![]() ![]() Charts of stock or currency changes over time do reveal a constant background of small up and down price movements-but not as uniform as one would expect if price changes fit the bell curve. Do financial data neatly conform to such assumptions? Of course, they never do. Typhoons are, in effect, defined out of existence. sured by its sigma, or standard de- viation) depicts how far price changes diverge from the mean events at the extremes are considered extremely rare. Modern portfolio theory poses a danger to those who believe in it too strongly and is a powerful challenge for the theoretician. The second presumption is that all price changes are distributed in a pattern that conforms to the standard bell curve. As a result, predictions of future market move- ments become impossible. First, they suggest that price changes are statistically indepen- dent of one another: for example, that today’s price has no influence on the changes between the current price and to- morrow’s. If the weather is moderate 95 percent of the time, can the mariner afford to ignore the possibility of a typhoon? The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. An inescapable analogy is that of a sailor at sea. But the picture it presents does not reflect reality, if one agrees that major events are part of the remaining 5 percent. It is true that portfolio theory may account for what occurs 95 percent of the time in the market. The mathematics underlying portfolio theory handles extreme situations with benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account. A cornerstone of finance is modern portfolio theory, which tries to maximize returns for a given level of risk. Predict that such precipitous events should never happen. The classical financial models used for most of this century In a reversal, the stock shot up 10 percent on the fourth day. Last September, for instance, the stock for Alcatel, a French telecommunications equipment manufacturer, dropped about 40 percent one day and fell another 6 percent over the next few days. Fortunes are made and lost in sudden bursts of activity when the market seems to speed up and the volatility soars. ![]() ![]() Sional stock and currency traders know better than ever that prices quoted in any financial market often change with heart-stopping swiftness. ![]() The geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet by Benoit B. ![]()
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