The Modern Portfolio Theory, therefore, defines the riskiness of a security as its
vulnerability to market risk. This vulnerability is measured by the sensitivity of the
return of the security vis-à-vis the market return and is denoted by the Greek letter beta
(ß). A beta of 2 implies that if the market returns increases of decreases by 10% over a
period, the security return increases or decreases respectively by 20%. Thus in this case
the security return moves twice as much as the market return. A beta of 0.5 on the other
hand implies that the security return moves only half as much as the market does. Market
portfolio which refers to the portfolio consisting of all securities in the stock exchange
has a beta of 1, since such a portfolio behaves like the market index and moves in line
with it. A beta of zero characterizes a risk-free security like a government bond whose
return is almost insensitive to the market return.
Thus beta measures the only kind of risk (the non-diversifiable risk) which matters; the
higher the riskiness of a security, the higher the value of its beta. A security with a beta
value greater than 1 is referred to as an aggressive security and one with a beta value less
than 1 is referred to as a defensive security.
The beta of a portfolio is nothing but the weighted average of the betas of the securities
that constitute the portfolio, the weights being the proportions of investments in the
respective securities. For example, if the beta of security X is 1.5 and that of security Y
is 0.9 and 70% and 30% of our portfolio is invested in the two securities respectively, the
beta of the portfolio will be 1.32 (1.5 X 0.7 + 0.9 X 0.3).
Estimating Beta Values
We have already seen that beta is the sensitivity of the security returns to changes in the
market returns. The statistical method of estimating this kind of dependence of one
variable on another is known as simple linear regression. If we have access to a
computer or to a good statistical calculator, we do not need to known the details of this
statistical technique at all. The machine does the hard work and gives us the results. In
the case of personal computers, the method of linear regression is available in standard
spreadsheet and other software packages.
Simple linear regression, measures the dependence of one variable known as the
dependent or Y variable on another variable known as the independent or X variable. In
our case, the Y variable is the security return and the X variable is the market return.
The security return on any day is defined as:
Today’s return = Today’s price – Yesterday’s price
Yesterday’s priceIf the market was closed yesterday, we must use the price of the previous trading day
instead of yesterday’s price. Instead of the daily returns defined above, we can compute
weekly returns using this week’s and last week’s price instead of today’s and yesterday’s
price in the above formula. Similarly, we can compute monthly returns also.