Portfolio Management in Cosmos-U.S.

by Mark Davis

This year BARRA will release the first phase of Cosmos-U.S., our new Windows-based portfolio management system for U.S. fixed income. Cosmos-U.S. is the U.S. module of The BARRA Cosmos System™, BARRA's suite of fixed income applications. This first release focuses on tools for analyzing the risk of single portfolios and multiple portfolios. Subsequent releases will bring performance attribution, scenario analysis, and optimization into the Windows environment, as well as making available a flexible report writer. This article explores some of the benefits of the new product from the perspective of an active separate account manager.

Controlling account dispersion

Suppose your firm has just landed a new account, to be evaluated by your client against a Government/Corporate index. You already have several accounts for the same product and have articulated an active strategy using a model portfolio. So, while your external benchmark is the public index, you are most concerned about how this new account looks compared with the model portfolio (and, by extension, to the existing accounts). You want to minimize the difference in return between the new and existing portfolios.

First, you can use the portfolio group analysis to compare the portfolios along the dimensions that are most important to you. Cosmos-U.S. allows you to define groups of portfolios, either as a static list (unchanging) or a dynamic list (changing according to selected criteria, such as portfolio manager, or benchmark). You can then view the portfolios in the group either separately or as an aggregate (for example, bringing together portfolios managed by sector specialists). In the current case, you will want to view the group of portfolios managed by you against the ALL_GCY index, and you will want to view them separately.

Figure 1 shows one such comparison. It displays the sensitivity of the new account (ACME), the existing accounts (ACUMEN, ALPHA, APEX), the model portfolio (MODEL), and the public index (ALL_GCY) to three types of term structure movements. By comparing the three existing accounts and the model portfolio, you can evaluate how well the existing accounts are tracking each other and the model portfolio. By comparing the model portfolio to the index, you can describe the strategy embodied in the model portfolio. And by comparing the new ACME portfolio with the existing accounts, you can assess how the new account will behave relative to the existing accounts.

Figure 1. Cosmos-U.S.: Comparison of the sensitivity to shift, twist, and butterfly movements for the new account (ACME), the existing accounts (ACUMEN, ALPHA, APEX), the model portfolio (MODEL), and the external benchmark (ALL_GCY).

Comparing the three existing accounts and the model portfolio reveals that the existing accounts should track each other and the model portfolio well, given any type of term structure movement. Comparing MODEL with ALL_GCY reveals several things about the strategy of the model portfolio. First, the strategy is to be a bit shorter than the index, as shown by the lower exposure to shift, which measures sensitivity to parallel movements of the term structure. Second, the strategy is designed to benefit from a flattening of the term structure, as shown by the lower twist exposure, which measures the impact of short rates rising and long rates falling. Finally, the strategy will underperform if short and long rates rise and intermediate rates fall, as shown by the greater butterfly exposure.

Comparing the ACME portfolio with the existing accounts shows that it has a similar sensitivity to shift, meaning a similar sensitivity to parallel movements of the term structure. If we had compared only the durations of the portfolios, we would probably not be too concerned about the new account tracking the existing accounts. But examining the twist and butterfly exposures shows that the term structure risk of the new account is somewhat different from the existing accounts, with greater exposure to twist and lesser exposure to butterfly.

Figure 2 provides additional insight into differences between the term structure exposures of the same portfolios. It shows the contribution to portfolio duration from different regions of the term structure, a measure of what part of the curve contributes the most to the interest rate sensitivity of each portfolio. As with many of the views in Cosmos-U.S., users can customize the displayed information to fit their way of looking at things. In this case, curve regions are user-defined.

Figure 2. Cosmos-U.S.: Comparison of the contribution to duration from different parts of the curve for the new account (ACME), the existing accounts (ACUMEN, ALPHA, APEX), the model portfolio (MODEL), and the external benchmark (ALL_GCY).

Once again, the existing accounts are in line with the model portfolio, and the strategy discussed in Figure 1 becomes clearer. The model portfolio has more of its duration at the short and long ends of the curve than the ALL_GCY index, and less in the intermediate region. In other words, it embodies a barbell strategy. As in Figure 1, ACME diverges from the existing accounts, most notably by having more of its duration in the 7-year to 10-year part of the curve and less in the long end, consistent with its greater exposure to twist and lesser exposure to butterfly.

One additional dimension of comparison worth exploring is the sector exposures of the portfolios, as shown in Figure 3. For the same group of portfolios, it highlights the percentage of portfolio value in each of four major market segments: MBS, Treasuries, Corporates, and Yankees. Once again, the existing accounts do a good job of mimicking the model portfolio strategy. The salient aspects of that strategy, as evidenced by a comparison of MODEL and ALL_GCY, are an overweighting in MBS (the index has none) and an underweighting in Corporates and Yankees, as a result of the tightness in Corporate spreads. Once again, ACME is different from the existing accounts, having a significantly greater portion of its value in Corporates and Yankees and a smaller portion of its value in Treasuries.

Figure 3. Cosmos-U.S.: Comparison of the percent of market value in major market segments for the new account (ACME), the existing accounts (ACUMEN, ALPHA, APEX), the model portfolio (MODEL), and the external benchmark (ALL_GCY).

The value of a risk model

Now you know that the new account is different in certain ways from the existing accounts. What is not clear is how important those differences are. In order to assess that, it is useful to quantify the combined effect of all those differences based on how important each difference is and how they interact with each other. A risk model lets you do just that.

Now you can run a risk analysis on the new account, using the model portfolio as the benchmark for comparison. Figure 4 shows a summary of such an analysis. This view provides a high-level understanding of the portfolio. The upper left-hand corner gives the portfolio value, the upper middle section displays sector and quality exposures, the upper right-hand corner quantifies portfolio volatility, the middle row shows the largest bet in each of the main areas of our risk model, and the lower section provides aggregate characteristics for the portfolio and its benchmark. From this high-level view, you can selectively drill down to explore whatever interests you; each button takes a different path to a greater level of detail.

Figure 4. Cosmos-U.S.: Summary risk analysis for the new account, using the model portfolio as a benchmark.

Since our goal is to quantify the impact of the differences between ACME and the model portfolio, let's focus on the upper right-hand corner. By combining the information about portfolio and benchmark exposure to factors in our risk model with our understanding of the volatility of those factors and the way in which they interact, we gain important insights. On the one hand, we see that the new portfolio and the model portfolio are comparably volatile, as shown by their respective risk—or annualized standard deviation—numbers (5.34% and 5.29%), and the portfolio relative volatility of 102%. At the same time, this volatility must result from somewhat different kinds of exposures, because the portfolio has an active risk or tracking error of 40 basis points. This means that, in approximately two out of three years, the ACME portfolio's return should be within plus or minus 40 basis points of the model portfolio's. This is probably not an acceptable range of possible dispersion given your initial goals.

Before exploring the sources of that active risk, it is worth focusing on the quantification of Value-at-Risk also included in this risk section. This calculation translates the portfolio volatility from a standard deviation or return number into a dollar amount at risk, for a given confidence level. The details of this calculation are user-defined—in this case, the number reflects dollars at risk for a one-year horizon and a 5% confidence level. Given its present structure, there is a 5% chance that ACME portfolio will lose more than %8.6 million of its value over the next year. But what are the sources of the new account's active risk? By clicking on the Risk Decomposition button you can drill down to a breakdown of the sources of risk. Figure 5 provides a graphical representation of that decomposition. The top half compares the absolute volatility of ACME and the model portfolio due to different sources (Term Structure, Sector, Quality, and Other), and the lower half shows the active risk due to each source. Predictably, term structure factors cause most of the absolute volatility of each portfolio. But what we did not know before is that the biggest source of tracking error is the difference in sector exposures between the two portfolios.

Figure 5. Cosmos-U.S.: Decomposition of the sources of absolute risk for the new account and the model portfolio, and of active risk or tracking error between the two.

We can drill down further from the Risk Decomposition level to gain a better understanding of this sector active risk. Figure 6 shows how the new account differs from the model portfolio with respect to sector bets, both in terms of value and in terms of exposure, or contribution to duration. It shows this information at two levels: user-defined aggregate market segments and sectors in the risk model (for example, the exhibit expands the Corporate segment to also show the BARRA sectors). As expected, the biggest differences are the underexposure to Treasuries and the overexposure to Corporates. If we want to identify Corporate bonds we might want to sell, we could drill down even further to view a list of the assets included in that segment. In fact, Cosmos-U.S. allows users to drill down to the asset level in all screens where the assets in the portfolio are grouped. From the asset list, we can perform individual asset analysis on any selected security.

Figure 6. Cosmos-U.S.: Sector exposures for the new account and the model portfolio.

Instead, you can use the power of the risk model to identify the trades that will most efficiently reduce the tracking error of the new account relative to the model portfolio. Figure 7 shows the two windows that will accomplish this. The top window (partially obscured) gives you a ranking of the assets by their marginal contribution to tracking error. The most diversifying assets, on the left, can help you reduce your tracking error if you increase their weight in the portfolio; the least diversifying assets, on the right, are already the biggest source of tracking error, and will increase it further if you add to these holdings. The lower window graphically shows the impact of trading between the most diversifying asset and one of the least diversifying assets. If you increase the Treasury bond's weight from 0.99% to 1.99% of the portfolio, while reducing the Hydro-Québec bond's share from 1.24% to 0.24%, you should expect to see the new account's active risk decreased by approximately 4 basis points (-0.79 for buying the Treasury and -3.21 for selling the Hydro-Québec). Push the Trade button and that's exactly what happens: All of the risk views are updated to reflect the trade, and the Risk Summary screen now shows a tracking error of 36 basis points. You can continue trading this way as long as necessary.

Figure 7. Cosmos-U.S.: Ranking of assets by their marginal contribution to tracking error (partially obscured) and analysis of a tradeÕs impact on tracking error.

Summary

This article has touched on only a few of the many features of Cosmos-U.S. We have designed this system to allow you to focus on the information you care about, present it in the way you want to see it, and leverage the power of a rigorous analytical framework that is applied consistently across all asset classes. These tools will allow you to make better informed investment and trading decisions.