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Fully-worked
illustration
The following
illustration shows how the consensus is calculated for a range
of broker forecasts of earnings per share. Each forecast is
date-weighted over 180 days, giving maximum emphasis to the
most recent forecast, and reducing progressively to zero emphasis
for a forecast six months old.
(NOTE:
When calculating the date-weighting, the reference point used
is midway between first publication date and the latest reconfirmation
date.)
First,
a date-weighted average is established to determine the
standard deviation of the eligible forecasts. This, in
turn, enables any outlying forecasts to be identified, and excluded.
Finally, a date-weighted average of the remaining forecasts
is taken to be the consensus.
A total of
nine brokers are providing forecasts in this example, and the
range is as follows:
Date-weighted
average:
The first
stage is to calculate a date-weighted average of all the forecasts
as follows, giving a result of 35.5p. The working figures
are shown beneath:
Step 1:
Date-weight each forecast by its age in days, subtracted from
180.
Step 2:
Add together the weighted EPS forecasts.
Step 3:
Divide the sum of the weighted EPS forecasts, 38442.5, by the
sum of the
weights,
1085, to find the weighted average EPS, 35.5p.
This can
be summarised as follows:
SUM OF THE
WEIGHTED
EPS FORECASTS
WEIGHTED AVERAGE
-------------------------
= EPS (p)
SUM OF THE
WEIGHTS
Working
figures:
38442.5
DATE-WEIGHTED
AVERAGE EPS = --------- = 35.5P
1085
Note that
the forecast from Broker 'A' gets zero weighting on account
of its age, being more than 180 days old, and is therefore excluded.
Standard
deviation:
Next,
the standard deviation is calculated so that outlying forecasts
can be identified. The calculation gives a result of 1.33p,
and involves four steps to establish the root mean square of
the deviations from the weighted average, as follows:
Step 1:
Calculate the deviation of each forecast from the weighted average
Step 2:
Calculate the square of each deviation
Step 3:
Find the mean of the squared deviations
Step 4:
Calculate the square root of the mean to give the standard deviation
The following
table illustrates how the standard deviation is derived from
the data in the example. The number of brokers is now eight
(one having been excluded by age of forecast) and the weighted
average EPS is 35.5p:
TOTAL OF
THE SQUARES OF EACH DEVIATION = 14.07P
MEAN OF THE
SQUARED DEVIATIONS
(14.07 DIVIDED
BY 8) = 1.76P
STANDARD
DEVIATION (SQUARE ROOT OF 1.76) = 1.33P
Note that
in order to lie within one standard deviation of the weighted
average, the forecasts in the above example must remain within
the range 35.5p + or - 1.3p, namely between 34.2p and 36.8p.
Brokers 'D'
and 'G', forecasting 38.8p and 34.0p respectively, are therefore
regarded as outlying forecasts, and are excluded from the final
consensus along with Broker 'A', whose forecast, being more
than 180 days old, is excluded already.
Consensus:
The consensus
is taken to be the date-weighted average of the remaining forecasts,
having excluded those which are old or outlying. The final calculation
is therefore as follows, giving a consensus EPS of 35.1p.
The working figures are shown beneath:
Step 1:
Date-weight each qualifying forecast by its age in days, subtracted
from
180.
Step 2:
Add the together the weighted EPS forecasts (27546.1p)
Step 3:
Divide the sum of the weighted EPS forecasts, 27546.1, by the
sum of the
weights,
784, to give weighted average EPS, 35.1p
This can
be summarised as follows:
SUM OF THE
WEIGHTED
EPS FORECASTS
WEIGHTED AVERAGE
--------------------------
= EPS (p)
SUM OF THE
WEIGHTS
Working
figures:
27546.1
CONSENSUS
EPS = ----------- = 35.1p
784
See Foreign
income dividends for further explanation.
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