Computing an Average

In order to properly manage and track the trends you will identify, you will need to compute averages. The average helps to smooth out your graph so that the trend represents a general movement rather than an individual aberration. Without averages, trends often look like random and uncertain movements.

To demonstrate how averages help to clarify a trend graph, we will use the example of current ratio.

Example: You have tracked the current ratio over the past three years, with each quarter's ending current ratio listed as follows:

FIGURE 7.1 Scaling of Graphs

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Period                                          Ratio

1:    year 1, first quarter                2.4-to-l

2:    year 1, second quarter            2.3-to-l

3:    year 1, third quarter               2.1-to-l

4:    year 1, fourth quarter             2.2-to-l

5:    year 2, first quarter                2.0-to-l

6:    year 2, second quarter           2.1-to-l

7:    year 2, third quarter               1.9-to-l

8:    year 2, fourth quarter             2.1-to-l

9:    year 3, first quarter                1.8-to-l

10:    year 3, second quarter            1.6-to-l

11:    year 3, third quarter               1.4-to-1

12:    year 3, fourth quarter             1.5-to-l

This listing of current ratios, by itself, would be difficult to interpret if that was as far as the trend analysis went. Figure 7.2 represents this history in scaled graphic form. Note that the ratio value of 2-to-l is at the midpoint of the graph. This is the proper scaling for this ratio, because 2-to-l is the standard. Any ratio at or above that level is considered positive; anything below that level is negative.

FIGURE 7.2 Current Ratio Trend

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From this graph, you can see that the trend is negative. Clearly, the trend shows a deterioration in the current ratio over the past three years.

The trend would be clearer still if reduced to overall averages. The list of current ratios can be expanded to include the average current ratio for the entire period. The following is such a listing. The last column represents the average for the entire period being studied. Thus, the second period's average involves adding together the first two periods, and dividing by 2, while the twelfth period's average involves adding together all 12 periods, and dividing by 12.

F

Period

 

Ratio

Average

1

year 1,

first quarter

2.4-to-l

2.40-to-l

2

year 1,

second quarter

2.3-to-l

2.35-to-l

3

year 1,

third quarter

2.1-to-l

2.27-to-l

4

year 1,

fourth quarter

2.2-to-l

2.25-to-l

5

year 2,

first quarter

2.0-to-l

2.20-to-l

6

year 2,

second quarter

2.1-to-l

2.18-to-l

7

year 2,

third quarter

1.9-to-l

2.14-to-l

8

year 2,

fourth quarter

2.1-to-l

2.14-to-l

9

year 3,

first quarter

1.8-to-l

2.10-to-l

10

year 3,

second quarter

1.6-to-l

2.05-to-l

11

year 3,

third quarter

1.4-to-l

1.99-to-l

12

year 3,

fourth quarter

1.5-to-l

1.95-to-l

Note that as the averaged period increases, changes have less effect on the overall average. That is because with more periods being averaged, the latest entry's change has less overall influence on the total. It is safe to presume that, given a long enough field of values, the effect of a new entry would be minimal or nothing.

The effect of the overall average on the trend is shown in Figure 7.3.

The point about larger numbers of fields is shown here. Note that as the averaging period grows, the effect of a deteriorating trend is shown, but only minimally. Even so, the comparison between straight ratios and overall average makes our point dramatically.

e KEY POINT

The larger the entries in a field to be averaged, the less effect each entry has on the overall average.

FIGURE 7.3 Current Ratio Trend with Average

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In this figure, we used a simple average. It involves adding together a field of values; there may be only two, or a dozen, or even hundreds. The total is then divided by the number of fields involved. As you saw in the previous example, the greater the number of entries in the field, the less impact the latest entry will have.

The formula for simple average is shown in Figure 7.4.

FIGURE 7.4 Simple Average

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FIGURE 7.5 Moving Average

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Simple average is the kind of formula most people think about when they talk about an average. However, for the purpose of studying fundamental information over a period of time, simple average might not be the most efficient or reliable measure of outcomes. You do not desire the leveling out effect achieved with averaging when a large number of fields is involved. A volatile situation should appear volatile on your graph.

With this in mind, you will find it more convenient to employ a variation of averaging, called the moving average. This is a form of averaging in which the field size remains the same; and it is updated with each new value entry. As a new value becomes available, it is added into the field, and the oldest value is dropped off.

The formula for moving average is summarized in Figure 7.5.

The moving average involves two steps, as shown in the illustration. First, the initial average is computed by defining the field size; adding the values; and then dividing by the number of values in the field. Second, the oldest value is dropped off and the newest value is added on. In the formula, this is indicated by subtracting "A" and adding in "E."

Referring back to the list of current ratios, let's assume that you were to apply a moving average calculation using three periods. The calculation would be as follows:

 

 

Moving

Period

Ratio

Average

year 1, first quarter

2.4-to-l

 

year 1, second quarter

2.3-to-l

 

year 1, third quarter

2.1-to-l

2.27-to-l

year 1, fourth quarter

2.2-to-l

2.20-to-l

year 2, first quarter

2.0-to-l

2.10-to-l

114        Mastering Fundamental Analysis

Moving

Period                               Ratio        Average

year 2, second quarter        2.1-to-l       2.10-to-l

year 2, third quarter           1.9-to-l       2.00-to-l

year 2, fourth quarter         2.1-to-l       2.03-to-l

year 3, first quarter            1.8-to-l       1.93-to-l

year 3, second quarter        1.6-to-l       1.83-to-l

year 3, third quarter           1.4-to-1       1.60-to-1

year 3, fourth quarter         1.5-to-l       1.50-to-l

In this example the average line would be dramatically different than that used for the simple average. You will recall that the simple average called for the use of divisors equal to the number of periods, so with a higher number of periods, there was a leveling out. Compare the average line in Figure 7.3 to that in the moving average, shown in Figure 7.6.

The average as represented in this latest version, using moving average, is more representative of what is occurring in the trend. For that reason, moving average is the more reliable method of the two.

FIGURE 7.6 Current Ratio Trend with Moving Average

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eKEY POINT

The selection of a representative moving average is more useful than an overly large simple average.

Another consideration may be that, because the latest entry in the trend is more relevant, it should be given greater weight than older, outdated data. The justification for this belief is that with financial results, the latest information has greater relevance to the test of investment value. With this in mind, you can adjust the computation of average in many ways. The weighted moving average is a popular device in charting and in trend analysis.

One method involves first identifying the field to be tested in the moving average. For example, we showed what occurs with a moving average using a field of three values. Then weight the values according to your formula. You may give the latest entry a value of two, with older values each having a value of one. Then a field of three values would be divided by four. (The latest entry is included twice, so it adds another divisor.) Another method involves giving the current value a weight of 3; the second a weight of 2; and the oldest a weight of 1. Under this method, the total would be divided by six.

Referring back to the same example as before, the worksheet shown in Figure 7.7 can be used for calculating the weight, and then for doing the calculation.

The worksheet is set up for flexibility. Below are two renditions of weighted moving average, both using the previously introduced current ratio results. In the first example, weighting involves using only the latest three values. The most recent is given a weight of "2" while the others are given a weight of "1."

Period
Value
Weight

Weighted

Value
Total
year 1, first quarter 2.4-to-l
2
4.8
 
year 1, second quarter 2.3-to-l
1
2.3
 
year 1, third quarter 2.1-to-l
1
2.1
9.2

 

The next step involves dividing the total by 4, which produces a weighted moving average as of the end of this period, of 2.3-to-l.

FIGURE 7.7 Weighted Average Worksheet

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The second method calls for weighting the latest period with "3" and the second latest with "2," while the oldest is given a weight of "1."

Period
Value
Weight

Weighted

Value
Total
year 1, first quarter 2.4-to-l
3
7.2
 
year 1, second quarter 2.3-to-l
2
4.6
 
year 1, third quarter 2.1-to-l
1
2.1
13.9

Next, the total is divided by six, for a weighted moving average of 2.3.