deciding on the target beta and duration, let us first show how the overall portfolio beta
and duration can be computed.
The beta of bonds and of money market instruments is negligible. Thus this risk affects
only the equity portfolio. The beta of the total portfolio equals the beta of the equity
portfolio multiplied by the proportion of the portfolio which is invested in stocks. For
example, if 70% of the total portfolio is invested in an equity portfolio which has a beta
of 1.2, the beta of the total portfolio is 0.70 X 0.12 = 0.84.
Interest rate risk on the other hand, affects not only bonds but also stocks. Changes in the
interest rate do affect stock prices principally through a change in the Price/Earnings
Ratio. It can be shown that for stocks
Market Price (MP) 1
Duration = ------------------------------------------ = Dividend yield
Dividend per share (DPS)
Where dividend yield equals DPS/MP. Since typically dividend yields are in the range of
3 - 4%, the typical duration of stocks is 25-30 years. Equity turns out to be the longest
duration asset available in the capital market with a duration exceeding that of the long-
term bonds.
Money market instruments are at the other end of the spectrum – their duration is
virtually zero. Some of these instruments may have a duration of 6 months or so (for
example, 182 day T-bills), but for all practical purposes, the average duration of the
money market portfolio as a whole can be taken as nearly zero.
Once again, we can compute the duration of the total portfolio as the weighted average of
the duration of its components. For example, if a portfolio is 30% equity, 5% in money
market and 65% in bonds with average durations of 25 years, 0 years and 4 years
respectively, the duration of the overall portfolio is 0.30 X 25 + 0.05 X 0 + 0.65 X 4 =
10.10 years.
Deciding the Target Beta
The most important consideration in deciding on the portfolio beta is the investor’s
attitude towards risk. The cautious investor who desires a stable source of income would
usually choose a beta below one. One the other hand, the aggressive investor would want
to seek out higher returns (at the cost of higher risk!), and would choose a beta above
one. The most practical methods of making such an assessment is to examine the
behaviour of the stock market index for the last 10 years or so. The fluctuations in the
market index shows how the value of our portfolio would have behaved if our portfolio
had a beta of one. If we find that this degree of fluctuation suits us fine, we would
normally choose a beta close to one. If, however, we feel that this degree of ups and
downs in the portfolio value is unacceptably high, we should consider choosing a beta
below one. On the contrary, we might find that this level of risk is not at all serious, and