Pension Funds Active Management Based on Risk Budgeting

Funds and Pensions Pension Funds Active Management Based on Risk Budgeting Chae Woo Nam, Research Fellow* When we look at changes in asset managers risk management systems including pension funds, we observe that the concept of risk has expanded from a passive restriction that risk should be controlled and managed at a minimum level to an active strategy that risk is a return-generating source. In this paper, I review the National Pension Service s risk budgeting system. I hope it will be helpful to the Korean asset management institutions risk budgeting systems in managing active risk. I. Introduction Many pension funds have increased risky assets such as equity and alternative investments to meet required returns in the low interest rate environment. Pension funds have been trying to improve performance through changes not only in asset allocation but also in management style. Pension funds tend to increase active management to get excess returns (α) since they are not satisfied with market returns through passive management. However, excess returns through active management involve corresponding active risk based on the basic financial assumption that increasing returns means taking more risks. In terms of risk management, this means that risk should be measured and managed not only by market risk generated from strategic asset allocation (SAA) * All opinions expressed in this paper represent the author s personal views and thus should not be interpreted as the Korea Capital Market Institute s official position. Tel: 02-3771-0827, E-mail: zeuss@kcmi.re.kr 20 2012 Vol. 4, No. 2

Pension Funds Active Management Based on Risk Budgeting but also by total risk including active risk generated from fund managers active management. This point of view assumes that risk is a restriction to asset management and should be minimized. Recent changes in risk management show that the perception of risk has expanded from a passive restriction that risk should be controlled and managed to a more active and strategic concept that risk is an available resource for generating excess returns within optimal levels. This concept is called risk based asset management and places risk budgeting within the context of asset allocation. The range of its application is rapidly spreading among advanced asset management institutions. In Korea, however, risk budgeting is used only by a few I suggest risk budgeting asset managers and the NPS within a limited range, as a way for pension funds with many and it remains a theoretical concept in most of the assets and managers industry. to effectively manage active risk generated Given this background, I introduce the case of the from pursuing excess NPS, an early adopter of the risk budgeting system, returns (α). then suggest the risk budgeting system as an optimal plan to efficiently manage active risk arising from asset management of large pension funds, which have huge assets and many managers. II. Risk Budgeting System 1. Theoretical background Budget for risk needs to be established along with budget for capital to achieve both short- and long-term asset management objectives. Capital budgeting is defined as an activity that allocates a fund s total capital by asset class or by stage of decisionmaking process. Based on this viewpoint, the fund s total capital is a return-generating source. This is commonly referred to as asset allocation in asset management. 21

Capital Market PERSPECTIVE On the other hand, risk budgeting, as with the concept of capital allocation, can be defined as a plan that allocates total risk to each asset class or decision-making process on an ex-ante basis with the percerption that total risk is a return-generating source in the long term. Chow and Kritzman (2001) defined risk Risk budgeting, similar to the concept of capital budgeting, can be defined as a plan that allocates the total amount of available risk budgeting as a kind of conceptual change from the allocation of total invested money in the traditional investment scheme to the allocation of total risk for an optimal portfolio construction. Mina (2005) described risk budgeting as the allocation of total risk to each asset class or investment decisionmaking and return-generating source through asset level on an ex-ante basis. The total risk can be perceived as a return-generating source to achieve investment objectives for the long term. management, and that risk budgeting is implemented by defining asset allocation or by allocating the budget to active risk for excess returns. Looking at these various definitions of risk budgeting, the actual risk budgeting implemented by various institutional investors such as pension funds, insurance companies, and asset management companies are different based on the definition of total risk managed and allocated. In this paper, I focus on pension funds risk budgeting system. 2. Risk budgeting of pension funds For pension funds, risk budgeting involves determining and allocating total risk perceived by the fund managing entity. The distinct characteristic of pension funds, in comparison to other asset management firms, is a consideration of liability, which is future payments to the beneficiaries of the pension scheme. That is to say, ALM risk 1) from mismatches between pension assets and liabilities is the fundamental risk that a pension fund faces. In terms of flow, ALM risk means that the return on assets under management will be lower than the liability cost. 1) ALM stands for asset liability management. ALM risk is also referred to as surplus risk or funding risk. 22 2012 Vol. 4, No. 2

Pension Funds Active Management Based on Risk Budgeting Therefore, for the pension fund s risk budgeting system, the definition of total risk generally includes ALM risk occurring from the discrepancy between asset structure and liability structure. Technically, this means a structure in which the risk budgeting system encompasses not only active risk but also systematic risk by strategic asset allocation. The picture below shows the risk budgeting process where total risk is systematically allocated to the active risk corresponding to investment managers at the bottom. Risk budgeting is implemented by determining total risk based on excess return by investment objective, and then through allocating the total risk to asset classes or to asset managers phase by phase. As shown in the picture, the total excess return occurs as the actual portfolio representing the asset structure grows apart from the liability portfolio representing the liability structure of the pension fund. Therefore, the total risk defined in risk budgeting is measured by the standard deviation of total excess returns. Figure 1. Pension funds risk budgeting system: risk budgeting steps Source: NPS 23

Capital Market PERSPECTIVE The total risk is then divided into ALM risk (surplus risk) occurring from the difference between the benchmark portfolio based on strategic asset allocation (SAA) and the liability portfolio. The active management risk occurs from the discrepancy between the actual portfolio and the benchmark portfolio. Active management risk consists of implementation risk resulting from tactical asset allocation (TAA), and manager active risk results from stock selection and market timing. In this paper, I try to help readers better understand the complex and sophisticated risk budgeting system by modeling the process with a simple formula, in which total risk is determined and then allocated to ALM risk and active management risk. The total risk of the pension fund is determined by return distributions on benchmarks by asset class and the excess returns generated from active management. The specific return model to implement risk budgeting is below. As shown in the chart, the excess return relative to liability, which means the ultimate excess returns of the pension fund, is attributed to the excess returns generated from strategic asset allocation and those from active management. In formula (1), the first term on the right side shows excess returns from the SAA portfolio relative to the liability portfolio, and the second term shows excess returns from the actual portfolio relative to the SAA portfolio. (1) : return on actual portfolio : return on liability portfolio : return on policy portfolio determined by SAA Formula (1) can be organized as a form of risk-adjusted return using return volatility as follows. In formula (2), the first term on the right side can be expressed by systematic risk resulting from SAA, and the second term is expressed by active risk called the tracking error. 24 2012 Vol. 4, No. 2

Pension Funds Active Management Based on Risk Budgeting (2) : Systematic risk resulting from SAA : Active risk resulting from active management The allocated variables to be determined as the first step for risk budgeting are the quantity of systematic risk ( ) and total active risk ( ). In formula (2), the coefficient before and is excess returns generated from unit risk, so-called risk-adjusted returns. Formula (2) shows that return on assets under management is a function of systematic risk, and total active risk, and excess returns generated from each unit risk, respectively. Therefore, expected excess returns per unit risk, standard deviation, and the correlation coefficient determine the distribution of return on assets under management by risk level, a determinant variable. In formula (2), expected excess returns per unit systematic risk is the risk-adjusted return known as the Sharpe ratio, which is assumed as a constant value. 2) The second term, expected excess return per unit active risk, is known as the information ratio. It is also assumed as a constant value for the same reason as the Sharpe ratio. In this case, the expected excess returns and the variable above are expressed with a function of the Sharpe ratio (SR) and information ratio (IR). (3) : correlation coefficients between excess returns As shown in formula (3), the distribution of excess returns is determined by systematic risk ( ) and total active risk ( ). Therefore, an optimal risk allocation for the pension fund can be derived from the maximization of expected returns subject to given total risk. In the following section, I review the case of the National Pension Fund (NPF) of Korea. 2) If the asset mix from SAA is located on the Capital Market Line (CML) and the liability cost ( ) can be funded at the risk free rate, then we can assume the Sharpe ratio as a constant value. 25

Capital Market PERSPECTIVE III. Case Study: National Pension Fund (NPF) 1. Risk budgeting without ALM There is a realistic restriction in applying the risk budgeting model introduced in the previous section to a pension fund like NPF because it has not established the concept of pension liability inherent in the measurement of excess returns. Therefore, it is unrealistic to assume a liability portfolio that replicates the future cash flow of pension liability. In this situation, ALM risk or the correlation between excess returns is difficult to calculate as a risk measurement. Figure 2. NPF s risk allocation Source: NPS Hence, NPF has given up the single-stage optimization that enabled it to derive the global optimum. Instead, NPF uses two-stage optimization in which systematic risk is primarily determined by SAA without considering liability, and then the optimal active risk allocation is derived with the restriction of total active risk given by exogenous factors. Certainly, the optimal allocation derived from the two-stage optimization can only remain at a local optimum level. Also, ALM risk, the ultimate risk that the pension fund is facing, is overlooked in the two-stage optimization. Above all, despite the 26 2012 Vol. 4, No. 2

Pension Funds Active Management Based on Risk Budgeting weakness in the two-stage optimization that total active risk is not endogenously decided, NPF has no choice but to temporarily apply the two-stage optimization until it introduces the ALM system in full scale. NPF uses two-stage Under the two-stage optimization NPF uses, the optimization in which active risk allocation model is as follows. I mentioned systematic risk is primarily determined that risk budgeting, starting from total risk attribution, by SAA without can ultimately go further down to the asset manager considering liability, level. As a result of expanding the logic in the and then optimal active risk allocation is derived methodology explained above that total risk is allocated using total active risk as to systematic risk and total active risk, excess returns a restriction. generated from active management can be attributed to tactical asset allocation (TAA) and actual management as follows. (4) : return of TAA portfolio : active risk TAA : active risk of th asset class The first term in formula (4) shows excess returns generated from active risk of tactical asset allocation (TAA), and the second term displays excess returns from each asset class or manager level. In allocating active risks, the information ratio (IR) corresponding to each active risk is assumed to be a constant value. The following formula describes the expected excess returns and the active risk generated from active management. 27

Capital Market PERSPECTIVE (5) : Information Ratio of TAA : return of th asset class : active risk of TAA : active risk of asset class As described above, total active risk is not endogenously decided in the risk budgeting process using two-stage optimization that does not define the liability aspect of pension funds. Therefore, the total amount of active risk should be decided exogenously based on policy factors, and the total risk given in this way is a restriction. That is to say, active risk allocation is to be decided to maximize expected returns under the total risk restriction. Therefore, active risk can be optimally allocated through the following optimization problem. (6) : total amount of active risk exogenously given In the optimization problem above, it has the unique and closed form solution in general. However, it is necessary to have significant estimates of the Sharpe ratio for systematic risk and information ratio for active risk in order to apply this optimization problem to risk budgeting practices. In addition, as stated above, a sensitive issue raised by public institutions like NPF is that the parameter of total active risk is not determined endogenously. 28 2012 Vol. 4, No. 2

Pension Funds Active Management Based on Risk Budgeting 2. The problem of parameter setting In order to establish an efficient and effective risk budgeting system, various parameters are required to be statistically estimated and systemically determined from the endogenous database. Therefore, a wide and extensive database is necessary. That, however, involves significant time and money. In this section, setting the information ratio (IR), the most sensitive issue in setting parameters, is reviewed because IR is directly related to the NPF s incentive scheme. IR means the efficiency of how much excess returns can be generated from unit active risk. IR is a function of managers skills and market inefficiency, in which the level of IR increases as managers skills and market inefficiency increase. It should be noted that in theory, there is some correlation between market returns (β) and excess returns (α) in determining the proper level of IR. This means that, for instance, the assumed IR level for Korea s domestic equity market is not linked to the market outlook, whether bullish or bearish, but is strongly dependent on the structural aspect of how inefficient the Korean market is compared to the US market. A required or target level of IR for the total portfolio of pension funds can be stated as an institution s characteristic. For instance, while NPF is an organization with the efficient level of about 0.5 IR, CalPERS, a famous public pension fund in the US, has an 0.1 IR. In order to increase the IR, skilled asset managers are necessary. From the perspective of manager research, in an efficiently managed market, the IR level of individual managers is ranked by track record, which affects a manager s annual salary. Therefore, the IR level an organization pursues is directly affected by the organization s incentive system in the long term. To set a proper IR target, the cross sectional analysis using peer group comparison is a more relevant method than the time series analysis using the historical data of the fund because the historical IR series show the typical properties of non-stationary time series. Generally, in cross-sectional analysis, the constituents of IR are classified based on forecasting ability, efficiency, and active management opportunities. Then, the IR targets can be reasonably estimated through relative comparisons of characteristics 29

Capital Market PERSPECTIVE corresponding to each asset management unit for each factor. It is difficult to find exact statistics but it is known that the IR of institutional investors is between 0.1 and 0.3 on average in the US market where performance evaluation and manager research are well developed. In the US, NPF s IR target of 0.5 is considered good, and OTPP s 3) target of 0.7 is on the higher end. These targets reflect the higher standards of the highly efficient US capital markets. Considering the inefficiency of the Korean domestic market, the IR target of 0.5 can be interpreted as above market average to some degree. In the current risk budget allocation, NPF assumes IR by asset class as a constant regardless of tracking error because expected excess returns increase linearly as active risk increases given minimal tracking errors. The actual IR, however, is known to drop dramatically when the tracking error is higher than a certain level. A more realistic risk budgeting model can be established by reflecting the non-linear relationship between active risk and IR. Going forward, this idea can be developed through research and the pension industry after sufficient data accumulation. IV. Limits and Implications In managing pension assets, the risk budgeting system is a widely used practice in overseas pensions such as Canada s OTPP and the Netherlands ABP 4) which are famous for achieving management efficiency as high as private asset managers. However, there are few cases where the risk budgeting system is used in Korea. Although some asset management companies use risk budgeting systems for active risk management, it is uncertain how effective and practical the systems are. Three restrictions cause the difficulty in spreading the risk budgeting system in the Korean asset management market. First, Korean asset management companies themselves lack active management skills and competence based on elaborate benchmarks. Therefore, there is no consensus on risk factors of the Korean stock 3) Ontario Teacher s Pension Plan in Canada. 4) Dutch Public Employees Pension whose asset management is unified into APG (All Pension Group). 30 2012 Vol. 4, No. 2

Pension Funds Active Management Based on Risk Budgeting market, and consequently, style indices, which are applicable to benchmarks, have been poorly developed. Second, the difficulty has been partially caused by the short history of Korea s manager research that should record and monitor the performance of active management. To implement risk budgeting, it is necessary to accumulate continuous and reliable performance data for individual managers or asset management institutions. Last, a direct restriction is that Korean pensions have relatively small assets under management except for NPF. Substantial data accumulation is a precondition for risk budgeting, and at the same time, it is costly to develop and maintain the database. Because of these realistic constraints, NPF is the only institution in Korea that practically applies the risk budgeting system to its asset management and incentive scheme. On the other hand, the risk budgeting system is already a universal concept in overseas pension funds. According to a CEM 5) survey on management efficiency for global pension funds, almost 90% of pensions that participated in the survey manage active risk based on the risk budgeting system (Halim et al., 2010). As for the measurement of active risk, 88% of the pensions establish the risk budgeting system based on tracking error (TE) and 43% using Value at Risk (VaR) 6). The risk budgeting system is already a universal concept in overseas pension funds. In Korea, however, there are few cases of its use except for some insurance and asset management companies. The risk budgeting system adopted by the NPF can be a direct benchmark for the industry. In spite of the realistic restrictions in the Korean domestic market, interest in the risk budgeting system is growing as pensions asset sizes are increasing and the market matures. Especially, since pension funds suffered from the global financial crisis, they have tried to adopt the risk budgeting system because they want to strengthen risk management for risky assets and overall active management. The risk budgeting system adopted by NPF can be a direct benchmark for the industry. 5) CEM, located in Canada, is famous for providing rankings in terms of management efficiency and cost for the global pension funds. 6) Many pension funds consider both tracking error and VaR for risk measurement. 31

Capital Market PERSPECTIVE References Cheong, M.K., Nam, C.W., Han, C.W., Hwang, G.H., 2009, Active Risk Management of NPF, National Pension Research Institute. Chow, G., Kritzman, M., 2001, Risk budgets, The Journal of Portfolio Management, Vol. 27-2, 56-60. Halim, S., Miller, T., Dupont, D., 2010, How pension funds manage investment risks: A global survey, Rotman International Journal of Pension Management, Vol. 3-2, 30-38. Mina, J., 2005, Risk budgeting for pension fund, Risk Metrics Journal, Vol. 6-1, 9-34. 32 2012 Vol. 4, No. 2