Cosmos-Japan: A Case Study

Cosmos-Japan, designed for managers of Japanese fixed income portfolios, is the latest addition to The BARRA Cosmos System™, BARRA's suite of fixed income applications. The Cosmos System also includes Cosmos-Global, for risk analysis of global fixed income portfolios, and Cosmos Global Optimizer, for global portfolio construction. U.S. coverage will be added to the Cosmos System this year. (See related articles in this Newsletter.)

Analyzing portfolio risk

In order to illustrate the capabilities of Cosmos-Japan, we will first create a sample portfolio (called "DEMO") of 50 assets, each with a holding (par value) of 100 million yen, for a total portfolio value of 5.48 billion yen (see Figure 1). The portfolio has been constructed to include representative assets from all sectors of the market. In the following case study, imagine yourself as a manager in charge of this portfolio, responsible for understanding its risks and controlling them against a benchmark.

Figure 1: Cosmos-Japan Initial Portfolio screen

Cosmos-Japan provides risk profiles of a portfolio with respect to a variety of BARRA-provided Nikko benchmarks as well as user-defined benchmarks. Here we analyze the risk of our portfolio versus the overall Nikko Bond Performance Index (NIK_BPI). The NIK_BPI, like our DEMO portfolio, contains assets from all sectors, but it is constructed in a more systematic manner: It is built to capture effects from relevant sectors, combining them into a complete model that describes the state of the Japanese bond market.

To analyze our portfolio against the NIK_BPI, we first specify our benchmark type and name, as shown in the Portfolio screen (see Figure 1). We then perform a risk analysis by selecting Risk from the Analysis menu, which takes us to the Risk Summary page. From here we can drill down to the Risk Decomposition screen (see Figure 2), which shows us summary numbers for the portfolio and benchmark, their risks, and the portfolio's active risk (tracking error). We see that our DEMO portfolio has an overall volatility of returns of 3.67% in annual terms, compared with the NIK_BPI's 4.62%. DEMO's active risk, or tracking error, is 1.11% per annum. The tracking error—the predicted standard deviation of the portfolio's return against the benchmark—tells us that the portfolio's annual return should fall within 1.11% of the NIK_BPI with a two-thirds probability.

Figure 2: Cosmos-Japan Risk Decomposition report

Portfolio risk decomposition

We can break down these risks into their subcomponents: sensitivity to interest rates (Term Structure), sector and quality spreads (Spread), specific issues in the portfolio (Specific), and the volatility and covariances of these factors (Covariance), as shown in Figure 2. From this Risk Decomposition report we see that our DEMO portfolio is underexposed to Term Structure risk with respect to the NIK_BPI but overexposed to the Spread factor, which is an accumulation of deviation-from-par, on-the-run, government, and sector and quality spreads.When we drill down to gain a detailed understanding of term structure risk, we see that our portfolio is less exposed to shift and twist volatilities of the term structure than the NIK_BPI (see Figure 3). This is a result of the portfolio having lower duration and convexity than the benchmark, a fact which is indicated elsewhere in Cosmos-Japan.

Figure 3: Cosmos-Japan Term Structure Risk Breakdown report

Taking our analysis further, we can examine the exposure to non-term-structure risks. Figure 4 displays the portfolio's sector exposure versus the NIK_BPI. The portfolio is underweighted in the Government sector compared with the benchmark but is overweighted in the Utility and Municipal sectors. Most of the risk of the Government sector is due to term structure effects as well as the spreads for six-year and mid-term (two to four years original time-to-maturity) government bonds. Non-government sectors, like Corporate and Municipal, have unique sector spreads corresponding to their spreads with respect to the government term structure. Our portfolio is overexposed to the Municipal, Utility, Corporate, and Samurai sectors (and therefore exposed to changes in the corresponding spreads for the Municipal, Utility, and Corporate sectors).

Figure 4 also displays useful information on our percentage of value duration. Every sector's percentage of the portfolio's value is multiplied by the duration of assets in that sector and then compared with the corresponding number for the benchmark. Note that our portfolio has a shorter duration than the benchmark in almost all sectors except Samurai. But viewed in terms of active exposures, we see that we are taking positive bets on not only the Samurai sector but also the Municipal, Utilities, and Corporate sectors.

An interactive, Windows-based tool, Cosmos-Japan offers these features: Portfolio management, including bond swaps and deriatives (futures and options on bond futures) Evaluation of portfolio positions in absolute terms as well as versus the Nikko Bond Performance Indexes (NIK-BPI) and/or customizeduser indexes, including liability streams Analysis of asset and portfolio risk using BARRA's factor model Valuation of assets and portfolios using a combination of sector, quality, and interest-sensitive spreads Daily and monthly BARRALINK updates of prices, market conditions, and terms and conditions (monthly only) Asset and portfolio return projections from multiple user-defined scenarios Complete constituent coverage of the Nikko Bond Performance Indexes plus additional assets

Figure 4: Cosmos-Japan Sector Risk Breakdown report

Being short duration will translate into superior performance for someone betting on a parallel increase in rates. For example, Figure 4 shows that we are 2.91% underexposed to the Government sector compared with the benchmark. This would indicate, roughly, that if there were a 100-basis-point positive shift in the yield curve, we would outperform the benchmark by 2.91%. We will have achieved this performance by virtue of a smaller bet on the Government sector (only 8% of our portfolio, compared with 60% of the benchmark's) and a slightly shorter duration of our assets in this Government sector (5.37 versus 5.56 for the benchmark).

Reducing tracking error

Having done due diligence on our portfolio's risk analysis, we can next turn our attention to reducing the tracking error (active risk) between the portfolio and the benchmark. Let us assume that our intention is to track the large NIK_BPI of some 2,625 assets with our 50-asset DEMO portfolio. Being conscious of transaction and management costs, we prefer a smaller portfolio to track the NIK_BPI.

Cosmos-Japan offers a simple but powerful means to do this. The "Marginal contribution to Tracking Error" (MCTE) analysis shows, for each security, how much the tracking error would change if 1% more of the portfolio were invested in that security. For instance, as shown in Figure 5, we can see that an additional 1% investment in the Tohoku Electric bond would reduce our portfolio's tracking error by 11.67 basis points. Of course, since we want to keep the portfolio value constant, we cannot simply increase our holding by 1% without surrendering a corresponding value in some other security.

Figure 5: Cosmos-Japan Marginal Contribution Ranking report

With Cosmos-Japan we can easily perform this MCTE trading of assets. Figure 5 displays the Marginal Contribution ranking of the most and the least diversifying assets in the DEMO portfolio. Our current tracking error is 1.11 (see Figure 2). In order to reduce it, we need to accumulate assets with greater diversification. For example, we can sell some of the Tokyo Metropolitan bond, which has an MCTE of -0.13, use the proceeds to buy more of the Tohoku Electric issue, and thereby reduce our projected tracking error.

Cosmos-Japan offers a pictorial "what-if" depiction of our MC Trade options. After selecting the "trading out" security Tokyo Metropolitan, clicking on the MC Trade button takes us to the Marginal Contribution Trade screen shown in Figure 6—which graphically depicts the effect of trading out of Tokyo Metropolitan to any other security (including cash). When we choose Tohoku Electric as the "traded to" security and the amount of 1% of Tokyo Metropolitan to be traded, its portfolio weight drops from 1.84% to 0.84%. In line with this value drop, our holding of Tohoku Electric increases from 100 million to 153 million. We can now click on Trade to execute the decision.

Figure 6: Cosmos-Japan marginal Contribution Trade (MC Trade) report

Cosmos-Japan then recomputes the portfolio risk and comes up with new forecasts (see Figure 7). We see that our trade has reduced the tracking error—giving us an active risk of 0.99%, compared with the previous Figure of 1.11%. Also notice, comparing Figure 7 with Figure 2, that our trade has increased the portfolio's total term structure and spread risk.

Figure 7: Cosmos-Japan Risk Decomposition report after MC trade

Bond swaps

Cosmos-Japan provides a convenient tool for exploring "what-if" analyzes for bond swaps, controlling for par amount, value, value duration, barbell, and butterfly. Suppose we expect a flattening of the yield curve and want to "buy" convexity. To accomplish this, we can execute a "barbell" trade—where we intend to preserve the yen duration and value of our DEMO portfolio by trading in one security (S) for a pair of other securities (B1, B2).¹

For instance, if we swap out of Sumitomo 3.1% 2002 and purchase a Kansai 5.05% 1998 and a Hokkaido 3.1% 2006, Cosmos-Japan calculates the holding of both the "buy" securities (Hokkaido and Kansai) required to fulfill the requirements of the barbell swap (see Figure 8). In the swap tables we see that with this trade we pick up 44 basis points of yield and 7 basis points of option-adjusted spread (OAS), while maintaining the same value and duration. Moving to a barbell also increases the convexity by 0.11 compared with a bullet of the same duration.

Figure 8: Cosmos-Japan Bond Swap screen: Barbell swap

Derivatives

Cosmos-Japan also provides derivatives such as bond futures and options on bond futures: 5-, 10-, and 20-year JGB (Japanese Government Bonds) bond futures and options on these bond futures are all available within the system.

To illustrate one application of these derivatives, assume that we want to reduce active exposure to interest rate changes. The hedge ratio is:

From our starting portfolio (see Figure 1), we will attempt to achieve a target duration of the benchmark's (NIK_BPI's); our portfolio has an active duration exposure of -1.37. We will use a JGB 5-year bond future as the hedging instrument. Figure 9 (first row) displays the summary numbers for the JGB 5-year future starting from 06/20/97. The duration of the future is 2.71, the price (as percent of par) is 1.1429, and the nominal value of a JGB 5-year bond future is 100mm yen. The hedge ratio is then 24.24.² In other words, we will need to buy 24 contracts to achieve this target duration. Going long on a future translates into going long duration. The effect of adding these 24 future contracts on our portfolio's duration is shown in Figure 10: Our duration differs from the benchmark's by only -0.01.

Figure 9: Cosmos-Japan: Adding futures

Figure 10: Cosmos-Japan: Effect of futures on duration

Summary

As we can see from the previous examples of only a subset of Cosmos-Japan's features, The BARRA Cosmos System™ helps fixed income portfolio managers to manage portfolios, control risk, and develop portfolio strategies. Additionally, Cosmos-Japan offers money managers the capability of "stress-testing" their portfolios with their defined scenarios of changing term structure and sector/quality spreads. Finally, Cosmos-Japan informs trading and hedging strategies required to maintain a portfolio's desired risk characteristics.

Footnotes

¹ The swap specification is:
N_SP_S = N_B1P_B1 + N_B2P_B2 and
N_SP_SD_S = N_B1P_B1D_B1 + N_B2P_B2D_B2
where N = number of bonds, P = dirty price (price plus accrued), and D = duration. (return to text)

² (-5.48 billion yen · -1.37) / (100 million yen · 2.71) = 24.24 (return to text)