management costs would amount to Rs.17.5 crores. Suppose that the rate of interest is
18%. What is the target duration for this mutual fund?
Solution
The target duration is the duration of the outflows calculated as follows:
Date Outflow
(Rs. Crores)
PV of Outflow
at 18%Year PV X Year01.01.1992 17.5 14.83 1 14.83
01.01.1993 17.5 12.57 2 25.14
0 1.01.1994 17.5 10.65 3 31.95
01.01.1995 17.5 9.03 4 36.11
01.01.1996 17.5 7.65 5 38.25
01.01.1997 17.5 6.48 6 38.90
01.01.1998 117.5 36.89 7 258.20
98.09 443.37
Target Duration = 443.37/98.09 = 4.52
We would like to add, however, that duration matching is not an end in itself. It is a
powerful tool for protecting the bond portfolio from interest rate fluctuations, but some of
us will want to assume part of the interest rate risk in the hope of getting higher returns.
It is often true that assets with longer duration than our desired holding period offer
higher returns. We will then have to decide whether this additional return is worth the
extra risk that we assume. The extent of duration mismatch then becomes a measure of
risk that we are taking. The investor’s attitude towards risk thus plays an important role
in deciding on the extent of duration mismatch and therefore the target duration of the
overall portfolio.
Portfolio Design: Achieving Target Beta and Duration
We have already pointed out that the three main asset classes differ widely in terms of
their duration and beta. Equities have high beta and long duration, bonds have negligible
beta and moderate duration, and money markets have negligible beta and near zero
duration. It is clear that by adjusting the proportion of these three asset classes in our
portfolio, we can achieve a very wide range of values for the overall beta and duration.
This range is even further enhanced if the investor can borrow and invest the borrowed
funds in addition to his own funds. For example, if the investor borrows Rs.100 and adds
that to his own funds of Rs.100 and invests Rs.200 in an equity portfolio with a beta of
1.00, his overall portfolio beta is actually 2.00. This is because his total portfolio is
Rs.100 (Rs.200 of equities less Rs.100 of beta), and his equity portfolio is 200% of his
total portfolio.