Risk management for a leveraged trading desk

Practical implications

This section draws some practical conclusions from the above analysis, and briefly
sketches some suggestions about risk measurement and risk management policy;
more detailed proposals may be found elsewhere in this book.
Since parallel and slope shifts are the dominant yield curve risk factors, it makes
sense to focus on measures of parallel and slope risk; to structure limits in terms of
maximum parallel and slope risk rather than more rigid limits for each point of the
yield curve; and to design flexible hedging strategies based on matching parallel and
slope risk. If the desk as a whole takes proprietary interest rate risk positions, it is
most efficient to specify these in terms of target exposures to parallel and slope
risk, and leave it to individual traders to structure their exposures using specific
instruments.
Rapid stress testing and Value-at-Risk estimates may be computed under the
simplifying assumption that only parallel and slope risk exist. This approach is not
meant to replace a standard VaR calculation using a covariance matrix for a whole
set of reference maturities, but to supplement it.
A simplified example of such a VaR calculation appears in Table 5.3, which summarizes
both the procedure and the results. It compares the Value-at-Risk of three positions,
each with a net market value of $100 million: a long portfolio consisting of a
single position in a 10-year par bond; a steepener portfolio consisting of a long position
in a 2-year bond and a short position in a 10-year bond with offsetting durations, i.e.
offsetting exposures to parallel risk; and a butterfly portfolio consisting of long/short
positions in cash and 2-, 5- and 10-year bonds with zero net exposure to both parallel
and slope risk. For simplicity, the analysis assumes a ‘total volatility’ of bond yields
of about 100 bp p.a., which is broadly realistic for the US market.
The long portfolio is extremely risky compared to the other two portfolios; this
reflects the fact that most of the observed variance in bond yields comes from parallel
shifts, to which the other two portfolios are immunized. Also, the butterfly portfolio
appears to have almost negligible risk: by this calculation, hedging both parallel and
slope risk removes over 99% of the risk. However, it must be remembered that the
procedure assumes that the first three principal components are the only sources
of risk.
This calculation was oversimplified in several ways: for example, in practice the
volatilities would be estimated more carefully, and risk computations would probably
be carried out on a cash flow-by-cash flow basis. But the basic idea remains
straightforward. Because the calculation can be carried out rapidly, it is easy to
vary assumptions about volatility/yield relationships and about correlations, giving
additional insight into the risk profile of the portfolio. Of course, the calculation is approximate, and in practice large exposures at specific maturities should not be
ignored. That would tend to understate the risk of butterfly trades, for example.
However, it is important to recognize that a naive approach to measuring risk,
which ignores the information about co-movements revealed by a principal component
analysis, will tend to overstate the risk of a butterfly position; in fact, in some
circumstances a butterfly position is no riskier than, say, an exposure to the spread
between on- and off-the-run Treasuries. In other words, the analysis helps risk
managers gain some sense of perspective when comparing the relative importance of
different sources of risk.
Risk management for a global bond book is harder. The results of the analysis are
mainly negative: they suggest that the most prudent course is to manage each
country exposure separately. For Value-at-Risk calculations, the existence of a ‘global
parallel shift’ suggests an alternative way to estimate risk, by breaking it into two components: (a) risk arising from a global shift in bond yields, and (b) countryspecific
risk relative to the global component.
This approach has some important advantages over the standard calculation,
which uses a covariance matrix indexed by country. First, the results are less
sensitive to the covariances, which are far from stable. Second, it is easier to add
new countries to the analysis. Third, it is easier to incorporate an assumption
that changes in yields have a heavy-tailed (non-Gaussian) distribution, which is
particularly useful when dealing with emerging markets. Again, the method is not
proposed as a replacement for standard VaR calculations, but as a supplement.