might feel inclined to seek even higher returns by taking higher risk. In that case, we
should choose a beta well above one.
Needless to say, in making this assessment about risk, we would have to consider the
expected returns. We know that higher returns are associated with higher risk. During
the last ten years, the average return in the market has been about 10% higher than the
return on risk free securities. This means that the risk premium for a beta of one is about
10%. If our portfolio has a beta of 1.5, we can expect to earn a risk premium of 1.5 times
the market premium, i.e., 15% over and above the risk-free rate of return. If our beta is
only 0.8, the risk premium will be only 0.8 times 10%, i.e. 8%. Considering this risk
return relationship in the light of our attitude towards risk, we can decide on the desired
level of beta. This becomes the target beta as far as we are concerned.
Deciding the Target Duration
We have seen in Chapter 8 that if our holding period matches the duration of a bond, then
the bond is not subject to interest rate risk. Clearly, therefore, the duration of the overall
portfolio must equal our desired holding period.
But we must define the holding period more carefully than we have done so far. In our
numerical examples in Chapter 8, we have assumed that the investor has cash need at
only one point of time which also defines his holding period. In general, however, an
investor or portfolio manager will have cash needs spread over a long period of time. For
example, an investor may say that he has a horizon of 5 years, but he may want to use a
large part of his interest income every year for his regular expenses. Similarly, a mutual
fund may say that the scheme has a life of 5 years, but it too will have to distribute some
dividends every y ear after defraying the management expenses. In both of these cases,
there is a cash need every year in addition to the major cash need at the end of 5 years.
How does duration matching apply to such investors? How do we define their holding
period? The answer is to work out an average holding period taking into account the
timing of all cash needs. It turns out that this average should also be a weighted average
identical to the average which we used in the formula for computing duration. In other
words, the investor must list out all his cash needs at various points of time, and compute
the duration of this stream of cash flows in exactly the same manner as he computes the
duration of a bond. This is his average holding period, and he must design a bond
portfolio which has duration equal to this average holding period. For example, a mutual
fund would have to estimate the annual operating expenses and income as well as the
capital distribution at the end of the life of the scheme, compute the duration of this
stream of cash flows and construct ka portfolio with this duration. The general principle
of duration matching can now be stated as follows: duration of assets must equal
duration of liabilities, or duration of inflows must equal duration of outflows.
Example 1
Consider a Rs.100 Crores mutual fund floated on 01.01.1992 with a life of 7 years. The
fund estimates that its annual outflow on account of dividends, operating and