Portfolio Duration
Overview
Hedging with Duration
Hedging
refers to the process of trading instruments in
a portfolio in order to make the portfolio immune to
fluctuations in the interest rate curve.
This definition of duration and convexity hints how to
hedge a fixed income portfolio. If we assume that interest
rates change in a continuous fashion, we can assume that
over a given short interval, the change in the bond yield
will be small, that is {% \Delta y %} is small. In this
case, the Taylor approximation to the change of the function
using only the first two terms (the duration and convexity
terms) is fairly accurate. This means we can ignore the
higher order terms and we get:
{% P(y_1) - P(y_0) = (y_1 - y_0) \times \frac{dP}{dy} + \frac{1}{2} (y_1 - y_0)^2 \frac{d^2P}{dy^2} %}
In particular we have truncated the higher order terms. Then,
to have a hedged portfolio is to say that the change in the price of the
bond is approximately zero.
In particular, we want to
rebalance the portfolio
