecting the size of the overall trading pool; this and other factors will make us under-estimate the magnification ratio. On the other hand, some investors may let funds sit in their accounts for a few days before making another trade, this would make us over-estimate the magnification ratio. Since we don't have a metrics of these factors, we'll still assume the ratio to be around 80 to 360.
The actual magnification ratio doesn't matter. What matters is we are aware that the crazy magnification exists.
Once we are aware of this magnification, we will also be aware that the vast majority of the stock market value -- perhaps 99% of it, -- is just imaginary money. We'll also begin to comprehend why the market is as volatile as it is. Although money itself is probably an imaginary concept, what's important now is to realize how fragile a concept it is, how easily it can be gone without a trace.
Cyclical Changes In the Trading Fund PoolSince we know the size of trading fund pool is directly related to the overall value of the stock market, it helps if we know about how the trading fund pool changes, and the approximate magnitude of those changes.
It seems to me that stock trading funds can come from the following categories, each of which may correlate to different chronological cycles.
(A) Retirement Saving Activity. The most notable of this component is the retirement funds of the so-called "baby boomer" generation, the generation of Americans bornt between 1945 and 1965. Much of the retirement saving would find its way into the stock market, and this trend will continue until at least the year 2010, when the first baby boomers will turn retirement age. By my own estimate, retirement saving adds up to between $20 to $50 billion dollars each month, a lot of which goes into the stock trading pool.
The great bull market since the early 1990s is directly powered by such retirement savings, and the basic trendline from the first half of the past decade is likely to continue on until at least 2010. This is the part of the market that correlates to the demographic cycle. (The market has since skewed upward due to various other factors mentioned below. When these factors are removed, the market will be corrected back to this basic trendline.)
(B) Governmental Activity. The federal government's shrinking deficit reduces government borrowing, and funds that would have gone to government bonds find their way into the stock market.
Another significant governmental activity is tax collection. Both last and this year, momentum stocks peaked toward April 15. This is directly related to tax paying liquidation, and it affects momentum stocks disproportionately. Because of the high percentage returns in these stocks, people would rather hold off until April, rather than liquidate them throughout the year to pay estimated tax. Tax paying liquidation can take perhaps 100 billion dollars out of the pool within a few weeks this year, depressing the momentum market for months. Later in the year, the government is going to discover the extra revenue and retire more of its debts, thus releasing more funds back to the trading pool.
(C) Corporate Activity. Corporations contribute to the trading pool by investing their excess cash. Corporations draw money from the trading pool through activities such as IPO, SPO, private placements, stock option excercises, and other funding activities. Heavy IPO activities typically depress the momentum market. If AT&T proceeds with its $10 billion IPO of its wireless business, it's going to have a noticeable effect on the market.
(D) New Investor Activity. Increasing number of new investors are participating in the stock market, withdrawing money from CDs to play the stock market. How many such people were lured into the stock market by the bull run last year is hard to say, but ought to be a significant number.
(E) Trading Activity. Traders move money between their trading accounts and money market or margin accounts constantly, resulting in daily fractuations in the trading pool. Through margin borrowing, traders can add significant new funds into the trading pool. Between last December and February, traders took out between $15 and $40 billion new margin loans each month, all of which went directly into the trading pool.
Of the various sources of the trading pool, the margin loans are the most fragile. After the recent margin calls, the amount of margin loans, or at least its growth rate, should diminish. The increase in funding from new investors is a one time deal, and such activity is likely to have peaked. IPO activities typically correlate with market cycles, when the market peaks, IPOs also peak, thus driving the market back down. Tax paying is an annual ritual, which, together with summer vacations, causes summer market downturns.. Retirement saving correlates to the longer demographic cycle. The remainder of the trading fund correlates to the economic cycle.
Take away the extra margin loans, the market should return to its pre-November trajectory. The supply of new investors is finite, once exhausted, the market should return gradually to its pre-1999 trajectory. When the economic begins to turn sour, the market may return to its pre-1995 trajectory, but retirement savings should continue to increase until at least 2010, so the market will still go up, albeit from a level that is lower than the current level.
Micro ClimatesEven if the overall trading pool stagnates, the trading pools for individual stocks can still change. These will be governed by additional factors related to the individual stocks and their sectors.
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04/08/2000