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Risk Allocation, Asset Allocation, Tracking Error Allocation 风险预算 资产配置 跟踪误差配置

Risk allocation emerged in the late 1900s, in response to concerns about the level of risk being accepted in a portfolio. The process involves setting up a plan for how much an investor plans on taking with the long-term investments. It is based on one’s estimation of multiple parameters over different time frames with different techniques. Till recent years, most large pensions, foundations, and endowments have realized the importance of this management tool.

Why A Risk Budget Is Needed?

Investors typically have different levels of confidence in predicting asset classes versus active returns, asset allocation versus active risk. The primary benefit of a risk budget is that it can help to illuminate how the risk of a portfolio is spread across investments, factors, or active management, thus enable an investor to evaluate risk exposure and make adjustments as necessary.

Differences Between Risk Allocation And Asset Allocation

Modern Portfolio Theory (MPT) revolutionized portfolio management by realizing the importance of correlations of asset returns, in addition to expected returns, expected volatility, and expected covariances. By the 1970s, asset allocation had become a dominant investment style, which seeks to achieve “efficiency.” The main differences between risk allocation and asset allocation can be examined from six perspectives:

  1. Goal – risk allocation is to allocate risk across assets such that the portfolio can achieve a desired return at the risk taken; asset allocation, however, is an allocation process across different asset classes such that the portfolio targets will achieve desired return on assets.
  2. Constraint – the constraint of risk allocation is that the total portfolio risk is limited; the constraint of asset allocation is that the allocations weights sum to one.
  3. Inputs – risk allocation emphasizes on volatility and correlation, while asset allocation emphasizes on expected return, which means, the initial asset allocation should be an optimization between risk and expected risk, with the center around generally accepted allocations for a portfolio with the desired level of risk. In contrast, risk allocation process may use measures such as Value at Risk (VaR) to determine the tolerance.
  4. Monitoring – in the monitoring process, risk allocation aims to monitor forecast errors in volatility and correlation, in addition to gains and losses; asset allocation monitors actual value changes of a portfolio, which typically ignores forecast errors on volatility and correlation.
  5. Rebalancing – risk allocation will need to be rebalanced when total portfolio risk deviates from target; while rebalancing in asset allocation will be required when values (money amount) of positions deviate from target. To be more specific, with stable asset allocation, the actual amount of risk an investor is taking and the maximum loss he may experience is fluctuation with market conditions, which exposes him to more or less risk than originally desired. Risk allocation, on the other hand, sees its process as the portfolio exposure to risk and return, so it will be rebalanced in response to changes in the short-term conditional volatility and correlation of assets, and it keeps the overall portfolio risk at the level defined as an investor’s tolerance.
  6. Focus – risk allocation focuses on overall portfolio, while asset allocation focuses on all sources and components of risk of a portfolio; risk allocation focuses on earning an expected return on a targeted level of risk, while asset allocation focuses on earning an expected return on assets.

Tracking Error Allocation

The theory of Tracking Error Allocation was developed by David Blitz and Jouke Hottinga (2001). The study has discovered a framework for allocating partial tracking errors for investment decisions in order to maximize the expected information ratio of an actively managed portfolio. It is a three-step process:

  1. Identify the independent investment decisions
  2. Rank the forecasting capabilities for the investment decisions
  3. Calculate the optimum partial tracking errors, given an overall tracking error limit

Biltz & Hottinga’s biggest contribution to the investment industry is a transparent rule that “the target tracking error for each investment decision should be proportional to the corresponding expected information ratio.”

Risk Allocation Framework

A risk allocation framework that explicitly differentiates between systematic risk and unsystematic or active risk enables an investor to improve the risk/return profile of a portfolio. In such framework, risk attribution from each component is equal to the budget of risk defined for an investor.

Risk Class Approach and Risk Factors Identification

Technically, Risk Class Approach is a structural, factor approach of modeling the covariance matrix of assets. The success of the approach depends on whether the investor can come up with a set of risk factors that not only are relevant to strategic and tactical concerns, but also effective in capturing the exposures of the assets with respect to all of these factors.

Chen, Roll, and Ross (1986) of The Rady School of Management identified a set of macro-economic factors as significant in explaining asset returns:

  • Surprises in inflation
  • Surprises in GNP as indicated by an industrial production index (IPI)
  • Surprises in investor confidence due to changes in default premium in corporate bonds
  • Surprise shifts in the yield curve

In the Risk Class Approach study, an optimal mix of assets is determined by achieving target exposures to different risk factors. It recognizes that investable and tradable assets in a portfolio are merely a vehicle for investors to gain exposures to a set of risks that are believed to be rewarded. The factor structure in the risk class approach was estimated using the sample period of monthly data from April 1953 to December 2010, and the three cases assumed were: i) factors only, ii) factors + uncorrelated specific risks, and iii) factors + correlated specific risks.

The Risk Class Approach adds a factor structure to the underlying assets in which the volatility reflects exposures to the risk factors as well as idiosyncratic volatilities, on top of asset allocation approach that entails modeling risk using a covariance matrix with different assets’ respective volatility and correlations of them.

A challenge of the Risk Class Approach is that the true factor structure is unobservable. However, recent history has suggested that one such factor could have been related to risk aversion, or what have been termed “flight to safety.”

Risk Budgeting Portfolio vs. Mean-Variance-Optimized Portfolio

Mean-Variance Optimization (MVO) requires inputs of expected returns and a covariance matrix, and is often used together with MPT. The main difference between a risk-budgeting (RB) portfolio and MVO portfolio is that the latter is based on optimization techniques, implying that MVO portfolios are very sensitive to the inputs. In addition, MVO has a tendency of maximizing effects of errors in the input assumptions.

Three Steps of Risk Allocation

  1. Define a target risk level for the portfolio
  2. Calculate the estimate of total portfolio risk and build a portfolio that matches the target risk
  3. Manage the portfolio to main the risk level close to the target level (rebalancing)

References:

  • Fama, Eugene F., M.R. Gibbons (1984)
  • Chen, Roll, and Ross (1986)
  • Sharpe, William (1992)
  • Yücel Özkaya (2006)
  • Maillard et al. (2010)
  • Benjamin Bruder and Thierry Roncalli (2012)
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