| Home | My photos | Forex | My trading | Contacts |
|
|
You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
|
Are Stocks Less Risky Than Bonds?Diversifying Stock Portfolios Long before my childrens fascination with Super Mario Brothers, Tetris, and more recent addictive games, I spent interminable hours as a kid playing antediluvian, low-tech Monopoly with my two brothers. The game requires the players to roll dice and move around the board buying, selling, and trading real estate properties. Although I paid attention to the probabilities and expected values associated with various moves (but not to what have come to be called the games Markov chain properties), my strategy was simple: Play aggressively, buy every property whether it made sense or not, and then bargain to get a monopoly. I always traded away railroads and utilities if I could, much preferring to build hotels on the real estate I owned instead. A Reminiscence and a Parable Although the games get-out-of-jail-free card was one of the few ties to the present-day stock market, Ive recently had a tiny epiphany. On some atavistic level Ive likened hotel building to stock buying and the railroads and utilities to bonds. Railroads and utilities seemed safe in the short run, but the ostensibly risky course of putting most of ones money into building hotels was ultimately more likely to make one a winner (especially since we occasionally altered the rules to allow unlimited hotel building on a property). Was my excessive investment in WorldCom a result of a bad generalization from playing Monopoly? I strongly doubt it, but such just-so stories come naturally to mind. Aside from the jail card, a board game called WorldCom would have few features in common with Monopoly (but might more closely resemble Grand Theft Auto). Different squares along players paths would call for SEC investigations, Eliot Spitzer prosecutions, IPO giveaways, or favorable analyst ratings. If you attained CEO status, you would be allowed to borrow up to $400 million ($1 billion in later versions of the game), whereas if you were reduced to the rank of employee, you would have to pay a coffee fee after each move and invest a certain portion of your savings in company stock. If you were unfortunate enough to become a stockholder, you would be required to remove your shirt while playing, while if you became CFO, you would receive stock options and get to keep the stockholders shirts. The object of the game would be to make as much money and collect as many of your fellow players shirts as possible before the company went bankrupt. The game might be fun with play money; it wasnt with the real thing. Heres a better analogue for the market. People are milling around a huge labyrinthine bazaar. Occasionally some of the booths in the bazaar attract a swarm of people jostling to buy their wares. Likewise, some booths are occasionally devoid of any prospective customers. At any given time most booths have a few customers. At the intersections of the bazaars alleys are sales people from some of the bigger booths as well as well-traveled seers. They know the various sections of the bazaar intimately and claim to be able to foretell the fortunes of various booths and collections of booths. Some of these sales people and some of the prognosticators have very large bullhorns and can be heard throughout the bazaar, while others make do by shouting. In this rather primitive setting, many aspects of the stock market can already be discerned. The forebears of technical traders might be those who buy from booths where crowds are developing, while the forebears of fundamental traders might be those who coolly weigh the worth of the goods on display. The seers are the progenitors of analysts, the sales people progenitors of brokers. The bullhorns are a rudimentary form of business media, and, of course, the goods on sale are companies stocks. Crooks and swindlers have their ancestors as well with some of the booths hiding their shoddy merchandise under the better goods. If everyone, not just the booth owners, could sell as well as buy, this would be a better elemental model of an equities market. (I dont intend this as an historical account, but merely as an idealized narrative.) Nevertheless, I think its clear that stock exchanges are natural economic phenomena. Its not hard to imagine early analogues of options trading, corporate bonds, or diversified holdings developing out of such a bazaar. Maybe thered even be some arithmeticians around too, analyzing booths sales and devising purchasing strategies. In acting on their theories, some might even lose their togas and protractors. Are Stocks Less Risky Than Bonds? Perhaps because of Monopoly, certainly because of WorldCom, and for many other reasons, the focus of this book has been the stock market, not the bond market (or real estate, commodities, and other worthy investments). Stocks are, of course, shares of ownership in a company, whereas bonds are loans to a company or government, and everybody knows that bonds are generally safer and less volatile than stocks, although the latter have a higher rate of return. In fact, as Jeremy Siegel reports in Stocks for the Long Run, the average annual rate of return for stocks between 1802 and 1997 was 8.4 percent; the rate on treasury bills over the same period was between 4 percent and 5 percent. (The rates that follow are before inflation. Whats needless to say, I hope, is that an 8 percent rate of return in a year of 15 percent inflation is much worse than a 4 percent return in a year of 3 percent inflation.) Despite what everybody knows, Siegel argues in his book that, as with Monopolys hotels and railroads, stocks are actually less risky than bonds because, over the long run, they have performed so much better than bonds or treasury bills. In fact, the longer the run, the more likely this has been the case. (Comments like everybody knows or theyre all doing this or everyones buying that usually make me itch. My background in mathematical logic has made it difficult for me to interpret all as signifying something other than all.) Everybody does have a point, however. How can we believe Siegels claims, given that the standard deviation for stocks annual rate of return has been 17.5 percent? If we assume a normal distribution and allow ourselves to get numerical for a couple of paragraphs, we can see how stomach-churning this volatility is. It means that about two thirds of the time, the rate of return will be between -9.1 percent and 25.9 percent (that is, 8.4 percent plus or minus 17.5 percent), and about 95 percent of the time the rate will be between -26.6 percent and 43.4 percent (that is, 8.4 percent plus or minus two times 17.5 percent). Although the precision of these figures is absurd, one consequence of the last assertion is that the returns will be worse than -26.6 percent about 2.5 percent of the time (and better than 43.4 percent with the same frequency). So about once every forty years (1/40 is 2.5 percent), you will lose more than a quarter of the value of your stock investments and much more frequently than that do considerably worse than treasury bills. These numbers certainly dont seem to indicate that stocks are less risky than bonds over the long term. The statistical warrant for Siegels contention, however, is that over time, the returns even out and the deviations shrink. Specifically, the annualized standard deviation for rates of return over a number N of years is the standard deviation divided by the square root of N. The larger N is, the smaller is the standard deviation. (The cumulative standard deviation is, however, greater.) Thus over any given four-year period the annualized standard deviation for stock returns is 17.5%/2, or 8.75%. Likewise, since the square root of 30 is about 5.5, the annualized standard deviation of stock returns over any given thirty-year period is only 17.5%/5.5, or 3.2%. (Note that this annualized thirtyyear standard deviation is the same as the annual standard deviation for the conservative stock mentioned in the example at the end of chapter 6.) Despite the impressive historical evidence, there is no guarantee that stocks will continue to outperform bonds. If you look at the period from 1982 to 1997, the average annual rate of return for stocks was 16.7 percent with a standard deviation of 13.1 percent, while the returns for bonds were be tween 8 percent and 9 percent. But from 1966 to 1981, the average annual rate of return for stocks was 6.6 percent with a standard deviation of 19.5 percent, while the returns for bonds were about 7 percent. So is it really the case that, despite the debacles, deadbeats, and doomsday equities like WCOM and Enron, the less risky long-term investment is in stocks? Not surprisingly, there is a counterargument. Despite their volatility, stocks as a whole have proven less risky than bonds over the long run because their average rates of return have been considerably higher. Their rates of return have been higher because their prices have been relatively low. And their prices have been relatively low because theyve been viewed as risky and people need some inducement to make risky investments. But what happens if investors believe Siegel and others, and no longer view stocks as risky? Then their prices will rise because risk-averse investors will need less inducement to buy them; the equity-risk premium, the amount by which stock returns must exceed bond returns to attract investors, will decline. And the rates of return will fall because prices will be higher. And stocks will therefore be riskier because of their lower returns. Viewed as less risky, stocks become risky; viewed as risky, they become less risky. This is yet another instance of the skittish, self-reflective, self-corrective dynamic of the market. Interestingly, Robert Shiller, a personal friend of Siegel, looks at the data and sees considerably lower stock returns for the next ten years. Market practitioners as well as academics disagree. In early October 2002, I attended a debate between Larry Kudlow, a CNBC commentator and Wall Street fixture, and Bob Prechter, a technical analyst and Elliot wave proponent. The audience at the CUNY graduate center in New York seemed affluent and well-educated, and the speakers both seemed very sure of themselves and their predictions. Neither seemed at all affected by the others diametrically opposed expectations. Prechter anticipated very steep declines in the market, while Kudlow was quite bullish. Unlike Siegel and Shiller, they didnt engage on any particulars and generally talked past each other. What I find odd about such encounters is how typical they are of market discussions. People with impressive credentials regularly expatiate upon stocks and bonds and come to conclusions contrary to those of other people with equally impressive credentials. An article in the New York Times in November 2002 is another case in point. It described three plausible prognoses for the market-bad, so-so, and good-put forth by economic analysts Steven H. East, Charles Pradilla, and Abby Joseph Cohen, respectively. Such stark disagreement happens very rarely in physics or mathematics. (Im not counting crackpots who sometimes receive a lot of publicity but arent taken seriously by anybody knowledgeable.) The markets future course may lie beyond what, in chapter 9, I term the complexity horizon. Nevertheless, aside from some real estate, I remain fully vested in stocks, which may or may not result in my remaining fully shirted. The St. Petersburg Paradox and Utility Reality, like the perfectly ordinary woman in Virginia Woolfs famous essay Mr. Bennett and Mrs. Brown, is endlessly complex and impossible to capture completely in any model. Expected value and standard deviation seem to reflect the ordinary meanings of average and variability most of the time, but its not hard to find important situations where they dont. One such case is illustrated by the so-called St. Petersburg paradox. It takes the form of a game that requires that you f l ip a coin repeatedly until a tail first appears. If a tail appears on the first flip, you win $2. If the first tail appears on the second flip, you win $4. If the first tail appears on the third flip, you win $8, and, in general, if the first tail appears on the Nth f l ip, you win 2N dollars. How much would you be willing to pay to play this game? One could argue that you should be willing to pay any amount to play this game. To see why this is so, recall that the probability of a sequence of independent events such as coin flips is obtained by multiplying the probabilities of each of the events. Thus the probability of getting the first tail, T, on the first flip is 1/2; of getting a head and then the first tail on the second flip, HT, is 1/4; of getting the first tail on the third flip, HHT, (1/2)3 or 1/8; and so on. Putting these probabilities and the possible winnings associated with them into the formula for expected value, we see that the expected value of the game is ($2 x 1/2) + ($4 x 1/4) + ($8 x 1/8) + ($16 x 1/16) + ... (2N x All of these products are 1, there are infinitely many of them, and so their sum is infinite. The failure of expected value to capture our intuitions becomes clear when you ask yourself why youd be reluctant to pay even a measly $1,000 for the privilege of playing this game. The most common resolution is roughly that provided by the eighteenth century mathematician Daniel Bernoulli, who wrote that peoples enjoyment of any increase in wealth (or regret at any decrease) is inversely proportionate to the quantity of goods previously possessed. The fewer dollars you have, the more you appreciate gaining one and the more you fear losing one, and so, for almost everyone, the likely prospect of losing $1,000 more than cancels the remote possibility that youll win, say, a billion dollars. |
|
|||||||||||||||
Previous Issues
|
| ©2007 Olesia | Home • My photos • Forex • News • My trading • Contacts |