Select the attribution framework that suits your investment process. BarraOne offers a highly flexible Allocation-Selection attribution methodology that can be applied to portfolios of any asset class, including balanced and multi-asset class funds.
BarraOne provides a large universe of popular equity and fixed income benchmarks pre-loaded into the platform and ready to be used. Barra risk models are developed by a cross-functional team of mathematicians, statisticians, financial engineers and investment industry experts. MSCI's research, data management and production departments consists of more than professionals, who are constantly monitoring new securities, global market shifts and industry trends in every major world market.
Data accuracy, a crucial piece of risk modeling, is one of the elements that sets Barra risk models apart. Barra Research Methods Diagnostics on Term Structure Estimation The estimation algorithm identifies bonds with large pricing errors and eliminates them.
This is done by an iterative process. First, a term structure which includes all bonds is estimated; bonds with pricing errors above a threshold are discarded. Then the estimation runs again. This procedure is repeated until there are no more bonds with large pricing errors.
We use a set of automated diagnostics to identify potential problems with the term structure estimation. Large daily or monthly changes are investigated. The root mean square pricing error is also computed. All other things being equal, this statistical quantity tends to increase with the number of bonds in the universe. In the U. Treasury term structure estimation, for example, there are approximately bonds and the root mean square error ranges between 30 to 50 basis points.
Although the number itself has no definitive interpretation, abrupt changes in its value are useful for flagging problems in the estimation. It minimizes the differences between market and fitted prices in the term structure.
Since the model price Q i depends on the term structure, changes in term structure give rise to changes in E1. The fitting routine works by moving rates until the minimum difference between fitted price and market price is found. Smoothing Function E2 Because term structures produced with only E1 in the objective function may have idiosyncrasies due to noise in the data or a mismatch between the data and the location of vertices, a second term, E2 , is included.
Short-End Shape Correction E3 The universe of bonds used to determine the term structure excludes bonds with remaining time to maturity under one year. These bonds tend to be relatively illiquid, hence their prices do not reflect current rates. As a result, there is generally not enough information in the objective function to reliably determine key rates under one year.
This problem can be handled in some markets by adding treasury bills or equivalent assets to the estimation. Therefore, the shape of the LIBOR term structure is used as an indicator of the shape of the short end of the government term structure.
Instead, we impose the assumption that the ratio between the government and one-year LIBOR rates is roughly constant for the short end of the term structure. This assumption is imposed with the addi- tion of a third term to the objective function, which is: EQ 1. For example, Japan and the United States have treasury bills. The 1-, 3-, and 6-month, and 1-year LIBOR rates are used to determine the short end of the term structure in the fixed-income risk models.
The weights on E1 are larger than the weights on E3, so if short bonds are available, they will be used to determine the short end of the term structure. For example, if treasury bill informa- tion is available, the resulting low E1 weights would de-emphasize the E3 term in the estimation. Treasury Term Structure 5 Because treasury bill information is available for the U. Treasury bill rate 2 1 0 0 5 10 15 20 25 30 35 Maturity in Years Maturity Factor Shape Determination The spot rate covariance matrix can now be generated from the historical term structure.
A time series of month-over-month dif- ferences in spot rates is first created for each of the standard verti- ces. From these time series, we obtain the key rate covariance matrix. The eigenvectors of this matrix, or principal components, correspond to uncorrelated movements of the term structure. In markets with a large number of bonds representing a broad spectrum of maturities such as the nominal U. In IPB markets, fewer factors are rele- vant.
Generally speaking, IPB markets consist of a small set of bonds with long maturity. For simplicity, we treat the shift factor in these real market as a uniform, parallel shift of the term struc- ture.
The twist factor—if present—is then the leading source of risk residual to the parallel shift. Only the U. IPB markets have a twist factor in addition to the shift factor. The absolute sizes of the factors are not determined. If a factor is scaled by a constant c, the exposure of a portfolio to this factor is scaled by c as well.
The shift factor is roughly a parallel change in interest rates. For non-callable bonds, therefore, the exposure to shift should be a number comparable to effective duration. The magnitude of the shift exposure can be controlled by changing the size of the shift factor. By convention, the factors are normalized so that their mean-squared value is the number of vertices a true parallel shift is normalized at a constant 1 and so that they are positive at long maturities.
The base shift is normalized so that the shift exposure is comparable to effective duration. The base twist and butterfly factors are normalized to have the same magnitude as the shift. For more details see, for example, Richard A. Johnson and Dean W. Wich- ern, Applied Multivariate Statistical Techniques, 4th ed. Factor Exposure Calculation Term structure factor exposures are computed by numerical differ- entiation.
The exposure of a bond or portfolio to a risk factor is the sensitivity of its value to changes in the factor level. For exam- ple, effective duration is the sensitivity of value to a parallel shift of interest rates. The term structure is shocked, or shifted up and down, by a small scalar multiple of the STB factor, and the bond is revalued.
In other words, we calculate how the price of a bond changes for a given change in the yield curve. The annualized numbers are obtained from the Twist In Butterfly The off-diagonals show the correlations between Butterfly Covariance Matrix Correlation In principle, factor returns can be estimated from a regression of changes in term structures onto the factors.
This simple method- ology results in a diagonal covariance matrix in sample. Therefore, we rejected this method. Regression based on bond returns, on the other hand, not only accounts for uneven distribution, but also changes dynamically with the distribution. Nonzero correlations of small magnitude would result from a difference be- tween the risk analysis date and the date at which the factors are fixed.
The bond-return regression used to estimate the factor returns,1 the initial smooth- ing process applied to the factors, and the out-of-sample factor returns contribute to the correlations.
Table Correlations Between U. These correlations carry information important to risk forecast- ing. As long as the correlations are not perfect, the explanatory power of the model is not compromised. For the U. The term structure is estimated on a daily basis, but the covari- ance of the risk factors is estimated on a monthly basis.
We run a cross-sectional regression on the asset returns for the previous month. This generates factor returns we use to update the covari- ance matrix.
The precise base forms of the shift, twist, and butterfly factors depend on the estimation period, smoothing technique, exponen- tial weight, and other details. Since the key rate matrices evolve slowly, factor re-estimation requires occasional, rather than fre- quent, review and re-estimation. Bond-return regression is the main contributor to the non-trivial correlations between the factors. Spread Risk Modeling In the past, international bond mangers focused largely on gov- ernment bond issues, which were the constituents of the domi- nant global fixed-income indexes.
Recently, managers have increased the exposure of their global fixed-income portfolios to corporate and agency bonds, foreign sovereigns, supranationals, and credit derivatives. These bonds are subject to spread risk.
Market-wide spread risk arises from changes in the general spread level of a market segment. For example, the spreads of BBB-rated telecom bonds might widen. Credit event risk arises when an individual issuer suffers an event that affects it alone. It is the risk associated with changes in com- pany fundamentals.
In each market, a single swap-spread factor accounts for changes in the difference between the swap and sovereign curves. For mar- kets with detailed credit models such as the United States, United Kingdom, Japan, and euro zone , we decompose credit spread risk into two separately modeled components: the swap spread component and the sector-by-rating credit spread compo- nent.
For emerging markets, we expose the bond to the swap spread factor and the appropriate emerging market spread factor. The market perceives varying levels of creditworthiness among EMU sover- eigns, giving rise to spreads between EMU sovereign issuers, so we estimate a term structure for each EMU sovereign. Dollars Volatility spiked during the cur- 20 rency crisis in autumn of Basis Points Points 10 and was followed by a period of Basis persistently high volatility.
Risk of 0 this type is modeled with spread factors. Data acquisition dors. In each market, swap spread risk is based on a single factor: 2.
Factor return estimation the monthly change in the average spread between the swap and treasury curve. The exposure is equal to effective duration. For bonds that do not have additional factors to explain their credit risk, the swap-spread factor is used to forecast risk for debts of widely varying credit quality. Hence, bonds with higher OAS will have corre- spondingly higher volatility forecasts.
The exponent takes into account the nonlinearity in the relationship between OAS and volatility. The spread risk in the U. A single set of inter- est-rate factors is not sufficient to capture the disparate credit qualities of the EMU sovereigns.
Consequently, we provide inter- est rate factors for each sovereign issuer as well as factors for changes in average euro zone rates. All other euro-denominated bonds will be exposed to the general EMU term-structure factors. Currency Dependence Bond credit spreads are not market independent.
To date, high- grade bonds issued in different markets by a single issuer often have no significant correlation between spread changes in the dif- ferent markets. If Toyota were to issue U. The differences will persist even if the bonds were to have an apparent hedge overlay that allows the conversion of a credit exposure in one currency to an equivalent one in another currency. For example, Canadian government bonds in the three 1. These are based on monthly changes in a yield curve estimated from the pool of actively traded EMU sovereign issues.
Bonds are weighted by the GDP of the issuer. Figure Cross-Market Volatility Compari- son bps volatility bps bps 80 A comparison of term structure Annualized Volatility shift, swap, and several credit 60 spread volatilities for the U.
The volatility of the sterling sec- tors consistently lies between the 0 two extremes. High correlations 0. For U. In addition, each non-gov- ernment security is exposed to the swap spread for its currency. For the yen block, rating dependence is restricted to the Samurai foreign and Corporate sectors. The exposure to the factor is equal to the difference between the market price and par market price — par. So a bond that has a par at but is trading at has an exposure of 3.
The farther from par the bond is trading at, the greater the expo- sure to this factor. For example, if there is no information on BBB-rated suprana- tional securities, we use generic BBB spread data instead.
This 1. Further discussion of this point can be found in A. Kercheval, L. Goldberg, and L. The spread indicates how much of a premium or discount the bond is trading at. Barra Research Methods Sector-by-Rating Framework Why does Barra use what looks like a tremendous excess of factors within each market, breaking up the market structure into individual sector-by-rating factors, rather than having each bond exposed both to a sector factor and a rating factor with far fewer total factors?
The explanation is fairly straightforward. Trying to represent bond spread changes as the sum of a sector spread change and a rating spread change fails in many cases. Spreads of different rating categories in different sectors behave independently. Consider what happens to bond spreads after a positive shock to energy prices. One expects energy company bond spreads to be unaffected, or perhaps even tighten and transport company bonds to widen.
The degree of this widening is likely to be strongly dependent on rating BBB-rated transport bonds will widen much more than AAA-rated ones. The changes for energy and finance bonds, while historically large, were not nearly so significant. The result is that the more restrictive model gives a poor fit for the higher rated sectors.
Although the magnitude of September 11 is extraordinary, less dramatic instances of the same phenomenon occur frequently. This was recently the case with A-rated supranational bonds. Data acquisition markets. Factor return estimation 3. Covariance matrix estimation Factor Return Estimation 4. Model updating We calculate monthly credit spread factor return series as weighted average changes in spreads for bonds present in a partic- ular sector-by-rating category at both the start and end of each period.
Covariance Matrix Estimation The covariances of risk factors are based on the historical factor- return series. The credit factor covariance forecasts are con- structed market by market. We separately estimate local covari- ance matrices for the U. The average is duration weighted. The exposure of a credit instrument to the factor with matching currency, sector, and rating is spread duration.
The dominant source of risk for these bonds tends to come from the creditworthiness of the issuer and not from the local market interest rate factors indi- cated by the currency of the bond.
This means that there are not, for example, sep- arate factors for Nigerian bonds issued in U. The effect of the credit quality of the issuer dominates any distinction one might make between the developed-market currencies in which the bonds could be denominated. Consider for example an Argentine corporate bond issued in ster- ling. It will be exposed to the local U. Figure Volatility Levels in Emerging Markets bps The spread of emerging-market bonds has both higher volatility Volatility bps and greater variability of volatility AnnualizedVolatility than investment-grade corporate and developed-market sovereign bonds.
In contrast, the volatility in Argentina ARG increased after continuing political and social pressures. Model Structure The emerging-market factor block forecasts risk for bonds issued in an external currency primarily, U.
As with the detailed credit spreads, emerging-market spreads are measured relative to the swap curve. As of June , the block is composed of 26 factors, one for each emerging market. We estimate the emerging-market block separately from other factors and rely on high-frequency data. Data acquisition and factor return estimation of the risk factors. Covariance matrix estimation 3. Model updating Covariance Matrix Estimation Stripped-spread factors for emerging-market bonds, like the cur- rency factors, can be quite volatile and tend to exhibit variable volatility over time.
The factor return variance and covariance estimates, which are based on weekly data, are weighted exponentially with an eight- week half-life. The block is subsequently integrated into the risk model. The adjusted price is then equated to the remaining non-col- lateralized cash flows, which is discounted at a spread over the base curve.
This constant spread over the default-free curve is the stripped spread. The J. The index includes both collateralized restructured Brady debt and conventional noncollateralized bonds. For more informa- tion on J. The eight-week half-life was chosen on the basis of out-of-sample tests. The numbers in the conversion constant, 52 and 12, are respectively the num- ber of weeks and months in a year.
The Latin America ex Ecuador eight-week half-life is considerably Asia shorter than the time scale of vol- Swap atility decrease in these markets, so the risk forecasts have only slightly lagged the changes in the Jun Dec Jun Dec 0 markets. Factor Exposure Calculation An emerging-market bond issued in an external currency is exposed to the spread indicated by the issuer. The exposure is the bond stripped-spread duration. We use monthly factor return data for the swap 1. Stripped-spread duration is the exposure of a bond to the credit spread.
It takes into account any collaterization. We update the covariance matrix with these factor returns every month. Specific Risk Modeling Common factors do not completely explain asset return. Return not explained by the common factors—shift-twist-butterfly and spread factors—is called specific return. The risk due to the uncertainty of the specific return is called specific risk.
Specific returns of bonds from different issuers are assumed to be approxi- mately uncorrelated with one another, as well as with common factor returns. Specific risk tends to be relatively small for government, agency, and high-quality corporate bonds.
This component of risk can be rather large for bonds with low credit quality. We forecast specific risk with three models: a heuristic model for sovereign bonds, a heuristic model for corporate bonds, and a transition-matrix-based model for bonds in U.
Heuristic Models Except for the U. The heuristic model for sovereign bonds has only one parameter to account for sovereign market risk. The heuristic model for cor- porate bonds has an additional parameter to account for the Heuristic Model Estimation credit riskiness of the corporate issuer. The heuristic models Process assume that specific risk of the bond is proportional to spread 1.
Data acquisition duration. Specific risk estimation a. Sovereign parameter determination Data Acquisition b.
Corporate parameter determination We obtain the terms and conditions TNC and the daily price 3. The option-adjusted spreads OAS for all bonds and MBS generics are calculated using local market term structure and daily prices. Sovereign, U. MBS is the assumption that specific risk is constant across assets of the same class, and can be captured by a single parameter.
A different ba is calculated for each market or asset class. MBS, and sovereign bonds of 25 domestic markets would each have a different value for ba. The parameter incorporates his- torical information using an exponential weighting scheme with a month half-life. Price return is related to spread return through spread duration: , where rprice is the price return variance due to spread change, rspr is the spread return, and Dspr is the spread duration.
A sec- ond term is added to address the additional risk surrounding credit events. The premise is that the specific return volatility of corporate bonds is proportional to the OAS level. Bonds with lower credit ratings are subject to higher spreads and greater volatility. The constants b and c are fitted with a maximum likelihood esti- mation.
Data acquisition orate model of specific risk is used. We estimate the specific risk 2. Transition matrix generation with rating spread level differences and with a rating transition 3.
Rating-specific spread level matrix, whose entries are probabilities of bonds migrating from calculation one rating to another from AAA to BB, for example in a month. Credit migration forecasting We compute the rating spread levels from averages of OAS values a. Spread migration of bonds bucketed by market and rating. Recovery rate estimation 5. Next, we standardize and analyze the data for inconsistencies. Next, we resolve inconsistent ranking data and obtain an improved estimate of the true transition matrix.
We obtain annual reports showing historical rating changes of issuers from credit rating agencies. They assign debt ratings based on their estimate of the likelihood of repayment.
The best transition matrix is determined by least-square minimization. The valid matrix closest to the original matrix is selected. To forecast the risk associated with rating migration, the size of the impact that a rating change has on spread level is estimated. To estimate the spread level, bonds are grouped by rating and market on each analysis date. The spread level is the average spread over the benchmark curve of all the bonds within each rat- ing group. This is simply: EQ 1.
Cox and H. BB B CCC The difference between rating spread levels gives a measure of the impact of a given rating change on spread. If the rating at the final period is different from the one at the initial period, one can forecast that the spread of the bond will have changed significantly as well.
The spread changes are zero when the initial and final ratings agree; they are negative if the initial rating is higher than the final rating. Figure Returns Generated by Spreads The chart shows typical rating spread return values for the U. The impact of such events on return is assumed to be per- fectly correlated for all the bonds of an issuer.
The first component accounts for credit migration from one rating to another. The sec- ond accounts for default. The parameter depends on the recovery rate and the current market value. The recovery rate is uncertain and situation dependent. The recovery value has only a small impact on the risk forecast for investment-grade bonds, but the recovery model may have a pro- nounced impact on bonds that are below investment grade.
In practice, the effect of the mean price return term, , is negli- gibly small. This allows a simpler form of the equation: EQ Using this form, the two terms of the formula, and , can be computed separately each month and stored for use in the application. The seven different ratings1 in the model give seven aj parameters and seven bj parameters. In circumstances where low-grade credit spreads signifi- cantly widen relative to high-grade ones due perhaps to expectation of increased default risk , the credit risk forecast would increase immediately by a corresponding amount.
In the parametric context, the main difference in calculation method between the empirical specific risk for sovereign bonds and the specific risk due to credit migration for corporate bonds is that the contributions of the former add independently that is, are diversified at the security level, while the contributions of the latter add independently at the issuer level. Note that the risk values have been converted from price-return risk to spread-return risk by dividing by spread duration.
For the rating-based credit risk forecasts, AA 22 18 a spread duration of five years is assumed. The first column shows A 22 33 average factor volatility forecasts for factors in different groups. The BBB 34 79 second column shows the specific BB 92 or credit risk forecast for a single security.
B CCC An interesting observation from this table is that the classification of issuers into investment BBB and above and speculative grade below BBB neatly corresponds to the split between bonds whose common factor and credit risk are each less than their interest rate risk, and those for which they are greater.
That is, the common factor and credit risks for ratings of BBB and above are all less than the 82 basis points of risk due to spot rate volatility, while those of lower-grade bonds are above this level. Interest rate risk is dominant for investment-grade bonds while credit risk is domi- nant for high-yield bonds. Updating the Model The specific risk parameters for the heuristic models and the tran- sition-based models are calculated monthly.
Currency Risk Modeling The fluctuation of currency exchange rates is a significant source of risk faced by international investors. Journal of Economics and Finance , 43 1 , Fama and French J Financ, 33, The CAPM identified the market factor as the only systematic risk factor; the three factor model added size and value as systematic risk factors.
The latter study validated the size and value risk factors by showing a correlation between portfolio and factor time-series returns. This model has been widely accepted but has proved open-ended as researchers have mimicked this effort to identify a large number of additional factors.
Harvey et al. Rev Financ Stud, 29, Motivated by this seemingly futile effort to find the correct set of risk factors, we contribute by suggesting necessary conditions to validate empirically identified risk factors. We apply these conditions to the factors of the original Fama-French model.
Based on our analysis we argue that neither the size nor value mimicking factors should be considered systematic risk factors.
Equity portfolio risk estimation using market information and sentiment , Mitra, L. Equity portfolio risk estimation using market information and sentiment. Quantitative Finance , 9 8 ,
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