REFS is
a mine of invaluable information for the private investor.
Selecting shares without its help is like trying to
clap with one hand tied behind your back.
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Beta
relative: Worked Example
The beta
relative of a given share is calculated by measuring the volatility
of the share price relative to the volatility of the portfolio
it belongs to. In Company REFS this is the notional market
portfolio represented by the FTSE Actuaries All-Share Index.
To illustrate
the calculation, the table below is based on observations at
regular month-end intervals of the FTSE Actuaries All-Share
Index and the share price of Marks & Spencer PLC over a
two year period (during 1992 and 1993).
Starting
with the first four columns, the table shows at each month-end
the value of the FTSE Actuaries All-Share index in column ‘a’,
the index return (i.e. the percentage change in the index) in
column ‘b’, the M&S share price in column ‘c’, and the share
price return for M&S in column ‘d’. The mean, or average,
values for columns ‘b’ and ‘d’ appear at the bottom as ‘x’ and
‘y’ respectively.
The beta
relative calculation is performed as follows:
Step 1:
Calculate the monthly index variance. This appears in column
‘e’, and is the index return ‘b’ for each month minus the average
index return ‘x’ over the two year period, of +1.56.
Step 2:
Calculate the monthly M&S variance. This appears in column
‘f’, and is the M&S return ‘d’ for each month minus the
average M&S return ‘y’ over the two year period, of +2.22.
Step 3:
Calculate the covariance between the M&S share price and
the index. This appears in column ‘g’, and is the index variance
‘e’ at each monthly interval multiplied by the M&S variance
‘f’. The average covariance of +18.57 is given at the foot of
the column.
Step 4:
Calculate the covariance of the index with itself. This appears
in column ‘h’, and is the index variance ‘e’ for each interval
multiplied by itself. The average covariance of +19.35 appears
at the bottom.
Step 5:
The beta relative is calculated by comparing the average covariance
between the M&S share price and the index, +18.57, to the
average covariance of the index with itself, +19.35, as follows:
+ 18.57
BETA RELATIVE
= ---------- = +0.96
+ 19.35
Beta relative
calculation - worked example:
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