In Depth

Portfolio Optimization in an Evolving Regulatory Environment

An Application to U.S. Bank “Available for Sale” Portfolios

Historically, banks have generated a material percentage of their net interest from loan activities. Since the 2008 crisis, the lack of loan demand and the need to rebuild liquidity and comply with proposed new Basel III requirements have caused U.S. bank securities portfolios to grow by roughly $1 trillion, nearly doubling in size and making them a substantial source of overall bank profitability. Additionally, because of the proposed Basel III capital rules, banks' capital requirements may be heavily influenced by the unrealized gains and losses within the available for sale (AFS) portion of the securities portfolio, including the performance of the AFS portfolio under supervisory stress scenarios.

Given the growing size of bank investment portfolios as a percentage of average earning assets, evolving supervisory requirements and the current low rate environment, banks are revisiting their asset allocation strategies within their investment portfolios to try to meet several competing objectives. Bank portfolio managers aim to prudently optimize the yield on their portfolio while following applicable internal investment guidelines. At the same time, they need to ensure that a certain portion of the portfolio is invested in relatively liquid assets, ensure the tail risk properties of the portfolio are in check, and that the asset mix does not generate additional regulatory capital requirements beyond the institution’s tolerable limits. Finally, portfolio managers have to be cognizant of the performance of their portfolios under both internally specified and external/supervisory stress scenarios.

Current AFS portfolio allocations are highly concentrated in U.S. Treasury securities and Agency mortgages and as such have substantial duration risk. As AFS portfolios have grown, banks have generally invested in relatively low-risk and liquid assets. We believe banking institutions of all sizes can notably increase risk-adjusted returns within their AFS portfolios despite these supervisory and institutional constraints through modest reallocations. Currently, AFS allocations to Agency mortgages may be too large, while credit, non-U.S. corporate bonds and select structured securities can be attractive for banks of all sizes. Moreover, certain banks might benefit from small increases in high yield exposure as well.

Asset allocation for U.S. banks: A case study
Recognizing the complex portfolio optimization/asset allocation needs of the U.S. banks, PIMCO has developed an analytical framework that integrates four key components (see Figure 1) to provide customized solution analyses that:

  • Utilize PIMCO’s forward-looking capital markets assumptions (CMAs), including its asset-class-level implications on returns1

  • Model banks’ internal and external constraints, such as risk-weighted assets (RWAs), investment guidelines, asset allocation and liquidity constraints

  • Impose multi-period, multivariate scenarios (such as risk Federal Reserve's CCAR / Dodd-Frank Act Stress Test [DFAST] scenarios) to assess portfolio performance over time

  • Suggest allocations that can potentially minimize tail risk in the portfolio per unit of return

First, we review an asset allocation analysis on benchmark U.S. bank AFS portfolios in the presence of sample investment guidelines, liquidity constraints, risk-weighted asset constraints, and performance constraints in key macroeconomic scenarios, and assess the resulting asset allocation outcomes across U.S. banks.

1. Assumptions regarding future returns and the investment universe
A key input to the optimization process is the set of forward-looking risk and return assumptions across various asset classes. PIMCO has designed a five-step framework to produce its capital market assumptions, or estimates of future asset-class-level returns, that combines empirical analysis, model-based results and qualitative surveys by investment professionals. The combination of qualitative assessment with quantitative grounding and review is designed to harness expertise regarding market forces and features that may be difficult to model quantitatively, yet still produce sound, internally consistent estimates across various forecasters and asset classes.

Figure 2 depicts the five steps in the PIMCO framework used to generate forward-looking return assumptions. Using this, or other processes as determined by the client, portfolios can be characterized by combinations of asset-class benchmarks and indexes, each with their own combinations of risk factor loadings and return assumptions. Asset allocations within bank AFS portfolios are represented in the below sample analysis by common asset-class benchmarks.

As Table 1 illustrates, the estimated returns are consistent with PIMCO’s outlook for a New Normal economy with returns for most asset classes expected to be well below their historical averages.

This is particularly true for fixed income asset classes, as rates and spreads are near historically low levels limiting both returns and the potential for future capital appreciation. For U.S. Treasuries, the secular real policy rate is expected to remain slightly negative for the next few years. U.S. Agency mortgage-backed securities (MBS) securities are heavily influenced by Federal Reserve activity in the market, and we expect their duration-matched returns to only slightly exceed Treasuries. While credit spreads seem to be relatively tighter than historical averages, they are not at the tightest levels historically. Emerging market (EM) economies are expected to continue to outpace the developed world over the secular horizon, though their path of expansion and transition will be more volatile. Finally, equities are expected to see performance better than the last decade, but worse than the long-term averages as demographics generate a headwind against outsized returns.

2. Bank AFS portfolios
In this example we model bank portfolios using asset-class- level weights on benchmark indexes that are representative of typical AFS portfolio asset allocations, where the asset-class portfolio weights are calculated by the PIMCO Financial Institutions Group. The bank portfolio data contains asset- class allocation weights for banks of five different sizes: banks with total assets less than $1 billion, between $1 billion and $10 billion, between $10 billion and $50 billion, between $50 billion and $250 billion, and, finally, larger than $250 billion in total assets.

Table 2 provides details regarding the asset allocations of bank AFS portfolios by institution size, as well as the implied portfolio-level estimated returns, volatility, and 99th percentile conditional value at risk (CVaR). In the table liquidity assets include cash and deposits, U.S. Treasuries, Agencies and Agency MBS; spread products include investment grade (IG) and high yield (HY) corporate credit, and structured finance instruments; international assets include exposures in the developed and emerging markets; and municipal and equity cover municipal bonds, and equity/mutual funds and equity strips respectively.

As Table 2 illustrates, typical U.S. bank AFS portfolios are quite concentrated in cash, government and Agency products, reflecting the emphasis on liquidity and self-insurance against tail risks. Estimated portfolio returns seem to increase nearly monotonically with total asset size, while risk measures seem to follow a slightly different pattern. Both total portfolio volatility and tail risk (99th percentile CVaR) initially decrease with institution size only to increase again amongst the very largest banks. This appears to be driven by an initial decrease in municipal allocations in favor of IG credit as we move from the smallest banks to the mid-sized organizations, and then the trend is reversed as larger bank allocations shift more resources into high yield, asset-backed securities and international corporates. Overall though, institutions of all sizes appear to hold substantively similar portfolios.

3. Tail risk and mean-CVaR optimization
Typical portfolio optimization routines generate “mean- variance efficient” portfolio allocations. However, given the AFS portfolio’s emphasis on income and providing a source of liquidity through the cycle, we believe that a focus on the second moment is inappropriate in this context, and that a more relevant focus is on the portfolio performance far into the tail of the loss distribution. To this end, we calculate a series of “mean–tail risk efficient” portfolios that seek to minimize tail losses as defined by the CVaR at the 99th percentile. As a result, the allocations generated by this optimization routine can be readily understood in the context of liquidity provision in extreme loss scenarios. The mean–tail risk efficient portfolio given a target level of return can be represented by the following optimization:


w is a vector of portfolio allocations across asset classes

r is the realized portfolio return

α is the percentile identifying the tail (99% in this analysis)

f(w,r) is the portfolio performance

VaRα(w) is the Value at Risk given allocation w and tail percentile α

[µ] is a vector of return assumptions for each asset class

This process is repeated for each candidate return (r) to determine the frontier of efficient mean–tail risk portfolios. In short, this specification alters the objective function so that the recommended portfolio allocations minimize CVaR rather than simply minimize variance.

4. Constraints
Liquidity and investment guidelines
As AFS portfolios are designed to provide liquidity throughout the economic cycle, we first place restrictions on the portfolio allocations to help guarantee a certain level of liquidity. We require AFS portfolios to have a minimum of 60% allocation to low-risk, liquid securities, such as cash (and cash equivalents), U.S. government and U.S. Agency securities. We also require the remainder of the portfolio allocation to be in a reasonable neighborhood around observable AFS portfolio allocations and retain some minimal level of diversification: Total allocations to any non-liquid product cannot exceed 15% of the total portfolio, except in the case of international bonds at 10%, and equities, where the maximum tolerable allocation is reduced to 5%.

Risk-weighted asset and scenario performance constraints
In addition to internal constraints on the overall asset allocation, there are several supervisory requirements that banks must monitor and manage. Among the most common are the risk-weighted asset (RWA) charges, which contribute to regulatory capital requirements. Bank AFS portfolio allocations must incorporate restrictions on admissible RWA levels. Accordingly, we estimate the current bank portfolio’s RWAs by calculating the risk-weighted asset total for each asset-class benchmark using the standardized approach to credit risk under Basel II. We combine the asset class level RWA estimates with the bank portfolio allocations to estimate total RWA for the typical bank AFS portfolio, and then constrain optimal AFS portfolio allocations to have RWA totals no greater than their current estimated value.

Stress and scenario-based performance requirements are another key constraint on bank AFS portfolio allocations. In the aftermath of the 2008 crisis, stress tests and scenario evaluations became an essential analytical tool for portfolio and risk managers in the banking industry. We expect scenario testing to become still more critical with the adoption of Basel III rules. In the current regulatory regime, provided that the bank’s capital plan passes supervisory stress tests, stress outcomes do not have a direct effect on the bank’s asset allocation decisions. However, with the onset of Basel III, stress tests are poised to directly affect capital requirements: Banks will be required to hold a larger portion of their total capital in the form of common equity with the creation of a new common equity Tier 1 (CET1) ratio. In calculating the new CET1 ratio, banks would be required to include accumulated other comprehensive income (AOCI) as part of CET1, where for many banks the primary driver of AOCI is unrealized gains and losses in the bank’s AFS securities portfolio. The current proposals include accounting for unrealized gains in regulatory capital calculations, e.g., via losses incurred in regulatory stress testing, by the removal of the AOCI filters from regulatory calculations, such as the Dodd-Frank Act Stress Testing program. At the same time, supervisory stress testing will be required of many more institutions: Among its many provisions, the Dodd-Frank Act (DFA) will expand the scope and breadth of stress testing practically to the entire banking system (to all banks with assets over $500 million). Needless to say, the adoption of Basel III and bank portfolio scenario testing programs, such as the Dodd-Frank Act Stress Testing program – with the AOCI filter turned off – are likely to contribute to unrealized losses in AFS portfolios, which in turn will translate to higher regulatory capital for U.S. banks. For these reasons, one can anticipate that the introduction of Basel III/DFA rules will further formalize and strengthen the existing links between stress scenario performance of bank portfolios and economic incentives of the banks in portfolio asset allocation.

Recognizing these emerging trends, PIMCO has expanded its capabilities to include an assessment of the sensitivities of any portfolio to key international macroeconomic and financial indexes. The analytical model covers 26 economic/financial variables and can be utilized to capture macroeconomic scenarios, such as those within the Federal Reserve’s Comprehensive Capital Analysis and Review (CCAR) program. The model translates shocks to supervisory macroeconomic variables into shocks to factors that more directly affect asset pricing and risk analysis through principal components analysis and multi-dimensional projection.

To characterize the importance of stress scenario performance on admissible portfolio allocations, we include in the optimization process performance-based constraints under a widely known external macroeconomic scenario: the Federal Reserve Bank’s “severely adverse” scenario from the 2013 Comprehensive Capital Analysis and Review of U.S. banks (please see Table A1 in Appendix for more information regarding the stress scenario).

Table 3 contains the restrictions on AFS portfolio liquidity, investment allocation constraints, risk-weighted asset charges and scenario performance used in this analysis by asset class.

Optimization results
In this section, we present the findings of the optimization problem described in the previous section. First, we consider the case where banks are only subject to the liquidity and investment guideline constraints without any supervisory restrictions. The resulting efficient frontier is portrayed in blue in Figure 3. Next, we incorporate the RWA charges and scenario-based performance constraints. These constraints shift the efficient frontier inward as displayed in gold in the same figure.

Based on Figure 3 (and Table 1) one observes that while there are some nuances and size-specific behavior, overall the portfolio compositions and risk-return profiles across banks of various sizes are quite similar. This is of import: It suggests that external asset-specific shocks, such as regulatory rules which provide asset-specific incentives/disincentives that shift the efficient frontier – may trigger reactions across the industry en masse.

Current allocations of AFS portfolios are located strictly within the interior of the efficient frontier. In the presence of the liquidity and allocation constraints alone, banks can markedly improve their portfolio returns while holding tail risk constant. In this sample analysis, these gains range from 44 bps – 59 bps depending on the size of the institution. Increases in returns of this magnitude would roughly double the estimated returns on AFS portfolios. Mid-size banks observe the smallest gains from the optimization, though the efficient frontier still attains a substantial increase in expected total returns relative to their current allocation. In terms of portfolio allocation, the optimization subject to liquidity and allocation constraints suggests a reduction in Agency MBS, and an increase in short duration credit, emerging market (EM) and equities exposures for banks of every size. The smallest and largest banks would benefit from a modest increase in high yield exposure as well. The detailed optimal allocations with liquidity and allocation constraints alone are included in Table A2 in the Appendix.

The addition of RWA and scenario performance constraints shifts the efficient frontier inward for the highest-return, highest-tail-risk allocations. Given current CVaR levels of bank portfolios, the introduction of the regulatory RWA and scenario constraints reduces the attainable level of returns relative to those that would be possible in the presence of only liquidity and allocation constraints. These reductions are the largest for the smallest banks in our sample analysis (19.9% in relative terms, or a 9 bps decline in absolute returns) and the largest banks (12.9%, 7 bps), where medium sized banks are affected relatively less (2.8%–4.6%, 1 bps–2 bps). The reduction in attainable tail-risk-adjusted returns can be thought of as the implicit cost of RWA and scenario requirements on bank AFS portfolios. Given the current size of these portfolios, such a reduction in returns would imply an industry-wide cost ranging from $750 million to $4.5 billion per year. The detailed portfolio optimization results that incorporate liquidity, allocation, RWA and scenario performance constraints can be found in Table A3 in the Appendix.

In terms of portfolio allocation across asset classes, the introduction of the RWA and scenario constraints does not alter the direction of asset allocation recommendations vis-à-vis the current portfolio compositions and the unconstrained frontier. The supervisory-constrained optimization suggests a reduction in Agency MBS and an increase in short duration credit, emerging markets (EM) exposure and equities across banks of all sizes. Similarly, we see an increase in high yield exposures for small banks and a decrease in ABS allocations for the largest institutions, though overall the recommended reallocations are extremely similar across institution size.

To summarize the impact of the different constraints, we have calculated the equal-weighted arithmetic average optimal portfolio across the five different size-specific portfolios utilizing the five asset groupings: liquidity, municipals, spread instruments, international exposure and equities. Figure 4 below illustrates the calculated average asset-class-specific distributions across banks of various sizes for three portfolios: the average current AFS portfolio; the average liquidity and allocation constrained optimal portfolio; and finally, the average liquidity, allocation, RWA, and scenario constrained optimal portfolio.

Figure 4 illustrates three key points: 1) impositions of constraints appear to have non-negligible asset allocation implications on AFS portfolios and 2) the optimization results suggest that AFS portfolios would benefit from a reallocation away from liquidity products, primarily in Agency mortgage holdings, and into spread (particularly short duration corporate credit), international (EM), and equity classes to the extent permitted by their liquidity constraints and institutional asset allocation guidelines, and 3) the further imposition of supervisory constraints makes certain spread products slightly less attractive in terms of controlling for tail-losses in the portfolio.

Our findings suggest that banks can markedly improve the performance of their AFS portfolio while holding their tail risk and regulatory metrics constant through modest portfolio reallocations. We find that:

  • Imposition of the internal/external constraints (such as liquidity, investment guidelines, RWAs, CCAR or other scenarios) appear to have non-negligible asset allocation implications on AFS portfolios

  • U.S. bank AFS portfolios may benefit from a reduction in Agency MBS exposure and an increase in short duration corporate credit, along with small increases in equity and emerging market holdings

  • The introduction of supervisory requirements on the sample portfolio above and beyond internal allocation constraints reduces attainable returns by 3%–19% (1 bp–9 bps), costing the banking industry between $750 million and $4.5 billion annually in forgone returns within the AFS portfolio

  • As the anticipated removal of the AOCI filter under Basel III will cause unrealized losses to flow through to regulatory capital calculations, regulatory stress scenarios and assorted supervisory restrictions are poised to have a larger impact on bank portfolio asset allocations

  • Finally, as banks across different sizes tend to hold similar assets in fairly similar allocations within their securities portfolios, the asset-class incentives and disincentives embedded within supervisory scenarios, combined with their direct effect on capital under Basel III, may induce market-wide reallocations across asset classes


1 PIMCO custom client reports are created in consultation with the client and may be based upon client, consultant, index or PIMCO capital market assumptions. Note: Capital market assumptions are derived from proprietary research and modeling and are not a guarantee of future results.


Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. Investing in the bond market is subject to certain risks, including market, interest rate, issuer, credit and inflation risk. Equities may decline in value due to both real and perceived general market, economic and industry conditions. Tail risk hedging may involve entering into financial derivatives that are expected to increase in value during the occurrence of tail events. Investing in a tail event instrument could lose all or a portion of its value even in a period of severe market stress. A tail event is unpredictable; therefore, investments in instruments tied to the occurrence of a tail event are speculative. Derivatives may involve certain costs and risks such as liquidity, interest rate, market, credit, management and the risk that a position could not be closed when most advantageous. Investing in derivatives could lose more than the amount invested. There is no guarantee that these investment strategies will work under all market conditions or are suitable for all investors and each investor should evaluate their ability to invest long-term, especially during periods of downturn in the market. Investors should consult their financial advisor prior to making an investment decision.

Return assumptions are for illustrative purposes only and are not a prediction or a projection of return. Return assumption is an estimate of what investments may earn on average over the long term. Actual returns may be higher or lower than those shown and may vary substantially over shorter time periods.

No representation is being made that any account, product, or strategy will or is likely to achieve profits, losses, or results similar to those shown. Hypothetical or simulated performance results have several inherent limitations. Unlike an actual performance record, simulated results do not represent actual performance and are generally prepared with the benefit of hindsight. There are frequently sharp differences between simulated performance results and the actual results subsequently achieved by any particular account, product, or strategy. In addition, since trades have not actually been executed, simulated results cannot account for the impact of certain market risks such as lack of liquidity. There are numerous other factors related to the markets in general or the implementation of any specific investment strategy, which cannot be fully accounted for in the preparation of simulated results and all of which can adversely affect actual results.

No representation is being made that the structure of the average portfolio or any account will remain the same or that similar returns will be achieved. The analysis may not be attained and should not be construed as the only possibilities that exist. Different weightings in the asset allocation illustration will produce different results. Actual results will vary and are subject to change with market conditions. There is no guarantee that results will be achieved. No fees or expenses were included in the estimated results and distribution. The scenarios assume a set of assumptions that may, individually or collectively, not develop over time. The analysis reflected in this information is based upon data at time of analysis. Forecasts, estimates, and certain information contained herein are based upon proprietary research and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product.

PIMCO routinely reviews, modifies, and adds risk factors to its proprietary models. Due to the dynamic nature of factors affecting markets, there is no guarantee that simulations will capture all relevant risk factors or that the implementation of any resulting solutions will protect against loss. Simulated risk analysis contains inherent limitations and is generally prepared with the benefit of hindsight. Realized losses may be larger than predicted by a given model due to additional factors that cannot be accurately forecasted or incorporated into a model based on historical or assumed data.

We employed a block bootstrap methodology to calculate volatilities. We start by computing historical factor returns that underlie each asset class proxy from January 1997 through the present date. We then draw a set of 12 monthly returns within the dataset to come up with an annual return number. This process is repeated 15,000 times to have a return series with 15,000 annualized returns. The standard deviation of these annual returns is used to model the volatility for each factor. We then use the same return series for each factor to compute covariance between factors. Finally, volatility of each asset class proxy is calculated as the sum of variances and covariance of factors that underlie that particular proxy.

Value at Risk (VAR) estimates the risk of loss of an investment or portfolio over a given time period under normal market conditions in terms of a specific percentile threshold of loss (i.e., for a given threshold of X%, under the specific modeling assumptions used, the portfolio will incur a loss in excess of the VAR X percent of the time. Different VAR calculation methodologies may be used. VAR models can help understand what future return or loss profiles might be. However, the effectiveness of a VAR calculation is in fact constrained by its limited assumptions (for example, assumptions may involve, among other things, probability distributions, historical return modeling, factor selection, risk factor correlation, simulation methodologies). It is important that investors understand the nature of these limitations when relying upon VAR analyses.

The 1-Month LIBOR (London Interbank Offered Rate) Index is an average interest rate, determined by the British Bankers Association, that banks charge one another for the use of short-term money (1 months) in England’s Eurodollar market. | Barclays Government Bond Index is an unmanaged index consists of securities issued by the U.S. Government with a maturity of one year or more. | The Barclays U.S. MBS Fixed Rate Index covers the mortgage-backed pass through securities of Ginnie Mae (GNMA), Fannie Mae (FNMA), and Freddie Mac (FHLMC). The MBS Index is formed by grouping the universe of over 600,000 individual fixed rate MBS pools into approximately 3,500 generic aggregates. | The Barclays Municipal Bond Index consists of a broad selection of investment-grade general obligation and revenue bonds of maturities ranging from one year to 30 years. It is an unmanaged index representative of the tax-exempt bond market. The index is made up of all investment-grade municipal bonds issued after 12/31/90 having a remaining maturity of at least one year. | The Barclays 1-5 Year U.S. Credit Index consists of publicly issued U.S. corporate and specified foreign debentures and secured notes that meet the specified maturity, liquidity, and quality requirements. To qualify, bonds must be SEC-registered. | The Barclays Investment Grade Corporate Index is an unmanaged index that is the Corporate component of the U.S. Credit Index. The index includes both corporate and non-corporate sectors and are publicly issued U.S. corporate and specified foreign debentures and secured notes that meet the specified maturity, liquidity, and quality requirements. The corporate sectors are Industrial, Utility, and Finance, which include both U.S. and non-U.S. corporations. The non-corporate sectors are Sovereign, Supranational, Foreign Agency, and Foreign Local Government. | The Barclays Intermediate U.S. High Yield Index is the intermediate component of the Barclays U.S. Corporate High Yield index, which covers the universe of fixed-rate, non-investment-grade debt, pay-in-kind (PIK) bonds, Eurobonds, and debt issues from countries designated as emerging markets (e.g., Argentina, Brazil, Venezuela) are excluded, but Canadian and global bonds (SEC registered) of issuers in non-EMG countries are included. Original issue zeroes, step-up coupon structures, and 144-As are also included. | Barclays Asset-Backed Securities Index has 5 subsectors: credit and charge cards, autos, home equity loans, utility, and manufactured housing. The index includes pass-through, bullet, and controlled amortization structures. It includes only the senior class of each ABS issue; subordinate tranches are not included. | The Markit iBoxx Eur Corp Index includes investment grade fixed and zero coupon bonds, step-ups, event-driven bonds, dated and undated callable subordinated corporate bonds (fixed-to-floater bonds that change to floating rate note after first call date), soft bullets with a minimum, time of maturity of 1 year. | JPMorgan Government Bond Index-Emerging Markets Global Diversified Index (Unhedged) is a comprehensive global local emerging markets index, and consists of regularly traded, liquid fixed-rate, domestic currency government bonds to which international investors can gain exposure. | The S&P 500 Index is an unmanaged market index generally considered representative of the stock market as a whole. The index focuses on the Large-Cap segment of the U.S. equities market. | It is not possible to invest directly in an unmanaged index.

This material contains the current opinions of the author but not necessarily those of PIMCO and such opinions are subject to change without notice. This material is distributed for informational purposes only and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.

PIMCO provides services only to qualified institutions and investors. This is not an offer to any person in any jurisdiction where unlawful or unauthorized. | Pacific Investment Management Company LLC, 840 Newport Center Drive, Newport Beach, CA 92660 is regulated by the United States Securities and Exchange Commission. | PIMCO Europe Ltd (Company No. 2604517), PIMCO Europe, Ltd Munich Branch (Company No. 157591), PIMCO Europe, Ltd Amsterdam Branch (Company No. 24319743), and PIMCO Europe Ltd - Italy (Company No. 07533910969) are authorised and regulated by the Financial Conduct Authority (25 The North Colonnade, Canary Wharf, London E14 5HS) in the UK. The Amsterdam, Italy and Munich Branches are additionally regulated by the AFM, CONSOB in accordance with Article 27 of the Italian Consolidated Financial Act, and BaFin in accordance with Section 53b of the German Banking Act, respectively. PIMCO Europe Ltd services and products are available only to professional clients as defined in the Financial Conduct Authority's Handbook and are not available to individual investors, who should not rely on this communication. | PIMCO Deutschland GmbH (Company No. 192083, Seidlstr. 24-24a, 80335 Munich, Germany) is authorised and regulated by the German Federal Financial Supervisory Authority (BaFin) (Marie- Curie-Str. 24-28, 60439 Frankfurt am Main) in Germany in accordance with Section 32 of the German Banking Act (KWG). The services and products provided by PIMCO Deutschland GmbH are available only to professional clients as defined in Section 31a para. 2 German Securities Trading Act (WpHG). They are not available to individual investors, who should not rely on this communication. | PIMCO Asia Pte Ltd (501 Orchard Road #08-03, Wheelock Place, Singapore 238880, Registration No. 199804652K) is regulated by the Monetary Authority of Singapore as a holder of a capital markets services licence and an exempt financial adviser. PIMCO Asia Pte Ltd services and products are available only to accredited investors, expert investors and institutional investors as defined in the Securities and Futures Act. | PIMCO Asia Limited (24th Floor, Units 2402, 2403 & 2405 Nine Queen’s Road Central, Hong Kong) is licensed by the Securities and Futures Commission for Types 1, 4 and 9 regulated activities under the Securities and Futures Ordinance. The asset management services and investment products are not available to persons where provision of such services and products is unauthorised. | PIMCO Australia Pty Ltd (Level 19, 363 George Street, Sydney, NSW 2000, Australia), AFSL 246862 and ABN 54084280508, offers services to wholesale clients as defined in the Corporations Act 2001. | PIMCO Japan Ltd (Toranomon Towers Office 18F, 4-1-28, Toranomon, Minato-ku, Tokyo, Japan 105-0001) Financial Instruments Business Registration Number is Director of Kanto Local Finance Bureau (Financial Instruments Firm) No.382. PIMCO Japan Ltd is a member of Japan Investment Advisers Association and Investment Trusts Association. Investment management products and services offered by PIMCO Japan Ltd are offered only to persons within its respective jurisdiction, and are not available to persons where provision of such products or services is unauthorized. Valuations of assets will fluctuate based upon prices of securities and values of derivative transactions in the portfolio, market conditions, interest rates, and credit risk, among others. Investments in foreign currency denominated assets will be affected by foreign exchange rates. There is no guarantee that the principal amount of the investment will be preserved, or that a certain return will be realized; the investment could suffer a loss. All profits and losses incur to the investor. The amounts, maximum amounts and calculation methodologies of each type of fee and expense and their total amounts will vary depending on the investment strategy, the status of investment performance, period of management and outstanding balance of assets and thus such fees and expenses cannot be set forth herein. | PIMCO Canada Corp. (199 Bay Street, Suite 2050, Commerce Court Station, P.O. Box 363, Toronto, ON, M5L 1G2) services and products may only be available in certain provinces or territories of Canada and only through dealers authorized for that purpose. | PIMCO Latin America Edifício Internacional Rio Praia do Flamengo, 154 1o andar, Rio de Janeiro – RJ Brasil 22210-030. | No part of this publication may be reproduced in any form, or referred to in any other publication, without express written permission. PIMCO and YOUR GLOBAL INVESTMENT AUTHORITY are trademarks or registered trademarks of Allianz Asset Management of America L.P. and Pacific Investment Management Company LLC, respectively, in the United States and throughout the world. ©2013, PIMCO