When learning to invest, note that the progression from constant-ratio formulas to variable ratios is completely logical. Once an investor understands the principles of constant-ratio planning, he might well wonder about the feasibility of adding some flexibility to a formula by increasing the ratio of common stocks when the market is low, and cutting back when the market is high, thus maximizing purchases of stock
at low prices and minimizing risks at high levels.

This is precisely what the variable-ratio plans attempt to do. Understanding the objective is easy—attaining it is somewhat less so. There have undoubtedly been more variable-ratio plans invented than any other type, and a high percentage of them have wound up in the ashcan. Some worked extraordinarily well over a period of time, and then became worthless because of changing conditions in the market. Others were obsolete almost as soon as devised. But variable ratios are by no means dead. On the contrary, at the present time there are probably more formulas of this type in use than any other.

Unfortunately, most of these plans can be used with difficulty, if at all, by the average investor. A good many of them have proved themselves to be of little value, and some of the others are either based on information which is not made public or require more work than most investors care to expend. However, they are presented here for the sake of completeness and to provide the reader with some possible sources of ideas which he may be able to apply to his own investing.

The major snag that variable-ratio inventors run into is the difficulty of deciding what are "low" and "high" markets. The whole success of the technique depends on a more or less successful advance charting of market levels, although it is a general assumption about the future range of prices that is made—not a precise prediction.

While learning to invest, in view of statements earlier in this book about the difficulty of forecasting stock prices, the necessity to do so in variable-ratio plans may seem contradictory. But the difference between the type of assumptions made in these plans about the market and a definite prediction might be compared with the difference between assuming a general range of temperature in New York City over the coming year and making a flat prophecy about how hot it will be at 3 p.m. next Tuesday.
Although methods for determining high and low markets vary from formula to formula, the operating principles are similar in all. In all of them, a "median" or "norm" (the terms are substantially identical, and are used interchangeably in this book) is determined, which refers to a "normal" level of stock prices, as measured by a stock average. Above this it is assumed that the market is on progressively more dangerous ground, and that below it, stocks are increasingly undervalued. Therefore, all variable-ratio formulas call for successive sales of stock above the median, and purchases below. Perhaps a clearer idea can be obtained from the following diagram, which will serve as a general depiction of variable-ratio plans (Figures below the line refer to the stock-bond ratios):
 

75%	50%	25%		25%	50%	75%
Below	Below	Below		Above	Above	Above
Median	Median	Median	Median	Median	Median	Median
80-20	70-30	60-40	50-50	40-60	30-70	20-80

The point on the diagram marked "Median" would indicate the "normal" level of the market, and would correspond to some figure—or range—in a market average. As shown, at this point the portfolio is to consist of half bonds and half common stocks. When the average rises 75 percent above the median, the proportion of stocks is to drop to 20 percent of the portfolio, and bonds rise to 80 percent. At the other points, the percentages of stocks and bonds are supposed to follow the indicated figures. This diagram is intended to give a general picture, and is not based on any particular formula.

The idea of increasing or decreasing the proportion of stocks (as the market crosses a predetermined point or moves into or out of a fixed "zone") applies to all variable-ratio formulas. The 50-50 proportion specified at the median can be changed, according to the needs and tastes of the investor, with other proportionate changes up and down the scale. For example, an investor willing to build more risk into his plan might fix a 65 percent proportion of stocks at the median, ranging from 35 percent at high market levels to 95 percent at the lows.

When learning to invest with variable-ratio plans note that they differ in specifying whether portfolio shifts are to be made when the market enters a "zone" of predetermined width, or when it crosses a point fixed in advance to signal a new stock-bond relationship. In any case, when the market average is between two action points—or within the limits of a zone—the portfolio is to be handled as under a constant-ratio plan, with the ratios determined by the rules of the variable-ratio formula. In the case of the "action point" method, where a ratio shift is indicated by a crossing of the point by a market average, different ratios are specified for the same market level, depending on whether the market crossed the point in an uptrend or a downtrend. This will become clearer as we examine some examples of variable ratios.

Another point on which plans differ is the question of the so-called "halfway rule." This rule stipulates that no purchases or stocks are to be made above the median, and no sales of stocks are to be made below it. For example, in a hypothetical plan based on the diagram above, if the market average happened to rise 75 percent above the median, calling for a 20/80 stock-bond proportion, enough stocks would be sold to bring the percentage of stocks down to 20 percent. If the average were then to fall to 50 percent above the median, theoretically calling for a 30/70 relationship, no stocks would be bought to bring the stock portion of the account up to the indicated 30 percent, if the halfway rule were in operation. No stock would be bought, in fact, unless the market average fell to the median, at which time the stock percentage would be brought up to 50 percent all at once.

As you are learning to invest, it might be interesting to note that apparently the original purpose of this rule was to allow a wide swing in stock prices to run for some time before the investor started chasing it. This would have been a good idea in the 1929-32 crash, when stocks bought even at levels long after the top turned out to have been purchased too soon. But rigorous application of the rule would prevent the investor from taking advantage of any intermediate-term fluctuations in prices. The 1957 market break, for example, carried the Dow-Jones Industrials down less than 20 percent, but the low point represented an excellent opportunity to buy stocks. A serious weakness of the halfway rule is that it tends to immobilize the account for long periods. It is generally agreed that the halfway rule is of little or no value over a period of time, and does at least as much harm to profits as it does good.

As in previously discussed formulas, portfolio changes from stocks to bonds or vice versa may be made at the precise time when the stock index gives a signal, or periodic examination may be made to determine if a change is indicated. Again, the practice of regularly spaced checks is recommended.

Variable-ratio plans fall into three general categories, classified by the method of determining the median. These are (a) trend-line plans, (b) moving-average, plans and (c) intrinsic-value plans. All have proved to be workable at one time or another. Trend line plans have fallen in prestige over the past several years, but the other two continue to be used.

The Vassar Plan
The Vassar Plan, although originally a moving average plan, changed so often while it was in use that it really fits in no single category, and was finally abandoned altogether. However, it was the first variable-ratio formula plan ever to receive wide publicity, is relatively simple in its principles, and will serve as a general introduction to the subject of variable ratios.

The plan was conceived in 1938 at a time when investors were still mindful of the dismal market experiences of the 1929 and 1937 declines. To begin with, the plan was based on "the monthly mean price of the Dow-Jones Industrial Average for the years 1930-38," which was 136.15.1 Therefore, 135 was taken as the median. The percentages of stocks and bonds to be held in the account were to be adjusted after each 10-point drop from this median, and after each 15-point rise. The exact percentages were as follows:

DJIA	STOCKS	BONDS
105	100.00%
115	83.3	16.70%
125	66.7	33.3
135	50	50
150	37.5	62.5
165	25	75
180	12.5	87.5
195	...	100

Adjustments were made only if the market crossed an action point going away from the median, which is another way of saying that the halfway rule was to be followed: no purchases of stocks above the median, no sales below.

The plan assumed, on the one hand, that the market would continue to follow a path similar to the one it traced during the 1930-38 period, but on the other hand it ignored the fact that the Dow-Jones average fell to around 40 in 1932, which is more than 60 percent below the maximum-stock position provided for. Oddly enough, however, the market limits in the plan—105 and 195—turned out to be remarkably close to actual experience for several years. The fund was fully invested in stocks at the low of about 90 in 1942, and was completely in bonds at the high of 212 in 1946. From that point on, the plan ceased to function at all well.

Actually, it was modified during this period to be based on a 10-year moving average of the market index, but the outer limits remained the same. The main difficulty with the formula, clearly, was that the median—and therefore the maximum point at which stocks could be held—was much too low. Also, the restrictions placed on operation of the fund by the halfway rule prevented taking advantage of the fluctuations of the 1947-1949 period, during which time a few profits could have been snagged even though the plan was essentially wrong. The median was moved up to 145 when it became apparent that the fund was being paralyzed by the formula, but this didn't help because the market never fell that far.

Finally, the old formula was given up entirely, and a new method worked out, which is important to know when you are learning to invest. The new method was based on an arithmetic trend, i.e., a trend line drawn on an arithmetic-scale chart of the average, following the general direction of market movement over the years. Since this moved the median only up to 160 (the market missed dropping this low by less than two points in 1949), it was not very effective in improving the formula.

The upshot of Vassar's experience was that the formula method was thrown out entirely, and the investment advisors of the fund now depend exclusively on their judgment. At last report,2 the college had 44.3 percent of its endowment in common stocks, a proportion presumably decided upon independently of mechanical rules.

Trend Line Formulas

CHART 1: The original Keystone channel, based on observed growth of the Dow-Jones Industrial Average from 1897 to 1941. (Supplied by Keystone Custodian Funds.)

Probably the best-known formula plan ever devised is the Keystone 7-Step Plan, shown in Chart 1. When the 7-Step Plan was first devised in 1941 by Robert Warren, the channel lines drawn on a logarithmic-scale chart of the Dow-Jones Industrial Average from 1897 to that year produced an almost perfect fit. It appeared that the upper and lower limits established by these channel lines conformed fairly well with the upper and lower limits of actual market fluctuations, and that the rate of growth of the lines—3 percent annually—was close to what had been the actual secular growth of market prices. The high point of 1929 and the low of 1932 were the only deviations, but this period was felt to be a freak, and not likely to occur.

The channels between the lines form "zones," and the operating principles of the formula dictated that specific proportions of stocks and bonds were to be held in each zone—progressively smaller percentages of stocks in the upper zones, and progressively larger percentages in the lower zones. It will be noted that the upper and lower limits of each zone change constantly from year to year.

As is shown on the chart, the Dow-Jones index rose beyond the upper limit of the channel in 1953, dictating a maximum bond position, and the formula has been largely frozen to the minimum percentage of stocks ever since. Mr. Warren wrote in 1953 that the channel lines should not be redrawn until it was proved that they were wrong.3 In 1957, new channel lines were in fact set up to give a choice of three different growth rates on which to base his portfolio changes.

The second channel, shown in Chart 2, (see p. 60) uses the secular trend beginning in 1934, the year the dollar was devalued and the U.S. economy became a much more money-managed one than had previously been the case. This channel extrapolates a growth rate of 4.4 percent a year.

The third channel is shown in Chart 3, (see p. 61) and begins in 1946, the year of the Employment Act, which sets forth the official U.S. policy of promoting economic growth and full employment. The growth rate is 8.8 percent a year.
 

CHART 2: Revised Keystone channel, based on the growth rate of the DJIA from 1933 to 1957. (Supplied by Keystone Custodian Funds.)

In the brochure explaining the later channels, Keystone refers to the original channel as being suitable for the "conservative" investor, the second for the "middle-of-the-road" investor, and the last for the "optimistic" (or perhaps more speculative) investor.

The investor who wishes to use a formula can thus fit himself into either of the three categories that he feels best describes his investment attitude. He has no assurance that the channel he picks will prove to be the right one, however.

All three plans are alike in that they set up a system of seven "zones"—five precisely marked off between the upper and lower channel limits, plus one each for the areas above and below the channel. Table 6 shows the zone limits for each of the three channels for 1959 and 1960. Notice that the formula does not use a median, as such, but a middle zone which is presumed to be "normal." A definite stock-bond relationship is established for each zone, but here, too, the investor is given a choice. Table 7 presents three sample proportion schedules for the various zones. A 7-Step planner thus can choose among three growth rates, as well as among three portfolio schedules, depending on the risks he is willing to assume.
The operating rules, as explained by Keystone, are numerous, but are the same no matter which of the plans is adopted.

TABLE 6
DJIA ZONE LIMITS
on the Three Keystone 7-Step Plans, 1959-60
 

	PLAN 1 "Conservative"		PLAN 2 "middle-of-the-road"		PLAN 3 "Optimistic"
ZONE	1959	1960	1959	1960	1959	1960
7	Above 363	Above 374	Above 502	Above-524	Above 712	Above 770
6	317-362	326-273	438-501	457-523	621-711	672-769
5	276-316	284-325	381-437	398-456	541-620	585-671
4	240-275	247-283	332-380	346-397	471-540	509-584
3	209-239	215-246	289-331	301-345	410-470	443-508
2	182-208	188-214	252-288	263-300	357-409	386-442
1	Below 181	Below 187	Below 251	Below 262	Below 356	Below 385

CHART 3: Third Keystone channel, based on growth rate from 1946 to 1957. (Supplied by Keystone Custodian Funds.)

TABLE 7
PROPORTION SCHEDULE
for Keystone 7-Step Plans
Percentages of Bonds and Stocks to Be Held in Various Zones.
 

	Schedule 1	Schedule 2	Schedule 3
Zone	Bonds/Stocks	Bonds/Stocks	Bonds/Stocks
7(Top)	90/10	80/20	70/30
6	80/20	70/30	65/35
5	65/35	60/40	57/43
4	50/50	50/50	50/50
3	35/65	40/60	43/57
2	20/80	30/70	35/65
1(Bottom)	Oct-90	20/80	30/70

The zones are numbered from 1 to 7, going from bottom to lop. Zone 1 takes in all the area below the channel, and zone 7 all the area above it. Zone 4 is the middle area. To begin the plan, it is necessary to know not only the current position of the Dow-Jones average, but also its history since it last moved out of Zone 4. If the average is in Zone 5, 6 or 7 (the three top zones) when the plan is initiated, "the account should start with the maximum" bond position required in the "highest zone reached since the average last crossed up through Zone 4." In other words, if the average is in Zone 5, but has arrived there by rising out of the middle zone, into Zone 7, and back down, the stock-bond ratio will be that of Zone 7, not Zone 5 (this is, of course, the operating procedure specified by the halfway rule). Similarly, if the average is in Zone 1, 2 or 3, the account must begin with the maximum stock position called for by "the lowest zone reached since the market last crossed down through Zone 4." If the average is in Zone 4 when the plan is launched, however, the ratios depend on whether the market is falling or rising: if the average rose into the middle zone, the stock portion should be the maximum stock position called for in the lowest zone previously reached by the average; if the average declined into Zone 4, the bond position should be that of the highest zone reached.

Adjustments are made, if called for, at regular quarterly reviews of the account, which is a kind of ongoing way of learning to invest. But the halfway rule is called into service, and no stock purchases are made if the average is above Zone 4, and no sales if the average is below. No action is ever taken while the average is in Zone 4. When the halfway rule prevents selling or buying action, the plan is operated as a constant ratio formula, with the ratio of the last operative zone requirement.

A test of the plan, starting in 1941, when the original channel was first devised, and ending in 1951, was made by Miss Tomlinson,4 with altogether remarkable results. At the end of the 11-year period, value of the account had increased by 81 percent, not counting income. The plan dictated buying stocks heavily at the 1942 low, holding them until the end of 1945, when substantial stock sales were made, thus getting largely out of stocks before the 1946 decline. And some advantage was taken of the fluctuations during the 1947-49 period. When the plan ended, the account was in Zone 6.

Unfortunately, the period during which the plan could show good results ended just around 1951, and if an account had been held intact, the minimum stock position would have been adopted soon after and no further stock purchases would have been permitted. The plan thus would have missed the big bull market of the fifties.

In the first plan, the top zone was reached in 1953, and the trend lines, even though they are moving gradually upward, have still not caught up. In the second plan, the market moved into the top zone about 1955, and has declined below the upper trend line only infrequently since. The market has been below the upper trend line of the third plan for quite long periods.

A glance at Table 6 will show that in both the first and second plans, an account operated under this formula now (late 1959) would be in the minimum stock position. In the third plan, it would be in Zone 6.
Naturally, the Keystone plan came in for some severe criticism when it became fairly apparent that the original channel was obsolete. Considering the unrepresentative nature of the Dow-Jones Index, some commentators were inclined to look on the whole principle as mere hocus-pocus, and the channel lines as so much coincidental doodling on graph paper misinterpreted as some sort of inevitable correlation.

Keystone Custodian Funds is a mutual fund sponsor, and its formula was originally publicized as a help in selling its own mutual funds. Keystone now places little faith in formula plans, and does not emphasize its channels in selling mutual funds.

There are other trend line formulas, but it would be impossible to cover them all. A well-known example is the Oberlin College plan, which established an arithmetic growth trend of about 2.7 points a year in the Dow-Jones Industrials. The trend lines of this plan turned out to be too low, and the formula was abandoned in 1955."'

Moving Average Formulas

The moving average idea is highly logical, but the results that come from it are somewhat less than brilliant. The basic principle is to construct a median from an average of the positions of the market for the past several years. Every time a new year is included in the average, an old year is dropped off. For example, assume that a 10-year moving average is to be constructed in 1961. Take the previous 10 years—from 1951 through 1960, and average the means of the market average for each of the years. Next year, add the 1961 figure, and drop off 1951. Thus the average "moves," and gradually shows the effects of any changes.

The median in a moving average formula works like any other median. This is, lines are set up at intervals of, say, 10 or 15 percent intervals away from the median, which represent points at which the portfolio is to be adjusted.

The principle is admirable, and it seems reasonable to expect that a moving average would, by reflecting the ups and downs of a 10-year period, strike more or less a balance between the extremes, and that this would serve well as a basis for a formula timing plan. Unfortunately, it doesn't quite work out this way in practice.

Tests have been conducted on moving averages of various durations, and the conclusion appears to be that none of them work too well. The shorter the average is, the more violently it swings. The longer it is, the less it fluctuates, and therefore it adjusts to recent changes in the market too slowly.
One moving average formula that has proved itself to be fairly good, however, is the DuPont Institutional Plan, developed in 1947. It was devised by the research department of Francis I. DuPont & Co., a stock exchange house.6

The plan is more complex than most formulas. The median is a 120-month moving average of the monthly mean prices of the Dow-Jones Industrial Average. While it may seem that it is somewhat similar to the moving averages discussed above, and thus shares their weaknesses, the average is actually much more effective. The large number of series serves to flatten out the fluctuations, which cause such serious dislocations of other moving averages. On the other hand, it must follow the market, since new market levels are constantly being included in the median.

The buying and selling techniques are unique, which is noteworthy when learning to invest. When the market rises 10 percent, stock is sold, as in some other plans, but the amount sold is not a fixed amount for each new stage of the market. It amounts to 10 percent of the proportion of stocks held at the previous adjustment point. Similarly, when the market drops 10 percent, 10 percent of bonds held at the last reshuffling are sold and the proceeds invested in stocks. (As set up by the DuPont firm, however, a rise is not treated in the same way as a decline, and bonds are sold at each 9.1 percent drop in the stock market, due to what is referred to as "percentage equivalents." What this does is make a 10 percent rise from one level to another exactly equal to a 10 percent drop from the lower level to the higher. For example, a 10 percent decline from 100 is 10, putting the average at 90, but a 10 percent rise would bring it back to only 99. The "percentage equivalent" takes care of this discrepancy.)

The halfway rule, forbidding sales of stock below the median and purchases above, is included in the plans ground rules.

Another unusual rule is incorporated. If stock purchases are indicated in a falling market, stocks are not bought until the market has risen for two consecutive months, i.e., until the monthly mean price of the Dow-Jones for one month is above that for the preceding month. And if stock sales are called for in a rising market, the sales are made only when the average has fallen for two consecutive months.

The plan worked well at least to the early fifties. DuPont constructed a hypothetical model of an account using the plan, running from 1895 to the end of 1954, in which an initial investment of $1 million grew to over $10 million, not including dividends and interest.

Intrinsic-Value Techniques
The category of variable-ratio plans generally known as "intrinsic value" formulas are without doubt the most sophisticated of all the formula investing techniques. For this reason they are also the most complicated, some of them so much so that they offer little practical guidance to the investor who manages his own portfolio.

Perhaps the simplest of all the intrinsic value formulas is one based on the "central value" method devised by Benjamin Graham, beyond all doubt the most brilliant security analyst in the U.S. The method is presented in his book, The Intelligent Investor.7 It calls for dividing the average earnings on the Dow-Jones Industrials for the past 10 years by twice the current interest rate on Moody's high-grade (Aaa) bonds, and multiplying the resulting figure by 100. Mr. Graham does not actually recommend using the central value as the foundation of a variable ratio formula, but simply as a practice of selling all stocks when the DJIA reaches 120 percent of the central value, and buying back when it dips to 80 percent of the central value. Tests of this technique's practicality have produced excellent results, although, as Mr. Graham points out, "the intervals between signals have at times been so long as to try the investor's patience." A test of the method over the 1924-1953 period showed only seven points at which action is to be taken. The investor who followed the technique would have been out of the market completely from October, 1925, to September, 1931, and after a buy signal indicated in March, 1942, no further action was dictated up to the end of 1953.

It is relatively easy to develop a formula with the Graham central value principle. The central value itself would, of course, be the median, and buying and selling points up and down the scale would indicate varying proportions of stocks and bonds, to avoid the all-or-nothing procedure outlined by Mr. Graham. Such a formula has been worked out, specifying a 50-50 stock-bond ratio at the median, with a 5 percent reduction in stocks at every 10 percent rise above the median and a 5 percent increase in stocks at every 10 percent drop below the median.8 Maximum percentage of stocks is set at 65, and the minimum at 35. Excellent results were shown in the test, which covered the 1926-50 period. Value of the original portfolio nearly doubled, despite the fact that the Dow-Jones Industrial Average increased only about 40 percent.

Although Mr. Graham states the calculations of the central value from 1881 to 1936 "fall quite consistently within the actual price fluctuations during the period," the method has not worked so well recently. At this writing, the central value has for some years been considerably below the actual market level. This has been because stock prices have risen far faster than corporate earnings, and interest rates have also soared.
However, it would be foolish to predict dogmatically that the historical soundness of the theory will never hold true again. The spread between the central value and the Dow-Jones corrected itself in 1929, and it may do so again. At any rate, a formula based on the central value is sound in its basic principles, easy to operate, and—in the past—profitable.

The Birmingham Plan
The First National Bank in Birmingham, Alabama, has used a formula in the management of trust funds for over 15 years, and has over $100 million of funds under formula management.

The median is based on a continuing valuation of earning power of common stocks. Though the basis for the median is book value, the book value is adjusted according to earnings on invested capital, so that the foundation of the median turns out to be more a method of capitalized earnings. To get the median itself, an historical relationship is worked out between market price of a particular stock and its adjusted book value. The median for the Dow-Jones Average is based on separate valuations of each stock in the Average, divided by the current divisor.

The plan was worked out by C. P. Heartburg, trust officer of the bank. Mr. Heartburg expresses complete satisfaction with the formula, despite the fact that the median has tended in recent years to fall below the Dow-Jones Industrial Average. He explains this by saying that there is frequently a considerable deviation between the market and the median, but that the relationship has always tended to fall back into line. He cites as an example the 1937 market, when the average was 70 percent above the median, but later fell to bring the two into closer harmony. Since the mid-forties, the median has had an average annual increase of about 9 percent.

One difficulty with the plan is the disposition of new money added to various funds from time to time. The rules of the formula call for application of the halfway rule, which prohibits buying above the median. This creates a problem, which has to be worked out in each individual case. Various proportions are used in different funds, of course, depending on the type of investor and his needs, and the bank's policy calls for using the plan as a guide, but not as an inflexible rule to be followed under all circumstances. The bank's clients, many of whom have had the formula thoroughly explained to them, are very happy with it—and with its results.

The Templeton, Dobbrow & Vance Formula
A formula has been in use by Templeton, Dobbrow & Vance, Inc., Englewood, N. J., investment counselors, for more than 20 years. It cannot be used by other investors, because the exact nature of its computation has not been made public. The median is essentially a valuation of common stocks, based on such factors as book value, retained earnings and depreciation, plus other factors in the general economy, such as inflation.

The median, as calculated periodically, is a "normal" zone of varying width. In mid-1961, this "normal" zone stood at about 30 percent below the actual market, as measured by a stock average. However, such discrepancies do not worry the firm to any great extent. John Templeton, president, points out that the market has been above the median in about half the months since the formula was first used in 1938, and below the median in the other half, and that discrepancies, of whatever duration, have a habit of correcting themselves eventually.
 

Chart 4 shows the normal zone (shaded area) plotted against Standard & Poor's 425 Stock Average, drawn on logarithmic paper. The arrows marked "S" indicate points at which clients were advised to reduce stock holdings, and the arrows marked "B" are times at which they were advised to buy more stocks. (These arrows are shown only from 1938, when the formula was devised; the chart up to that time is of the hypothetical record.) As the chart shows, the formula pinpointed virtually every top and bottom in the market since it was first begun.

Firm And Client Agree
Most of the portfolios under the firm's management are managed according to indications given by the formula, although the precise manner in which the formula is used varies from account to account. When management of any new account is begun, the firm and the client agree on the levels above and below normal at which the proportions of stocks should be changed, and to what degree. Other features may also be included in the management philosophy of any particular account, such as a stipulation that the proportion of stocks not be changed until after a definite market trend shows signs of reversing itself (as shown by a moving average), or that at no point shall the proportion of stocks be reduced to zero or raised to 100 percent. The formula and its various modifications are described as "non forecasting" programs, which you will need to know as you are learning to invest.

Some portfolios managed by the firm are not under the formula but are—by agreement with the client—invested entirely in common stocks at all times. In others, proportions of stocks are determined by a constant-ratio plan (which the firm calls "constant percentage common stock programs"). The firm also offers to manage clients' investments on the basis of forecasting the general trend of the market, but it does not recommend this approach. Mr. Templeton remains enthusiastic about formula plans in general, and more than satisfied with the success of his own firm's formula. He emphasizes that an essential element in such plans is the avoidance of rigid and inflexible ideas. The TD&V formula has, in fact, undergone some revisions over the years as circumstances warranted, but none of them has apparently changed the basic principles involved.

The Genstein Formula
One of the newest—as well as one of the best—formulas was worked out by Edgar S. Genstein, a New Jersey industrialist (now retired), and made public for the first time in 1954 in his book, Stock Market Profit Without Forecasting." Mr. Genstein devised his formula originally for his own use and as a result of research carried out over a number of years. The copyrighted data for the Genstein Formula are presented here by special permission of Mr. Genstein.

While the Genstein plan compares favorably with many of the more complicated formulas, the median itself is based on readily available data and can be computed by anyone who has a modicum of patience.

In contrast to Graham's central-value median (which is based on earnings), the Genstein current-dividend median uses the historical relationship between market prices and dividends as a standard by which current figures are measured. Three sets of data are required: (1) a 10-year record of the price range of the DJIA, (2) a 10-year record of dividend payments, and (3) the most recent annual dividends. (All these figures are published at irregular intervals in the "Market Laboratory" section of Barron's.)

The median is arrived at in the following steps:
1. Calculate the 10-year average of the quarterly high and low prices for the DJIA. This means adding the highs and lows for each quarter over the most recent 10-    year period, and dividing by 80.
2. Calculate the 10-year average of annual dividends on the DJIA. This is done by adding all the quarterly dividend payments over the past 10 years and dividing by
    40.
3. Divide (1) above by (2) above. This gives the average price-to-dividend ratio.
4. Calculate the dividends paid on the DJIA during the latest four quarters. This is simply a matter of adding the figures for the four most recent quarters.
5. Multiply the result obtained in (3) above by (4) above. This is the median.

Mr. Genstein stresses the importance of using the quarterly figures. This means that, if a plan were to be started in the third quarter of 1959, for example, the dividend and price-range figures will be used from 1950 through 1958, plus the last two quarters of 1949, and the first two of 1959. The median should be brought up to date every three months, as soon as the dividend figures become available, which is shortly after the end of each quarter.

What the plan amounts to is capitalizing current dividends at the rate, which has been determined by the market over the past 10 years. Any changes in the market's opinions about how much should be paid for a dollar of dividend payments will be reflected in the median—not so soon as to cause violent fluctuations in the median, but soon enough to avoid rendering the plan useless while it catches up.

Table 8 shows the calculation of normal value, as well as the actual range of the Dow-Jones, from the beginning of 1948 to mid-1959, using figures supplied by Mr. Genstein. Chart 5 illustrates normal value plotted against the Dow-Jones actual ranges. As shown, the median detected the sharp undervaluation of market prices in reference to their true worth up to the middle of 1952, and again in mid-1953 and at the beginning of 1954. Since that time, the market has pulled gradually away from the median.

Buying and selling in the formula is operated according to a predetermined schedule of price levels set in terms of deviation from normal. Mr. Genstein's studies have indicated that "as far back as definitive figures are available, every major top has been characterized by prices that were at least 1.40 times the computed normal, while every major bottom has been characterized by prices that were at least as low as normal divided by 1.40."10 Mr. Genstein assumes that when price deviations from normal are greater than these 1.40 levels, the market is in a major selling or buying zone. Schedules are set up for future fluctuations of prices to 1.45-1.60 times normal, and normal divided by 1.45-1.60, as shown in Table 9, reproduced from Mr. Genstein's book.11 Four plans are set up, referred to in the table as A, B, C and D, going from the most to the least aggressive.

TABLE 8
THE GENSTEIN FORMULA, 1948-59*

10-Year 10-year Djia       Moving P/D Divs. Normal Range Year *  Average Normal Latest Value Actual Quarter Prices Divs Ratio 12 Mons Djia Djia 1948-1 146.7  - ^  6.91 21.2 X   9.46 201 165-181 2 148.4 7.06 21 9.83 206 177-193 3 149.5 7.19 20.8 10.16 211 176-192 4 150.3 7.49 20.1 11.5 231 171-191 1949-1 151.1 7.65 19.8 11.93 236 171-182 2 152.1 7.79 19.5 12.19 238 162-177 3 152.9 7.88 19.4 12.09 235 168-183 4 153.9 8.16 18.9 12.79 242 182-200 1950-1 155.3 8.32 18.7 13.21 247 197-211 2