Read an Excerpt
Professional Perspectives on Fixed Income Portfolio Management, Volume 4
By Frank J. Fabozzi
John Wiley & Sons
Copyright © 2003
Frank J. Fabozzi
All right reserved.
Risk/Return Trade-Offs on
Fixed Income Asset Classes
Laurent Gauthier, Ph.D.
Laurie Goodman, Ph.D.
In fixed-income markets, investors often pay inadequate attention to
the historical risk/return characteristics of different asset classes. Thus,
for example, if one asset class consistently outperforms another on a
risk adjusted basis, then total rate-of-return money managers (whose
performance is measure against an aggregate fixed income index) should
consistently overweight that particular asset class.
In this chapter, we look at the risk/return characteristics of major
fixed-income asset classes over time in order to see if such opportunities
exist. Wewill delve into Treasuries, noncallable Agency debentures,
callable Agency debentures, mortgage-backed securities, asset-backed
securities, and corporates (also referred to as "credit"). For robustness,
we use several risk/return measures, each valuable for different purposes.
Our plan of attack is as follows. We first focus on the Sharpe ratios
for each asset class, then compare those to the duration-adjusted excess
returns (which are returns over the relevant benchmark Treasury securities).
In the second section, we run a principal components analysis to
identify the common factors in the performance of fixed income asset
classes. In the final section, we review a regression analysis of the
returns over the risk-free rate.
Our conclusion is that overweighting spread products over time
pays. Within spread products, mortgages and asset-backed securities
tend to have a very favorable risk/return profile over time.
For this study, we used the total rate-of-return for the components of
the SSB (Salomon Smith Barney) Broad Investment Grade (BIG) Index.
Monthly return data on the major asset classes of Treasuries, mortgages,
Agency debentures, and corporates is available going back well
into the 1980s. However data quality on the callable Agency series
looked suspect in its early years, and data for asset-backed securities
were not available prior to January 1992. As a result, we only used data
as far back as January 1992, and ran it up through March 2003, which
is the most recent available when we were writing this article.
SSB also calculates a duration-adjusted excess return series for each
asset class in their index, which is available back to January 1995. That
particular return series is calculated by subtracting out the weighted
returns on each of the benchmark Treasuries that characterizes each
index, with weightings determined by the partial effective durations.
We began our analysis by calculating the risk/return trade-off (the
Sharpe ratio) for each of the major assets classes. This Sharpe ratio is
given by the following equation:
= Average excess return/Standard deviation of return
= [r.sub.a] - [r.sub.f]/[sigma]([r.sub.a] - [r.sub.f])
where [r.sub.a] is the return on the asset class, and [r.sub.f] is the risk free rate.
We used 1-month LIBOR as the risk-free rate for our analysis.
Exhibit 1 shows our findings. As can be seen, the average return (and
average return over LIBOR) for noncallable Agencies and corporates is
higher than that for the other asset classes (callable Agencies, MBS,
ABS, and Treasuries). However the standard deviation of the return for
both the credit and noncallable Agency categories is so much higher
than that on other asset classes, that their Sharpe ratios end up lower.
Meanwhile, the ABS, MBS, and callable Agency categories have much
lower standard deviations than do the other asset classes. Thus, they
end up with higher Sharpe ratios (0.27 on ABS, 0.24 on MBS, and 0.22
on callable Agencies.)
In fact, the standard deviation of returns is strongly related to the
duration of a security. That is, securities with higher durations will end up
having higher returns when interest rates drop, and lower returns when
interest rates rise compared to their shorter duration counterparts.
Longer duration securities will have a higher standard deviation of
excess returns, due to the historical volatility of interest rates.
However, the problem with using Sharpe ratios as a guide to performance
is that it assumes investors can leverage without limit, and that
money can be freely borrowed ad infinitum at the risk-free rate. Thus along
those theoretical lines investors should lever up shorter instruments rather
than holding the longer duration instruments that constitute a chunk of
SSB's BIG Index. But in reality most total rate-of-return money managers
do have leverage constraints and therefore cannot leverage without limit.
Thus, while Sharpe ratios are certainly one good measure of risk/return,
that should not be the only measure; as portfolios containing only the
asset classes with the highest Sharpe ratios would require more leverage
than most portfolio managers are permitted. Besides, most fixed income
portfolio managers are unwilling to put on a huge curve bet, which
would be implicit in buying leveraged short paper versus non-leveraged
DURATION-ADJUSTED EXCESS RETURNS
A duration-adjusted excess return removes both implicit leverage and
the curve bet. It essentially looks at the return on each asset class versus
what a duration-equivalent portfolio of on-the-run Treasuries would
have provided. The results of such an analysis are shown in the bottom
section of Exhibit 1 (with returns also on a monthly basis). For example,
Exhibit 1's Agency NC return of 0.0555 means that Agencies have,
on average, provided a duration-adjusted excess return of 5.5 basis
points/month. Just as with the Sharpe ratio analysis the ABS and MBS
categories provided the highest excess returns, while the noncallable
credit series provided returns similar to Agency debentures. One interesting
point about this analysis is that callable Agencies look worse than
noncallable Agencies, which is the opposite of results from using Sharpe
ratios. Also, the differential between MBS and Agency noncallables is
much less pronounced than under Sharpe ratios.
The reason for this point of interest is that OAS-based models are
used in determining the partial durations implicit in duration-adjusted
excess return calculations. To the extent that the market does not
behave according to how the models work-there will be a bias in duration-adjusted
Let's now attempt to quantify the effect of this bias that throws
awry the effective duration. Exhibit 2 shows the average effective duration
of each of the indices over our 11 plus-year period, as well as the
latest duration. Obviously, in the current low rate environment, durations
for the callable indices (Agency callables and mortgages) are considerably
shorter than historical averages. Agency bullets are also much
shorter than historically as the GSEs have altered their debt mix over
the last decade, and are now issuing more at the front end of the curve
(where they fund more favorably relative to LIBOR). The third row of
Exhibit 2 is the empirical duration of each of the indices over the period
we looked at. It is calculated as minus the coefficient of the regression of
monthly returns over changes in 10-year Treasury yields. Basically this
measure shows the sensitivity of returns to interest rate levels. Now we
could compare this empirical duration (Exhibit 2's third row) to the
exhibit's first row (average effective duration). But since the interest rate
environment has changed a great deal over the time period covered, and
there have been changes in the indices' composition, such a juxtaposition
would not be very telling.
To pinpoint directionality more accurately via a single numerical
reading, we first constructed a specific measure for the discrepancy
between empirical and effective durations. We used a 2-year rolling window
(12 months of data before the observation + 12 months of data
after the observation) to obtain the empirical duration of returns, which
was expressed as a percentage of the average effective duration over the
same period. To get a specific measure of directionality of durations, we
then regressed the duration discrepancy over the 2-year average of 10-year
Treasury yields, with our measure of directionality taken from the
slope of that regression.
Our results are shown in the bottom row of Exhibit 2, and we have
a handy intuitive interpretation that aids in understanding the results.
For example, the coefficient for duration directionality on MBS is 12%,
which suggests that a 100-basis-point rally would shorten the duration
by 12% more than would be suggested by option-adjusted spread (OAS)
models. Note that duration directionality is extremely low for both
Agency bullets and for Treasuries, as would be expected. It is also
higher for MBS and callable Agencies than for ABS. The only surprise
may be the result listed for corporate bonds. However, realize that periods
of low rates tend to be correlated with times of crises, during which
corporates typically underperform. Thus, corporates should behave as if
they have a shorter duration during time of low yields.
This produces a bias in the average duration adjusted returns. Since
the market has rallied over the period under consideration, the SSB
average duration adjusted excess returns on the sections with high duration
directionality are biased downward. This helps explain the weaker
performance of ABS, MBS, and callable agencies on the duration
adjusted excess return measures versus those using Sharpe ratios.
The row just before the end of Exhibit 1 captures the standard deviation
of excess returns. The conclusions are somewhat obvious: Treasuries
have a very low standard deviation of excess returns (as we are
simply capturing the on-the-run versus off-the-run basis), while the
credit series has a very high standard deviation of excess returns (as
duration alone is inadequate, since it only explains part of the return
variability). The standard deviations for MBS, ABS, and callable and
noncallable Agency series lie between those two extremes.
The last line of Exhibit 1 shows (duration-adjusted excess returns)/
(standard deviation of these returns). We do not regard this number as
particularly useful, as it overstates the standard deviation of sectors with
high duration directionality, and hence understates the attractiveness of
these sectors. Even so, some market participants do look at this measure.
FIXED INCOME RETURNS, BY ASSET CLASS
To try to figure out what factors are important in determining excess
returns and duration-adjusted excess returns, we ran a principal components
analysis. The factors, or "components," emerging from that process
can then be matched to market factors to "explain" performance.
Exhibit 3 shows the results of our principal component analysis.
1. Let's look first at the top part of the exhibit, which "explains" nominal
returns. Note that the first component explains 92.7% of the variation
and looks exactly like the exposure to interest rates (duration). Note
also that the order of magnitude of the coefficients on each of the indices
looks very much like the average duration given in Exhibit 2.
Exhibit 4 confirms this, showing a scatter plot of the return on Factor 1
versus the change in the 10-year Treasury yield. Factor 1 has a very
clear linear relationship to changes in interest rates. Identification is
provided in Exhibit 5, which looks at the correlation of each factor to
various market measures (such as the slope of the 2-10 spread; 5-year
cap volatility, etc.). Looking across the row labeled "Factor 1," we see
that the 10-year yield has a correlation of -89% to the first factor of
2. The second most important factor in "explaining returns" by asset
class is the credit specific factor. This alone explains another 3.1% of
the nominal returns, which brings the cumulative total part
"explained" up to 95.8%. Our identification of this factor was relatively
easy-a high negative weighting on the credit index combined
with a high positive weighting on Treasuries. Exhibit 6 confirms this
identification, showing a strong relationship between Factor 2 and
the S&P 500; and our correlation analysis in Exhibit 5 confirms this
intuition as well. Factor 2 has a correlation of -50% to the S&P 500.
Note: The weight on the credit index is -0.82, indicating that the
lower the S&P 500, the lower corporate bond returns will be, and
3. The third aspect explaining returns by asset class is very clearly an
optionality factor. Note that the coefficient on the assets classes that
have some optionality (callable Agencies, MBS, and ABS) is positive,
while the coefficient on the noncallable series (Treasuries, noncallable
Agencies, and credit) is negative. Optionality actually involves several
market factors, such as the shape of the curve and volatility. Exhibit 5
shows that the optionality factor has a very positive correlation with
curve slope, but a negative relationship with 5-year cap volatility. This
suggests that the steeper the curve (the slope), the better a callable
series should do (as the options that have been implicitly written are
now more out-of-the-money). The higher the volatility, the lower the
return on the callable series. Exhibit 7 confirms the negative relation-ship
between Factor 3 and volatility. Because the shape of the curve is
also quite important, the relationship between volatility and Factor 3 is
slightly less clear than it was between the first two factors. But the significant
point is that the three factors together-Treasury yields, credit,
and volatility-explain 98.1% of the variation in nominal returns of
aggregate fixed-income indices.
We now turn to explaining the duration-adjusted excess returns.
These are actually much harder to "explain," as we have already eliminated
changes in interest rates (which we just showed to be the most
important factor, accounting for 92.7% of return variation).
1. Look first at the coefficients on Factor 1 in the bottom section of
Exhibit 3. It is very clear from these that the most important factor is
one governing all spread product.
Excerpted from Professional Perspectives on Fixed Income Portfolio Management, Volume 4
by Frank J. Fabozzi
Copyright © 2003 by Frank J. Fabozzi.
Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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