Somewhat similar to the constant-dollar plan in investing in stocks is the constant-ratio formula. It is one of the oldest formulas in existence, having been used as long as 20 years ago. More important, it still stands up today, and is widely used, despite the drastic changes which have taken place in the market.

It fulfills, perhaps better than any other formula, the basic theoretical requirements of formula investing. It permits the investor to participate to some extent in bull markets, while at the same time protecting him from serious price declines. And because it is not married to a fixed-dollar amount in stocks (as in the constant-dollar plan) or a "norm" (as in the variable-ratio plans to be discussed in the next chapter), the method has a high degree of flexibility. One reason for its durability and its effectiveness is that no forecast whatsoever is made about the character of future markets, other than that they will continue to fluctuate, which is hardly a hazardous assumption.

Because of the clear-cut advantages of this plan in investing in stocks, it has been widely used by institutions, such as trust, endowment and pension funds. Its first use, as will be seen later, was in a college endowment fund. In past years, however, its popularity with some institutional investors has waned (although others are still quite satisfied), and it has been adopted more and more by individuals.

Here is how it works: The total investment fund is divided into two equal portions, one half to be invested in stocks, the other in bonds. As the market rises, stocks are sold and bonds are bought to restore the 50-50 relationship. If the market goes down, the reverse procedure is followed, bonds being sold and stocks bought to return to the 50-50 ratio.

At first glance, it may seem that the plan is very similar to the constant-dollar formula, as described in the last chapter. The two plans do share some characteristics, of course, and the object of both is the same. But the constant-ratio plan does not present the investor with quite so many knotty decisions during its operation, and results over the long term have tended to be somewhat better.

As in the constant-dollar plan, the bond and stock portions of the account may be readjusted according to changes in the value of stocks held, or in a stock index. As before, the adjustments can be made as shifts of a certain specified minimum percentage occur, or at regular intervals. Here again, it is recommended that the investor make the necessary shifts of bonds and stocks at regular intervals. Studies show that this procedure produces good results—in addition, of course, to its greater convenience.

How It Operates
 

TABLE 5
CONSTANT-RATIO PLAN
Hypothetical Example
 

The hypothetical example shown in Table 5 assumes the same fluctuations in the market index as in our constant-dollar example. A $20,000 account is assumed, with a 50-50 ratio between stocks and bonds, and the account is readjusted with every 20 percent rise or decline in the stock index. The stock index rises from 100 to 207.4, falls to 54.4, and climbs back to 100, thus completing the market cycle. (At the last stage shown, no readjustment takes place, since the index has not risen a full 10 percent from the last adjustment point.)

At the end of the complete market cycle, the total value of the portfolio is $21,115. Commissions, not figured in the example, would have amounted to about $230 on the basis of round-lot transactions in listed stocks, leaving our investor with a net profit after commissions of $885, or just under five percent of the starting value of his portfolio. This profit is less than half that produced by the constant-dollar plan under the same conditions. Does that mean the constant-dollar plan is better? The answer is no. A close look at the two tables shows that, at the high point (when the average stood at 207.4), the constant-ratio portfolio has a market value of $29,281, against only $28,000 for the constant-dollar portfolio. Furthermore, it is obvious that the constant-ratio portfolio would continue to benefit in larger measure from any subsequent market rise, since its portfolio contains over $15,000 in stocks, while the constant-dollar portfolio has stocks worth only $10,000.

At the low point touched by the average (54.4), the constant-ratio formula's portfolio is worth only $15,554, while that of the constant-dollar portfolio has a value of $16,000. However, any further decline in the stock market would do much more damage to the constant-dollar portfolio than to the constant-ratio portfolio, since the amount of stocks held in the constant-dollar portfolio must remain the same, while the percentage of bonds —which are intended to provide protection against falling stock prices—will continue to shrink.

A Less Flexible Plan
The point is that the constant-dollar plan is far less flexible than the constant-ratio in investing in stocks, and far less able to function well under changing market conditions. If you could be certain that the market would always trace a complete cycle of the type postulated in our example, then you could choose the constant-dollar plan with assurance that you were making the right choice. It is doubtful that such an opinion would be very reliable, however.

Another comparison of the two methods was made over the 1926-1950 period. Using essentially the same method of shifting funds between accounts, a $10,000, 50-50 constant-ratio plan would end up with a profit of $5,839, compared with $5,773 for the constant-dollar. Were the lest examples to be continued a few more years into the fifties, the constant-ratio plan would pull even farther ahead, due to its built-in advantage in a rising market. This would be especially significant in this case, because by the end of the test the constant-dollar formula is only about 30 percent in stocks, while the constant-ratio plan is still at 50 percent.

Automatically Adaptive
It might be worth pointing out that, since the long-term trend of the American economy has always been irregularly upward, the constant-ratio plan in investing stocks promises to be able to adjust itself to this gradual rise somewhat better than the constant-dollar plan. Naturally, the uptrend is subject to frequent declines or periods of stagnation—sometimes of considerable duration—but the upward movement has always reasserted itself in time. The constant-ratio plan provides some protection during these periods of decline, while continually adapting itself automatically to changing market conditions.

Lucile Tomlinson presents results of a series of five hypothetical constant ratio plans, each covering 11 years in the 55-year period 1897-1951.2 This study includes a varied assortment of markets. Adjustments were made on a once-a-year basis, no adjustment to be made unless a certain specified percentage of upward or downward movement in the market had occurred. In three of the periods, the constant-ratio formula turned in a significantly better performance than did a "buy and hold" plan (i.e., a portfolio consisting of half bonds and half stocks at the start of each period, with no adjustments of proportions during the plan), and in the other two fell only slightly behind.

The best profit performance of the constant-ratio plan showed up in the 1919-1920 period, with a gain of 89.4 percent. The worst was in the 1930-1940 period, which produced a loss of 12.7 percent (the Dow-Jones Industrials dropped 47 percent in the same span of time). Miss Tomlinson concludes that the best results are produced by the constant-ratio formula "when stock prices fluctuate over a fairly wide range but there is no extreme in either direction."

How do you start?
Before beginning a constant-ratio plan, there are two decisions the investor must make. First, there is the problem of what ratio to adopt. In the examples referred to so far, a 50-50 ratio has been used, and in fact the plan is sometimes called the "equalizing" formula, because the stock and bond portions are "equalized" periodically.

But there is no reason to stick to the 50-50 ratio. Some conservative investors prefer a higher percentage of bonds, and the more venturesome choose a higher percentage of stocks. The investor who can afford the risk will still obtain some of the advantages of using the formula method even if he hikes the stock percentage to 75 percent, and will profit more in case the market heads upward. And the investor who decides to use a higher percentage of bonds will get the advantage of equity investments—protected to some extent by his use of the formula method—while maintaining a higher degree of safety because of the larger bond portion of his account.

Another problem to be met is the question of when to start the plan. As in the case of the constant-dollar method, the level of the market at which the plan is begun is of no small importance. The effect on final results will not be as great as in the constant-dollar method, since the constant-ratio plan is continually adjusting the amount of stocks held as the market shifts.

One study, comparing plans with various starting dates, points up the importance of this.8 A hypothetical fund started in 1935 shows a profit immediately, while an account begun in 1930 shows an immediate loss and takes about 15 years to move into a profit position.

Obviously, the investor can never be sure whether the market level at any particular time will turn out to be high or low, and there is no ready answer to the problem of the starting date. If the investor who wants to use a constant-ratio formula is to be expected to predict the future direction of the market, then the formula method is not as "automatic" as its supporters claim, and if he is capable of making such a prediction, he doesn't need a formula.

One solution is to combine the constant ratio plan with a dollar averaging approach. Assuming a 50-50 stock-bond ratio has been decided on, 10 percent of the account can be invested in stocks immediately, say, with the account being treated as a 10-90 constant-ratio plan for the first year, after which time the account is adjusted to a 20 percent position in stocks. After another year, the account is adjusted again to a 30-70 proportion, and so on, until it reaches the 50-50 point, in four years. This would not necessarily mean buying exactly the same dollar amount of stocks each time, since market fluctuations would inevitably change the percentages between adjustment points. Let us assume, for example, the investor starts with a $10,000 fund, and buys $1,000 of stocks and $9,000 of bonds. After a year, when he is ready to re-adjust, the market has gone up 10 percent, bringing the value of his stockholdings to $1,100, which makes his total account $10,100. He now adjusts to a 20 percent stock position, or $2,020 of stocks. Since he already holds $1,100 of stocks, he buys $920 more, leaving the bond account at $8,080.

The intervals and percentages used above are arbitrary, of course, and can easily be modified by the investor to suit his own preferences. But this procedure is a solution—and a workable one—although it does delay getting the formula into full swing for some time. The previous chapter on dollar averaging demonstrated the practicality and good results of the technique, and the procedure outlined here is actually the dollar averaging approach applied to a fixed sum of money, except that it stops before putting the investor entirely into stocks. It will be recalled that this was precisely the procedure the New Mexico Investment Council selected for the investment of its Permanent Fund. Only 25 percent of the total portfolio was to be invested in common stocks, with a specific amount to be so invested each month over a period until the 25 percent proportion was reached. After that time, the portfolio was presumably to be operated as a 25-75 constant ratio plan.

Adding new funds to a constant-ratio fund presents no appreciable problems. They may be added at one of the adjustment dates, half in bonds and half in stocks, or added slowly, using a dollar averaging approach.

Improving Profit Performance
Many other such gimmicks have been suggested for improving results of the formula in investing in stocks, but most of them were derived for the purpose of boosting profits during a market period that was already past. There is no reason to believe the improvements cannot be worked out (the writer has one of his own, in fact, which will be unveiled in the final chapter), but most of the trickery that has been used is very much like telling the investor to sell out just before a market break, without letting him in on the secret of when the market breaks are supposed to occur. This type of thing led one caustic commentor on modifications of formulas to observe that they "can reintroduce the principal opportunities for capital and income gain only to the extent to which they permit the return through a back entrance of the 'forecasting element' which they earlier let out through the front door."

The constant-ratio formula can, of course, be modified at will to fit individual needs. One such modified plan was tested on the period from Jan. 31, 1943, to Jan. 31, 1951, a more or less arbitrary set of dates." A $100,000 fund was assumed, established with 33 percent in stocks (since that was the approximate percentage of stocks held in trust funds at the starting date).

The rule for making shifts specified that the market must move 20 percent before a shift would be made. The unusual twist is added by a rule that the original percentage is not to be re-established at the adjustment point, but that if the trend is up, only enough stocks are sold to bring the stock portion down to 36 percent, and if the trend is down, only enough are brought to bring it up to 30 percent. If the trend still goes in the same direction, the next shift will move the stock percentage to 39 percent or 27 percent, depending on direction of the trend. No further upward or downward percentage adjustments are made, if the market continues in the same direction, but at each transfer date thereafter, the 39 percent or 27 percent figure is still observed, but now at every 10 percent move in the market, instead of at 20 percent. But when the market reverses its trend, by at least 20 percent, then the original 33 percent figure for stocks is re-established, and the plan starts all over again.

During the period tested, the total $100,000 account grew to $130,319, while the Dow-Jones Industrials were increasing by over 80 percent. The formula is a conservative one, but does have the advantage of allowing larger purchases of stocks in a wide bull swing. This plan indicates the many variations that may be introduced in the constant ratio principle to suit varying preferences.

Yale And Kenyon
The first widely publicized use of the constant-ratio formula —in the late thirties—was the "Yale Plan," so-called because Yale University managed a part of its endowment fund according to the formula. The fund was started with stocks at 30 percent. If the stocks held advanced to a point where their total value amounted to 40 percent of the total fund, they were cut back to 35 percent. If an advance in stocks again brought the figure up to 40 percent, stocks were to be cut back again to 35 percent. If the market declined—at the beginning of the plan or otherwise—to as low as 15 percent, they were to be brought up to 20 percent.

The plan was subsequently revised at various times to allow for more fluctuations in stock prices, but the principle remained essentially the same, and resembled somewhat the modified plan discussed above, where ratios are adjusted in order to take advantage of trends continuing in the same direction over a long period of time. Yale apparently had fairly satisfactory results with the plan, but has in recent years changed it to such an extent that the University can now be said to have all but abandoned the formula method.

Kenyon College, however, also an early user of formulas, is still using the original plan, but the one it uses has never been, strictly speaking, a formula at all, since its investment committee has always felt free to depart from the plan whenever such a course seemed advisable. The ratio used is 40 percent in stocks, the remainder in bonds, and the plan is not to buy any stocks when the percentage is above 40, or to sell any when the percentage is below 40. When or whether to adjust the portfolio is up to the committee. Investment results have been highly satisfactory since the formula was first adopted about 20 years ago.

Undoubtedly the widest use of the constant-ratio plan in investing in stocks is in large investment portfolios managed by trust departments of commercial banks and investment counselors. Many such investment professionals specify when a management contract is agreed to that the account will contain certain percentages of stocks and bonds, the exact figures depending on the needs of the client. In some cases, adjustments are not made by buying or selling securities already in the portfolio, but only in the disposition of new money which is added from time to time. The obvious advantage of this method under such circumstances is that both the portfolio manager and the client have a clear understanding of the principles according to which the portfolio is to be managed, which can help prevent disputes from arising. This, of course, is in addition to the investment advantages of the technique.

The fact that so many institutions have used the constant-ratio formula—even on an informal basis—is evidence of the valuable guidance that this investment technique can give.