The performance of most portfolio managers is measured against a bench- mark index. Active management exposes investors to beta, which is defined as portfolio volatility relative to the market, and to alpha, the value added by the portfolio manager’s luck or skill. Sharpe (1991) observes that the market as a whole is made up of all market participants, and therefore the average return of all participants equals the return of market, before fees and costs. After fees and costs, however, the average return of all market participants is below market return. Consequently, to beat the market consistently, investors need to have special skills. Interestingly, if one asks market participants what active return they expect to earn, 90 percent of them say they expect an excess return of 1–1.5 percent. Obviously, this contradicts conventional wisdom.
A good starting point for the analysis of active management concepts is the Evans–Archer diagram depicted below. As portfolios become more diversified portfolio risk declines until it asymptotically reaches a level that is known as undiversifiable, systematic or market risk. Portfolios are usually managed against fully diversified benchmark indices that are designed to reflect market performance and market risk as good as possible. In other words, the performance of broadly diversified benchmark indices repre- sents the reward to market risk.
The component above the horizontal line in Figure 2.2 is usually known as idiosyncratic, unsystematic or diversifiable risk. In this context we use
Figure 2.2 Evans–Archer diagram of risk versus diversification
Source: Union Investment Diversification
Risk
Market risk Active risk
the term active risk because it is the risk of an active manager who deviates from the benchmark in order to beat the market. Establishing the right portfolio structure requires skill or the portfolio will underperform the benchmark. Active risk therefore means accepting a certain amount of idiosyncratic risk over and above market risk in order to add value through active management. However, as idiosyncratic risk is diversifiable, it is usually not rewarded, except from luck. Consequently the unconditional expected return of taking on active risk is zero. If a portfolio manager has special skill in active management, his conditional expected return, how- ever, is proportional to skill and hence positive.
Grinold (1989) introduced an interesting concept that relates the excess return generated by the portfolio manager to the risk he incurs relative to the benchmark. In this framework the manager’s opportunities can be described by the ex ante information ratio IR, defined as the ratio of expected active return divided by active risk, that is
,
where RAdenotes active return and Adenotes active risk. If the benchmark is the riskfree rate, the ratio is identical to the Sharpe ratio. The original form of the “Fundamental Law of Active Management” suggests that
Consequently, the information ratio depends on the information coefficient IC and the number of independent decisions in the actively managed portfolio.
The information coefficient IC is defined as the correlation of the forecasts with the actual outcomes. Combining both formulas, the fundamental law reads
The expected active return consequently depends on skill, breadth and the amount of risk that is taken by the portfolio manager. Grinold (1989) and Thomas (2000) highlight the approximate nature of the fundamental law and recommend its use as a strategic tool. The lesson from the fundamental law is that the value added by active management is determined by the quality of the decisions of the portfolio manager as well as the diversifica- tion of investment ideas. The law therefore encourages managers to exploit independent sources of information whenever available. Whereas very focused strategies often are easy to explain they may lead to a high volatil- ity of excess returns. Diversifying not only with respect to asset classes or sectors, but also with regard to risk factors and sources of information is likely to produce consistently favorable risk/return profiles, especially over the medium to longer term.
E(RA) ⫽ IC兹NA. IR ⫽ IC兹N.
IR ⫽ E(RA)
A
Assuming that a portfolio manager acts in a way that is mean-variance efficient the value added, VA, is proportional to the information ratio squared. Expressed in terms of skill and breadth the portfolio manager’s ability to add value is
where Rrepresents the level of risk aversion. Consequently, to double his information ratio or the value added for a given level of active risk, the portfolio manager must double his skill, or quadruple the number of inde- pendent bets in the portfolio. Figures 2.3 and 2.4 illustrate this relationship.
The more independent decisions are made the lower is the skill required to achieve a target information ratio. If the number of independent trade ideas is very low, for instance because the portfolio manager chooses to imple- ment only strategic duration bets, a high level of skill is required to generate a favorable risk-adjusted return. Clarke, de Silva and Thorley (2002) point out that portfolio managers often face constraints that reduce the degree to which trade signals are transferred into active weights. Typical constraints for real-money investors would include “no short sales” and maximum leverage restrictions. In practice, the observed transfer coefficients lie between 0.3 and 0.8. If the transfer coefficient is 0.5 only 25 percent of the variation in realized excess return, that is, tracking error, is attributable to
VA ⫽ IC2·N 4R
,
Figure 2.3 Skill required to achieve a certain information ratio depends on the frequency of the implementation of independent trades
Source: J.P. Morgan 0
10 20 30 40 50 60 70 80 90 100
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Information ratio
Skill (%)
Annual Quarterly
Monthly Biweekly Weekly Daily
the success of the signal. The remaining 75 percent are due to constraint- induced noise. The success rates, or skill levels, that are required to achieve a certain information ratio is therefore the higher, the more restrictions exist. Managers with substantial constraints will experience frequent periods where the investment ideas are successful, but performance is poor.
Conversely, there will also be periods when performance is good although the quality of return forecasts is poor. Portfolio managers who may only take long positions, for example, government bond managers who are allowed to diversify into corporate bonds temporarily, face a particularly disadvantageous situation, because the number of potential trades is limited. Thus, the required success rate is significantly higher than the one of an investor with an aggregate benchmark who is able to benefit from overweight as well as underweight positions.
In practice, it often proves difficult to assign an accurate level of skill to a certain portfolio manager as well as to estimate correctly the number of independent trade ideas. Nevertheless, before launching a major research project, improving the technical infrastructure or optimizing internal processes to increase skill, a quick calculation of this sort may be valuable, considering the costs and the uncertainty of success related to these measures. From a cost and a portfolio management perspective, broadening the spectrum of investment ideas is often more promising.
Traditionally, credit investors have primarily diversified investments within an asset class. The fundamental law of active management suggests
Figure 2.4 A given information ratio is achieved by various combinations of skill and breadth
Source: J.P. Morgan –5
5 15 25 35 45 55 65 75
0 10 20 30 40 50
Number of independent trades
Skill (%)
IR = 0.75 IR = 0.5 IR = 0.25
that this is not enough. Trade ideas on the issuer level should be comple- mented by sector and, if permitted, asset allocation bets. Diversifying into risky asset classes like high yield, for example, may not necessarily increase portfolio volatility if correlations with the core portfolio are low enough. In addition, active management of duration, yield and credit curve position- ing and currency risk can add value. Finally, a combination of various sources of information helps to generate a variety of independent trade ideas. Remember that the frequency of deviating from the benchmark has substantial impact on the expected information ratio and excess return.