From this point on, all the formulas treated in this book on how to invest stock deal with an established fund, rather than with a constant flow of new money to invest, as in the case of dollar averaging. However, just as dollar averaging can be adapted to the requirements of a fixed sum, so can most of these other plans be used in managing a fund, which is constantly being added to. These techniques are all broadly classified as "ratio" formulas.

The Ratio Principle
Like dollar averaging, ratio plans are aimed at combating the danger of losses due to unforeseen fluctuations in the stock market. Ratio plans are all alike in that they are concerned solely with the proportion of the investor's capital which is held in stocks as against that used to purchase bonds. The percentage of stocks is intended to be increased when the market is low, and decreased when it is high. The idea is to reduce the amount of risk securities held when prices are high, and conversely to purchase stocks at what are presumed to be bargain levels when the market is low.

A couple of comments are in order concerning the practicability of these formulas for the average investor. First, it is hardly realistic to talk about techniques which involve the sale of a few hundred, or even a few thousand, dollars' worth of stocks in order to replace them with bonds. Most small investors (and a great many large investors) have neither sufficient knowledge of the bond market nor sufficient capital to make buying bonds a practical matter. For most investors, therefore, an indication to sell a certain amount of stocks and buy bonds with the proceeds can most effectively be interpreted as a direction to withdraw the specified amount of money from the stock market and divert it to a savings account or an account with a savings and loan association, or hold it in cash.

As will be made clear for the purpose of how to invest stock, the whole object of placing a portion of one's capital in "bonds" is to reduce the percentage of one's account that is subject "to fluctuations. Obviously, bonds do fluctuate, with the interest rate cycle as well as with the financial condition of the issuer, but the ups and downs in the bond market tend to be much less pronounced than those in the atock market. However, the principal in a savings account is always guaranteed, can (generally) be converted into cash at any time, and usually earns a satisfactory rate of return. Most investors can make the same use of these formulas as large investors who actually do hold most of the fixed-interest portion of their portfolios in bonds. These larger investors cannot, of course, make any practical use of savings accounts, but they usually are able to use a combination of bonds, preferred stocks, commercial paper, bills and other fixed-interest investments to attain the desired degree of stability while still earning a satisfactory return on this portion of their portfolios.

Regardless of actual investor practice, the term "bonds" is consistently used in this book to refer to that part of the portfolio not subject to fluctuations, since this is the standard terminology in discussions of formulas, and the illustrative examples assume that this portion does not in fact fluctuate.

Some comment should also be made about the stock portion of the portfolio. This means all investments subject to substantial price risks—common stocks as well as convertible bonds and preferred. The reader will note that the Dow-Jones Industrial Average or some other stock market index is used to indicate the movement of the market in the illustrative examples. There are several valid objections to this: the various stock averages are calculated according to different principles, all have imperfections, and none of them agree exactly with one another. Furthermore, even if the averages did indicate with any precision what the market is doing (which they don't), they certainly cannot be a reliable indicator of individual investor experience.

Nevertheless, it is necessary to have some indicator of stock market movements, and all the popular averages have proved themselves to be generally satisfactory for this purpose. And for the purpose of managing investments according to a formula, it is not the intention to find an indicator which will exactly match the investor's own results. The whole purpose of using an average is to indicate changes in the degree of risk through reference to changes in the level of the average. It may be assumed that if the market as a whole is subject to a high degree of risk, the stocks held by any particular investor will also be subject to a high degree of risk, no matter how unrelated the previous movement of these stocks might be to the movement of the average.

The Constant-Dollar Plan
Simplest of all ratio formulas is the constant-dollar plan. Its terms dictate that a stated dollar amount of stocks will be held at all times. For example, the investor who has, say, $20,000 in total investment funds may decide on a figure of $10,000 as the amount of stocks he wishes to hold, which would leave $10,000 in the bond account. If the market goes up a specified percentage, stocks are sold to bring the stock account back to $10,000, and if the market declines by a similar amount, sufficient funds are transferred from the bond portion to the stock portion to boost stocks back to $10,000. This means that, although the dollar value of stocks always remains the same, the percentage of stocks held in the total account will drop as the market rises, and increase as the market declines. The implicit assumption here, of course, is that as the market moves up, it is that much more vulnerable, and the percentage of stocks should be reduced; as it drops, stocks are just that much more worth having hence it is a good way for how to invest stock.

TABLE 4
CONSTANT-DOLLAR PLAN
Hypothetical Example
 

No attempt is made, of course, to define what constitutes "high" or "low" points in terms of market averages. Shifts from stocks to bonds (or vice versa) can be indicated either by the actual change in the value of the stock portion of the account, or by a change in one of the popular market indexes. As discussed above, it is recommended that the signal be taken from an average, rather than from the value of the account, for two reasons: (a) changes in the value of an individual portfolio of stocks (especially if the portfolio is small) have far less significance in indicating the vulnerability of the market as a whole than an index of the whole market; (b) the task of calculating the value of a portfolio at frequent intervals could be a burdensome task, requiring an undue amount of attention.

Changes can be made either at the precise time a stated percentage advance or decline occurs in the stock portion of the account—say, 10 or 20 percent—or the account can be re-examined quarterly, semi-annually or annually—and the stock portion readjusted to its original figure. This latter procedure seems the more sensible approach. A study of a number of case histories of the method seems to indicate the advantages of checking up daily are negligible.

Table 4 presents a hypothetical constant-dollar plan followed over a complete market cycle. Starting with a total portfolio of $20,000, the investor puts $10,000 in both the bond and stock portions. With every 20 percent change in the market, he re-establishes the stock portion at the original amount by selling stock and buying bonds or vice-versa. (As the example is not based on actual market conditions, it is not possible to assume quarterly re-evaluations, even though this is the recommended procedure.) For simplicity's sake, we are assuming that the stocks in our investor's portfolio move exactly with the market, even though—as mentioned earlier—this is unlikely in actual practice.

When the plan is begun, our hypothetical stock average is at 100. It rises to 207.4, then goes into a decline which takes it to 54.4, after which it rises again to 100. At the final point in the table, the average is brought up to 100, but no portfolio changes are made, since the average did not move a full 20 percent since the previous adjustment. Note that the investor did not profit to the full extent of the bull market, since the value of his portfolio rose to only $28,000—an increase of 40 percent —at the high point, while the market more than doubled. When the market fell, however, his bond position protected him to some extent, and his portfolio's value was $16,000 at the low point— only 20 percent below its original value—even though the market as measured by the average fell by slightly more than 45 percent.

Most important, however, is the final value of our investor's portfolio—$22,627, or a gain of about 13 percent. Commissions, not considered in the table, would have been about $365 on a round-lot basis for listed stocks, bringing the net increase in the portfolio's value to about 11.5 percent. This is not a bad gain, when you consider that the market as a whole is right back where it started from. If the portfolio had been invested in either all stocks or all bonds, there would have been no profit at all. But our investor managed to secure a respectable profit over the entire cycle merely by using a very simple formula.

Note that no time indications are given, or required, in a constant-dollar plan on how to invest stock. Operation of a plan such as the one presented in the table might stretch over a period of many years, or be completed in only a fraction of that time. If the market fails to move 10 percent for an extended period, no changes need be made in the portfolio.

At the end of the plan, the stock portion of the portfolio— which stood at 50 percent at the start—has dropped to about 47 percent. This is not much, but with wider market, swings, extending over a longer period, quite a discrepancy could develop. If it was reasonable for the investor to hold 50 percent of his funds in cash when the stock index stood at 100 at the beginning of the plan, is it not still logical to do so when the index returns to that figure? The investor can, of course, adjust his portfolio to a 50-50 figure when the change becomes considerable. A faithful follower of the constant dollar plan who began operations at an extremely low point of the market would find himself permanently frozen to an arbitrarily established dollar figure of stocks, and barred from participating to any great extent in bull markets. If he were to re-adjust the original percentage figure after, say, a substantial market rise, he would be putting himself in the position of market seer, which is the very thing a formula is supposed to avoid. Some authorities suggest certain percentage limitations on the amount of deviation from the original dollar figure which should be tolerated before a readjustment is made. For example, it might be specified that the original proportions be re-established when the percentage of stocks in the portfolio rises to 55 or drops to 45. Another suggestion is that the portfolio be readjusted to its original percentage division after a certain period of time—say three or four years. But such rules must of necessity be arbitrary and do not solve the central problem.

Another weakness of the constant-dollar plan is the problem of what to do with additional funds which may become available. In the example above, suppose our investor suddenly won $5,000 at the race track. Should he divide this among the two sections of his portfolio according to the original percentage he had set up, or should he use the current percentages as a guide? Or, since the money is surplus funds he wasn't counting on, should he commit it all to risk investments? Or, inasmuch as he has already decided how much money he wants to commit to equity investments, should he not add the entire sum to the bond portion? Such a difficulty does not destroy the value of the plan, but it can cause some confusion.

An Informal Plan
Actually, the plan is an extremely informal one for how to invest stock, and the disadvantages mentioned above are not terribly serious in practice. Investors who use such a plan are interested in getting some advantages of owning common stocks, without incurring undue risks, and the constant-dollar formula presents a practical approach. The amount of stocks to be held is a matter of individual preference. Our investor above could have chosen $5,000 as his stock proportion, just as well as $10,000.

Over a long period of time, the method produces satisfactory results. One study1 shows results of a hypothetical test of the method over the 1926-1950 period, starting with a $10,000 fund, $5,000 of which was to be held in stocks, and using the Dow-Jones Industrials as an action indicator. Additional purchases are specified at every 20 percent decline in the Dow-Jones Industrials, and sales at every 25 percent advance. By the end of 1950, total value of the fund amounted to $15,773, and had produced an average yield of 5.46 percent over the total period. This capital appreciation of about 50 percent compares with a net rise of about 46 percent in the Dow-Jones Industrials. At the end of 1945, however, when the average had traced a complete market cycle and had returned only to the starting point, the constant-dollar portfolio gain already amounted to about 50 percent, and changed little in succeeding years.

In order to arrive at this result, the authors of the study (who are unenthusiastic about this formula) had to choose an extremely advantageous beginning date—1926. An investor who wants to begin a plan might reasonably not know whether the market is in fact at a suitable point. If it turns out that he began his plan at a market peak, then successive drops in the averages will dictate additional purchases of stock until he may have no funds remaining in the bond account with which to buy anything, which will relieve him of the task of calculating his position, but will not do his finances much good.

Actually, an investor who uses the constant-dollar plan for how to invest stock is saying, in effect, that the point at which he begins is a "normal" market level, above which it is wise to sell some stocks, and below which it is advisable to purchase more stocks. Thus the formula presents a sizable obstacle at the very beginning, which is not easy to overcome. This, undoubtedly, is the most serious weakness of the constant-dollar method. (A partial solution to the problem appears in the following chapter.) It appears in some other formulas, too, but does not usually place such severe limitations on the plan's operations. On the plus side, however, it may be said that few periods in the market would have proved completely disastrous as a starting point.

Simplicity is the main feature of the plan, and it may appeal to some investors for that reason. It has the virtues of a methodical hedging against fluctuations in the market, which can be quite valuable, and at the same time the convenience of an essentially informal plan.

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