Corporate Finance

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Corporate Finance

Academic studies in the US and Canada have shown that the long-term bonds are not completely riskless.
The government bond returns are positively correlated with stock market returns. That is, government bonds
have systematic risk (beta). The beta of T-bonds in the US is about 0.25. To arrive at riskless rate, the sys-
tematic component of bond yield should be deducted from the prevailing bond yield. To illustrate, suppose
risk premium = 6.7 percent, beta of T-bonds = 0.25, and current bond yield = 5.5 percent.

True risk-free rate = Current bond rate – Systematic component

= 5.5 – (0.25 × 6.7) = 3.81 percent

Estimation of Beta

In the Capital Asset Pricing Model, beta is the sole company specific factor. The estimates of risk-free rate
and market premium are same for all stocks. Beta is the only link between investor’s expected return from
the stock with the expectations of market returns. So the estimate of beta should be accurate. Often academics
and practitioners estimate the historical beta and use it as proxy for the future. The CAPM is supposed to be
a forward-looking model. So, what we really need is ex-ante beta. The standard practice is to regress stock
returns against returns from an index representing the market portfolio. The plot of security returns versus
market returns is called a security characteristic line (a typical characteristic line is illustrated here).

Rj

Rm

Intercept

Each dot corresponds to return from the stock and the market return in that period. A line can be fitted
to the array of points to explain the relationship. The line of best fit minimizes the distance from the dot and
the line.
The regression equation we obtain is of the form:

Rj = a + bRm

where
‘a’ is the intercept,
‘b’ is the beta of the stock,
Rj is the return on the stock, and
Rm is the return on the market index.

To estimate beta, calculate the holding period return for both the stock and the market for some interval of
time.