The following article is reprinted from the January, 1997 issue
of On the Edge, the Interactive Data Fixed Income Analytics bimonthly newsletter.
The Tracking Summary and Value-At-Risk
Wesley Phoa, Ph.D.
President of Research
BondEdge offers a comprehensive set of
tools for monitoring and controlling portfolio risk at a highly detailed level. However,
at a management level it is often useful to step back from all this detail and to get a
view of the overall risk of the portfolio. This capability is provided by the Tracking
Summary report, available through the Compare subsystem of the Structured Products module.
This report can show:
- relative risk, arising from potential tracking error; or
- absolute risk, comparable to VAR (value-at-risk).
The calculations use the four-factor duration framework which forms the basis of the
Compare subsystem. In this framework, market risk is broken down into the following four
components:
- Parallel yield curve risk
- Non-parallel yield curve risk
- Corporate spread risk
- Pass-through spread risk
There is a duration measure corresponding to each kind of risk. Four-factor durations
are computed for both the user's portfolio and the relevant bond index. This enables
BondEdge to compare portfolio and index returns under any given scenario, where a scenario
consists of (1) a parallel shift, (2) a slope shift, (3) a shift in corporate spreads and
(4) a shift in MBS spreads - all occurring over a predetermined time horizon.
To compute relative risk, the Tracking Summary in essence compares portfolio and index
returns under 174=83,521 different market scenarios, and hence calculates
confidence levels for return differences. To compute absolute risk, one simply substitutes
an empty portfolio for the bond index. This has zero return under any scenario, so in this
case the Index Tracking Summary computes confidence levels for absolute returns - this may
be interpreted as a value-at-risk measure for the portfolio.
The Tracking Summary differs from a standard value-at-risk calculation in a number of
ways. Notably, it can measure relative risk versus a benchmark as well as absolute risk,
and it is designed to handle nonlinear return profiles - this is essential when dealing
with option-embedded bonds, which can have highly skewed returns.
Some examples will help explain the meaning of the calculation. Consider a typical
portfolio containing Treasury and corporate bonds and mortgage-backed securities. The
Tracking Summary versus the Lehman Aggregate Index might look like:
PORTFOLIO VS. SLAG |
- - - - - - - MONTHS - - - - - - - |
| |
|
(3) |
(6) |
(9) |
(12) |
| 10% C.L. |
0.59 |
0.87 |
1.10 |
1.31 |
|
| 25% C.L. |
0.37 |
0.56 |
0.72 |
0.87 |
|
| MEAN |
|
0.06 |
0.12 |
0.18 |
0.24 |
| 75% C.L. |
-0.32 |
-0.41 |
-0.47 |
-0.51 |
|
| 90% C.L. |
-0.58 |
-0.79 |
-0.93 |
-1.04 |
|
For example, this means
that over a 12-month horizon, we can be 90% confident that the portfolio return will be no
worse that -1.04% relative to the index; i.e. it has a worse relative performance under
only 10% of all possible scenarios. On the other hand, there is a 25% chance that it will
outperform by at least 0.87%.
The Tracking Summary versus an empty portfolio might look like:
PORTFOLIO VS. SLAG |
- - - - - - - MONTHS - - - - - - - |
| |
|
(3) |
(6) |
(9) |
(12) |
| 10% C.L. |
3.43 |
5.89 |
8.19 |
10.40 |
|
| 25% C.L. |
2.75 |
4.92 |
7.00 |
9.03 |
|
| MEAN |
|
1.77 |
3.53 |
5.30 |
7.07 |
| 75% C.L. |
0.68 |
2.00 |
3.42 |
4.90 |
|
| 90% C.L. |
-0.08 |
0.93 |
2.11 |
3.38 |
|
This means that over a
3-month horizon, we can be 90% confident that the portfolio will have a negative absolute
return of no worse than -0.08%. On the other hand, there is a 25% chance that it will have
a return of 2.75% or more.
To ensure that it is an objective measure of portfolio risk, the Tracking Summary makes
strictly market neutral assumptions: it weights each scenario by its probability, based on
historically computed volatilities for the level and slope of the Treasury curve, and the
level of corporate and MBS spreads. Since historical correlations tend to be quite
unstable, the Tracking Summary currently makes the simplifying assumption that all
correlations are zero. However, to allow users to assess the impact of changing
correlations, risk computations using non-zero correlations will be implemented in a
future release.
It must be reemphasized that the Tracking Summary only provides an overview. Potential
tracking error and value at risk are tools for high-level risk control; for detailed
portfolio management, sharper measures are required. In a strategic context, the
Probability Weighted Scenario tool lets investors analyze portfolio risk in the context of
their own market views, and the Compare subsystem offers many other tools for breaking
down risk in the four-factor duration framework. At a security level, the advanced risk
measures computed by BondEdge can provide valuable guidance.
