Example 4
Consider the asset allocation of Example 2. What happens to the overall beta and
duration if there is a sharp rise in interest rates and bond prices drop by 20%?
Solution
Asset class Original
percent
Original Value Current value Current
percent
Bonds 80 80 64 68
Equities 20 20 30 32
Total 100 100 94 100
The average duration of bonds was 5 years and of equities 30 years. We shall assume
that the average beta of the equities was 1.0. We assume for simplicity that the rise in
interest rates has not significantly changed the average duration of the bond portfolio.
Original duration = 5 x 80/100 + 30 x 20/100 = 10 Years
Original beta = 0 x 80/100 + 1 x 20/100 = 0.20
Current duration = 5 x 68/100 + 30 x 32/100 = 13 years
Current beta = 0 x 68/100 + 1 x 32/100 = 0.32
The second question is more fundamental. Does the choice of a target beta mean that we
should always maintain our portfolio beta at this target value? Not necessarily. Our
portfolio beta should hover around this target value, but, in the short run, it may deviate
quite substantially from this target value. If, for example, we feel that a slump in the
market is around the corner, we might want to temporarily switch over to a defensive
portfolio which provides us some protection in case of such a slump. A defensive
portfolio is a portfolio whose beta is low (less than one); since beta measures the
vulnerability to market risk, such a portfolio suffers less loss when the market slumps.
Obviously, when we switch over to such a defensive portfolio, our beta will be below our
target value. But this position is temporary; at the earliest opportunity, we would try to
restore it to our target value. Correspondingly, if we accept a boom in share prices, we
might temporarily switch over to an offensive portfolio. An offensive portfolio is a high
beta portfolio(beta above one) which is very sensitive to the market index and, therefore,
appreciates greatly when the market booms.
To summarize, therefore, our attitude towards risk determines our target beta, i.e. the long
run value of beta around which our portfolio beta would tend to fluctuate. Our view of
the market would determine the short run fluctuations in the portfolio betas as we switch
to offensive or defensive portfolios to exploit anticipated market movements in the short
run. In exactly the same way, our view about the likely changes in interest rates can
cause us to temporarily change the overall duration beta and duration of our total
portfolio.