Do the math

By citing the hyper-inflated values of stocks at their apex in comparison to recent lows, the press frequently claims that billions of dollars have been 'lost' in the recent market downturn. But to what extent are these losses real?

A recent column in The Wall Street Journal about the Neuer Market points up a consistent and persistent error in the way stock market gains and losses are represented. The piece is called 'A Teutonic Tail Spin,' by Bryan Carney (WSJ, Oct. 1, 2002).


The market cap of all the stocks on the Neuer Market peaked in March 2000 at $200bn and is now down about 96 per cent. That leads analysts to suggest that investors have lost '$200bn'. However, the point Carney makes in passing deserves attention. As he says, 'and of that $200bn, most of which has been wiped out, much of it resided in the hands of company insiders (i.e., entrepreneurs) rather than speculators or investors.'


Let's take a market with 300 firms, each trading at a market cap of $1,000 for a total market cap for the stock market itself hypothesised at $300,000. Suppose, then, each of the listed firms trades one share in the period we have selected for measurement, and in each case the trade is ten times the last trade, so that the notional market cap of each of the firms, based on the last trade, goes up from $1,000 to $10,000. The market cap of the entire market in the aggregate, therefore, is not $300,000 but $3m. Then, let's assume there is only one other trade of one share in each of the companies during the remaining portion of the period we have selected, and that trade is at the old price, i.e. a trade which yanks the market cap back down to $1,000 per company or $300,000 for the entire market.


Obviously, trading volume is a good deal higher in a real market but the hypothetical illustrates our point. During any period one selects, most of the shares in the listed companies do not trade at all. Nonetheless, their notional market capitalisation is calculated on the basis of the last trade, which could be one share or it could be 10m shares. However, for purposes of the calculations we see in the newspapers, the number of shares traded does not make any difference. Thus, in our hypothetical, one could argue that investors in the 300 listed stocks lost $2,700,000; the fact is, however, that almost nobody lost any money at all.


To pursue the same point, let's assume that you and I are active traders and we came into the stock market in 1995, with $1,000. We bought some, sold some, plowing our profits in the rising market back into the market until, at the peak in March 2000, we owned stocks valued by the market quotes at $100,000. Then, the meltdown occurs and we neglect to sell at the right time, optimists such as we are. At the end of the day, it turns out … the stocks sitting in our account are worth a total of $1500.


Given this situation, the question arises, have we lost $98,500 or have we made $500 (ignoring the time value of money)? When one says investors in the NASDAQ have 'lost' several trillion dollars, the question is: are we talking about investors who came in with assets they had acquired outside of the stock market (say, in real estate or oil or gas) invested at the peak and then saw their assets in essence destroyed? Or are they (like our hypothetical investors) somebody who had an initial stake in the market, say, five years ago, made and then lost billions of dollars, so that their returns over the five year period are modest? In the latter case, did they lose 'billions of dollars' or did they simply fail to achieve more than a modest return?


Perhaps the above exercise is only factitious. But perhaps it illustrates how bad math is feeding into the market's current malaise.