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Q4 2013
BETA, PART DEUX
By Anish Ramachandran, CFA
Last year, I wrote about the metric
Beta and discussed its strengths and
limitations when assessing risk. I
said that Beta is probably the most
abused and misinterpreted concept
in investment valuation because of
is association with the Capital Asset
Pricing Model. I thought that I did
a good job clearing up some of the
common misconceptions related to
Beta, but little did I know that, since
then, I would encounter new ways
that Beta can be misused! In this
article, I will discuss some of these
flawed interpretations and give one
a little background so they can ask
relevant questions regarding risk in
their portfolio.
What is Beta?
At a very basic level, Beta is a number that
describes how the return of an asset is
predicted by market movements, where the
market is typically defined by the Standard
& Poor’s 500 Index. Beta is calculated as the
product of the (correlation between the asset
and the market) x (standard deviation of the
asset I standard deviation of the market).
Correlation (with values ranging between +
1 and -1) is defined as the strength and the
direction of the “linear” relationship between
two variables.
For example, if two figures move in perfect
lock-step with one-another, they would have
a correlation of+ 1.0. If one always has the
opposite movement of the other, that would
be a correlation of -1.0. Standard deviation
quantifies the amount the variation in the
asset’s returns relative to its average. To
illustrate this, if you have two groups with the
same average of 5, but one has components
that range between 4.9 and 5.1 and the other
has components ranging between 2.0 and 8.0,
the second group would be considered to have
a larger “standard deviation” than the first,
as it has a higher degree of dispersion of its
components. Having a basic understanding
of the components will help us refute some of
the common misconceptions regarding Beta.
Let us begin.
Misconception #1: Beta tells us
exactly how much an asset’s return will
change given the return on the market.
On the surface, there seems to be nothing
wrong with the above statement, but many
troubling issues appear when one starts to
dig a little more in how Beta is calculated.
The most common way Beta is calculated
is by using a technique called regression,
where the returns of one asset are compared
to those of the market. The Beta estimate
using this technique can vary with both
the frequency and the length of the data
used. That is, the Beta estimate I get using
monthly return data over five years can be
different from the estimate I get using weekly
data over three years. In addition, how “valid”
each Beta is measured by a statistic called the
R-squared, which tells us what proportion of
the variation in asset returns can be explained
by market movement.
If the R-squared is 1, then 100% of the
variation in the asset returns can be explained
by the market movements. If R-squared is 0.3,
however, then 70% of the variation cannot
be explained by the market movements and
is related to asset specific news. In addition,
every Beta can also be measure in terms of
something called a “standard error,” which
tells us how imprecise our Beta estimate is.
If we estimate Beta to be 1.2 with a standard
error or 0.3, the only precise thing that we can
say about this imprecise measure is that with
95% probability, the true Beta lies between
0.6 and 1.8. Therefore, using one number in
the interval to assess risk can lead to errant
investment decisions.
So, when you see a Beta on yahoo.com, make
sure you take it with a grain of salt – if you
don’t know the corresponding R-squared
or the standard error, the Beta that you are
taking as a fact may be more of a general
range.
Misconception #2: A stock with
a Beta less than 1 implies that it is less
volatile than the market.
This is a statement that I commonly hear
and every time I do, it makes me cringe a
little. For purists, the volatility of a stock is
measured by its standard deviation and not
by its Beta. It is very possible for a stock to
have twice as much standard deviation as the
market but still have Beta less than 1. How is
that possible? All one has to do is go back to
the Beta components discussed above. If the
volatility is twice as much as the market but
the correlation between returns is less than
.5 (or even negative!), the Beta will be less
than 1. When assessing the Beta for a stock,
it is important to understand whether the
Beta is less than 1 because of lower volatility
(continued on next page)
Q4 2013
2
because of a lower correlation. If, in above
statement, we were to replace the word “stock”
with the words “diversified portfolio,” then the
statement would have merit. A diversified
portfolio includes many assets where the
weight of each asset is small, so that the asset
specific risk in the portfolio is minimized. The
risk of a diversified portfolio approximates
the systematic risk of the overall market; i.e.,
the return of the portfolio is a function of the
portfolio Beta and the return of the market.
Therefore, if a portfolio has a Beta of less than
1, it is reasonable to expect it to have lower
variation than the market. A portfolio Beta
of greater than 1 would imply and expected
variation greater than that of the market.
Misconception #3: The Beta of a
portfolio of securities is calculated by
using theportfolios historical returns.
While we are on the subject of portfolio Beta,
it is important to differentiate between the
methods used to calculate Beta of a portfolio
and Beta of an individual stock. The Beta of
an individual stock is commonly calculated
by comparing the stock’s historical returns
to those of the market. However, a portfolio
Beta is not calculated by using historical
portfolio returns. A portfolio Beta is simply
the weighted average Beta of its current
holdings. For example, if we have a portfolio
with the three following components:
symbol
% weight
in portfolio
beta
A
40%
1.2
B
30%
1
C
30%
2
the Beta of the portfolio is calculated
(0.4xl.2)+(0.3x1)+(0.3x2) = 1.38.
This may seem counter intuitive because
there is hardly any similarity between the
Beta calculation method for a stock and a
portfolio, but let me explain with the help
of an example. Let’s say your portfolio only
consists of an S&P 500 index fund. By
definition, the Beta of your portfolio is 1,
since the historical returns of that market
basket are going to be almost exactly equal
in direction and magnitude to the market
that it’s being compared to, differing by only
transaction costs.
Now, as an investor your view changes and
your sell half of your position in your index
fund and leave the proceeds from the sale
in cash. So, your portfolio now contains
50% S&P 500 index fund and 50% cash.
Does it make sense to say that the Beta of
the portfolio is still 1, because that is what
the historical returns tell you that it is? It
seems clear that the current portfolio will no
longer mirror the market moves in direction
and magnitude. The new portfolio will
vary half as much as the market since only
index fund comprises of 50 per cent of the
portfolio, which equates to a current Beta of
.5. Direction - yes. Magnitude - definitely not.
When the current composition of a portfolio
is clearly different from the historical portfolio
the figure was based on, using historical
figures is of limited use in assessing portfolio
risk. This is a much more pronounced in
portfolios that frequently see significant
variations in holdings. For a portfolio that
is always invested in domestic equities, the
swings in Beta are likely to be significantly
less than they would be in a Tactical fund,
which is constantly moving back and forth
between different asset classes.
Conclusion
As one can see, there is still a fair bit of
confusion regarding Beta, its calculation and
its application. The discussion above is clearly
not exhaustive or mathematically detailed.
For more detail, I would recommend looking
at Shannon Pratt and Roger Grabowski’s
book, Cost of Capital. The goal of this article
was to help one ask the relevant questions
regarding Beta so one can better assess the
risk in their portfolio. As a tool for risk
management, portfolio Beta can be a very
important one. At KS&A, we employ a
holistic approach, looking at how each piece
fits into the portfolio as a whole, so that we
can manage the overall exposure to the level
that is appropriate for each client. If you need
more information about how our portfolios
are structured and managed to an appropriate
risk level for each investor, your KS&A
Advisor looks forward to hearing from you.
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