Heterogeneous unwinding periods and liquidity risk

As mentioned in the previous subsection a realistic risk assessment needs to incorporate
the various unwinding periods present in a portfolio. If a position takes 5 days
to liquidate, then the 1-day VaR does not fully reflect the potential loss associated
with the position. One approach to incorporating liquidity effects into the VaR
calculation involves associating an unwinding period with each instrument. Assuming
that changes in the portfolio’s value over non-overlapping time intervals are
statistically independent, the variance of the change in the portfolio’s value over the
total time horizon is equal to the sum of the variances for each time-horizon interval.
In this way, the VaR computation can be extended to incorporate liquidity risk.
Example
Consider a portfolio consisting of three securities, A, B, and C, with unwinding
periods of 1, 2, and 5 days, respectively. The total variance estimate is obtained
by adding a 1-day variance estimate for a portfolio containing all three securities, a
1-day variance estimate for a portfolio consisting of securities B and C, and a 3-day
variance estimate for a portfolio consisting only of security C.
The above procedure is, of course, a rather crude characterization of liquidity risk
and does not capture the risk of a sudden loss of liquidity. Nonetheless, it may be
better than nothing at all. It might be used, for example, to express a preference for
instrument generally regarded as liquid for the purpose of setting limits.