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You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
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Fundamental analysis is described by some as the best, most sober strategy for investors to followValue Investing and Fundamental Analysis It was especially smitten with WorldComs critical Internet division, UUNet. The Internet wasnt going away, and so, I thought, neither was UUNet or WorldCom. During this time of enchantment my sensible wife would say UUNet, UUNet and roll her pretty eyes to mock my rhapsodizing about WorldComs global IP network and related capabilities. The repetition of the word gradually acquired a more general antiPollyannish meaning as well. Maybe the bill is so exorbitant because the plumber ran into something he didnt expect. Yeah, sure. UUNet, UUNet. Smitten, rhapsodizing, and Pollyanna are not words that come naturally to mind when discussing value investing, a major approach to the market that uses the tools of so-called fundamental analysis. Often associated with Warren Buffetts gimlet-eyed no-nonsense approach to trading, fundamental analysis is described by some as the best, most sober strategy for investors to follow. Had I paid more attention to WorldCom fundamentals, particularly its $30 billion in debt, and less attention to WorldCom fairy tales, particularly its bright future role as a dumb network (better not to ask), I would no doubt have fared better. In the stock markets enduring tug-of-war between statistics and stories, fundamental analysis is generally on the side of the numbers. Still, fundamental analysis has always seemed to me slightly at odds with the general ethic of the market, which is based on hope, dreams, vision, and a certain monetarily tinted yet genuine romanticism. I cite no studies or statistics to back up this contention, only my understanding of the investors Ive known or read about and perhaps my own infatuation, quite atypical for this numbers man, with WorldCom. Fundamentals are to investing what (stereotypically) marriage is to romance or what vegetables are to eating-health ful, but not always exciting. Some understanding of them, however, is essential for any investor and, to an extent, for any intelligent citizen. Everybodys heard of people who refrain from buying a house, for example, because of the amount they would have paid in interest over the years. (Oh my, dont get a mortgage. Youll end up paying four times as much.) Also common are lottery players who insist that the worth of their possible winnings is really the advertised one million dollars. (In only 20 years, Ill have that million.) And there are many investors who doubt that the opaque pronouncements of Alan Greenspan have anything to do with the stock or bond markets. These and similar beliefs stem from misconceptions about compound interest, the bedrock of mathematical finance, which is in turn the foundation of fundamental analysis. Speaking of bedrocks and foundations, I claim that e is the root of all money. Thats e as in ex as in exponential growth as in compound interest. An old adage (probably due to an old banker) has it that those who understand compound interest are more likely to collect it, those who dont more likely to pay it. Indeed the formula for such growth is the basis for most financial calculations. Happily, the derivation of a related but simpler formula depends only on understanding percentages, powers, and multiplication-on knowing, for example, that 15 percent of 300 is .15 x 300 (or 300 x .15) and that 15 percent of 15 percent of 300 is 300 x (.15)2. With these mathematical prerequisites stated, lets begin the tutorial and assume that you deposit $1,429.73 into a bank account paying 6.9 percent interest compounded annually. No, lets bow to the great Rotundia, god of round numbers, and assume instead that you deposit $1,000 at 10 percent. After one year, youll have 110 percent of your original deposit-$1,100. That is, youll have 1,000 x 1.10 dollars in your account. (The analysis is the same if you buy $1,000 worth of some stock and it returns 10 percent annually.) Looking ahead, observe that after two years youll have 110 percent of your first-year balance-$1,21 1. That is, youll have ($1,000 x 1.10) x 1.10. Equivalently, that is $1,000 x After three years youll have 110 percent of your second year balance-$1,331. That is, youll have ($1,000 x 1.102) x 1.10. Equivalently, that is $1,000 x 1.103. Note the exponent is 3 this time. The drill should be clear now. After four years youll have 110 percent of your third-year balance-$1,464.10. That is, youll have ($1,000 x 1.103) x 1.10. Equivalently, that is $1,000 x 1.104. Once again, note the exponent is 4. Let me interrupt this relentless exposition with the story of a professor of mine long ago who, beginning at the left side of a very long blackboard in a large lecture hall, started writ ing 1 + 1/1! + 1/2! + 1/3! + 1/4! + 1/5!(Incidentally the expression 5! is read 5 factorial, not 5 with an exclamatory flair, and it is equal to 5 x 4 x 3 x 2 x 1. For any whole number N, N! is defined similarly.) My fellow students initially laughed as this professor, slowly and seemingly in a trance,kept on adding terms to this series. The laughter died out, however, by the time he reached the middle of the board and was writing 1/44! + 1/45! ... . I liked him and remember a feeling of alarm as I saw him continue his senseless repetitions. When he came to the end of the board at 1/83!, he turned and faced the class. His hand shook, the chalk dropped to the f l oor, and he left the room and never returned. Mindful thereafter of the risks of too many illustrative repetitions, especially when Im standing at a blackboard in a classroom, Ill end my example with the fourth year and simply note that the amount of money in your account after t years will be $1,000 x 1.10`. More generally, if you deposit P dollars into an account earning r percent interest annually, it will be worth A dollars after t years, where A = P(1 + r), the promised formula describing exponential growth of money. You can adjust the formula for interest compounded semiannually or monthly or daily. If money is compounded four times per year, for example, then the amount youll have after t years is given by A = P(1 + r/4)4t. (The quarterly interest rate is r/4, one-fourth the annual rate of r, and the number of compoundings in t years is 4t, four per year for t years.) If you compound very frequently (say n times per year for a large number n), the formula A = P(1 + r/n)nt can be mathematically massaged and rewritten as A = Pert, where e, approximately 2.718, is the base of the natural logarithm. This variant of the formula is used for continuous compounding(and is, of course, the source of my comment that e is the root of all money). The number e plays a critical role in higher mathematics, best exemplified perhaps by the formula en` + 1 = 0, which packs the five arguably most important constants in mathematics into a single equation. The number e also arises if were simply choosing numbers between 0 and 1 at random. If we (or, more likely, our computer) pick these numbers until their sum exceeds 1, the average number of picks wed need would be e, about 2.718. The ubiquitous e also happens to equal 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... , the same expression my professor was writing on the board many years ago. (Inspired by a remark by stock speculator Ivan Boesky, Gordon Gecko in the 1987 movie Wall Street stated, Greed is good. He misspoke. He intended to say, e is good.) Many of the formulas useful in finance are consequences of these two formulas: A = P(1 + r)t for annual compounding and, for continuous compounding, A = Pert. To illustrate how theyre used, note that if you deposit $5,000 and its compounded annually for 12 years at 8 percent, it will be worth $5,000 (1.08)12 or $12,590.85. If this same $4,000 is compounded continuously, it will be worth $4,000e(-8 X 12) or $13,058.48. Using this interest rate and time interval, we can say that the future value of the present $5,000 is $12,590.85 and that the present value of the future $12,590.85 is $5,000. (If the compounding is continuous, substitute $13,058.48 in the previous sentence.) The present value of a certain amount of future money is the amount we would have to deposit now so that the deposit would grow to the requisite amount in the allotted time. Alternatively stated (repetition may be an occupational hazard of professors; so may self-reference), the idea is that given an interest rate of 8 percent, you should be indifferent between receiving $5,000 now (the present And just as George is taller than Martha and Martha is shorter than George are different ways to state the same relation, the interest formulas may be written to emphasize either present value, P, or future value, A. Instead of A = P(1 + r)t, we can write P = A/(1 + r)t, and instead of A = Per`, we can write P = A/ert. Thus, if the interest rate is 12 percent, the present value of $50,000 five years hence is given by P = $50,000/(1.12)5 or$28,371.34. This amount, $28,371.34, if deposited at 12 percent compounded annually for five years, has a future value of $50,000. One consequence of these formulas is that the doubling time, the time it takes for a sum of money to double in value, is given by the so-called rule of 72: divide 72 by 100 times the interest rate. Thus, if you can get an 8 percent (.08) rate, it will take you 72/8 or nine years for a sum of money to double, eighteen years for it to quadruple, and twenty-seven years for it to grow to eight times its original size. If youre lucky enough to have an investment that earns 14 percent, your money will double in a little more than five years (since 72/14 is a bit more than 5) and quadruple in a bit over ten years. For continuous compounding, you use 70 rather than 72. These formulas can also be used to determine the so-called internal rate of return and to define other financial concepts. They provide as well the muscle behind common pleas to young people to begin saving and investing early in life if they wish to become the millionaire next door. (They dont, however, tell the millionaire next door what he should do with his wealth.) The Fundamentalists Creed: You Get What You Pay For The notion of present value is crucial to understanding the fundamentalists approach to stock valuation. It should also be important to lottery players, mortgagors, and advertisers. That the present value of money in the future is less than its nominal value explains why a nominal $1,000,000 award for winning a lottery-say $50,000 per year at the end of each of the next twenty years-is worth considerably less than $1,000,000. If the interest rate is 10 percent annually, for example, the $1,000,000 has a present value of only about $426,000. You can obtain this value from tables, from financial calculators, or directly from the formulas above (supplemented by a formula for the sum of a so-called geometric series). The process of determining the present value of future money is often referred to as discounting. Discounting is important because, once you assume an interest rate, it allows you to compare amounts of money received at different times. You can also use it to evaluate the present or future value of an income stream-different amounts of money coming into or going out of a bank or investment account on different dates. You simply slide the amounts forward or backward in time by multiplying or dividing by the appropriate power of (1 + r). This is done, for example, when you need to figure out a payment sufficient to pay off a mortgage in a specified amount of time or want to know how much to save each month to have sufficient funds for a childs college education when he or she turns eighteen. Discounting is also essential to defining what is often called a stocks fundamental value. The stocks price, say investing fundamentalists (fortunately not the sort who wish to impose their moral certitudes on others), should be roughly equal to the discounted stream of dividends you can expect to receive from holding onto it indefinitely. If the stock does not pay dividends or if you plan on selling it and thereby realizing capital gains, its price should be roughly equal to the discounted value of the price you can reasonably expect to receive when you sell the stock plus the discounted value of any dividends. Its probably safe to say that most stock prices are higher than this. During the 1990 boom years, investors were much more concerned with capital gains than they were with dividends. To reverse this trend, finance professor Jeremy Siegel, author of Stocks for the Long Run, and two of his colleagues recently proposed eliminating the corporate dividend tax and making dividends deductible. The bottom line of bottom-line investing is that you should pay for a stock an amount equal to (or no more than) the present value of all future gains from it. Although this sounds very hard-headed and far removed from psychological considerations, it is not. The discounting of future dividends and the future stock price is dependent on your estimate of future interest rates, dividend policies, and a host of other uncertain quantities, and calling them fundamentals does not make them immune to emotional and cognitive distortion. The tango of exuberance and despair can and does affect estimates of stocks fundamental value. As the economist Robert Shiller has long argued quite persuasively, however, the fundamentals of a stock dont change nearly as much or as rapidly as its price. |
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