- Active equity and passive fixed-income allocations make sense if positive active returns can be expected in the equity market and only in the equity market.
- Evidence in favor of such a contention would be information ratios in active equity universes that thoroughly dominate those for fixed-income universes.
- In the manager universes studied here, for sample periods including 2007-08, equity manager information ratios were slightly higher than those for fixed-income managers, but not so much higher as to indicate thorough domination. Furthermore, for sample periods ending prior to 2007, information ratios for fixed-income managers were generally higher than those for equity managers.
- Looking at managers’ active returns over time, it is clear that the financial crisis of 2007-08 was a disaster for active fixed-income, but not traumatic for active equity. In contrast, the worst periods for active equity were precisely those years when the stock market in general enjoyed its strongest bull runs.
- In aggregate, these findings do not indicate the kind of thorough domination of active equity over active fixed-income that would justify an active equity/passive bonds allocation. They also suggest that such an allocation would function best as a defensive tactic: a way of reducing downside risk during prospective financial crises, but not an effective way of opportunistically improving returns during more normal market environments.
Some analysts currently recommend that institutions move to passive-only exposure in fixed-income while maintaining active management in equities. In order for such tactics to be advisable, an investor should have a firm conviction that positive active returns—or alpha—can be reliably obtained in equities and only in equities. Evidence supporting that conviction would be a finding that information ratios for equity managers thoroughly dominate those for fixed-income managers.
This paper discusses the reasoning behind this assertion and then examines relevant evidence on active manager returns. The analysis covers annual holding period returns from 1989 to the present for the Investworks asset manager database. As the number of managers participating in this survey is larger the more recent the reporting date, results are presented for successive sample periods, with the shorter, more recent periods encompassing larger numbers of managers.
The findings differ somewhat depending on whether the sample periods in question contain the last two years of financial crisis. When 2007-08 is included, equity managers did generate somewhat higher average alphas and higher information ratios than did their fixed-income counterparts. Even for these sample periods, active equity’s relative performance is not so strikingly superior as to constitute thorough dominance. Moreover, for sample periods ending in 2006, before the onset of crisis, not only were information ratios generally higher for fixed-income managers, but also average alphas for fixed-income managers were usually as high as or higher than those found among equity managers.
These results suggest that active equity has fared better than active fixed-income during the current financial crisis. However, it also appears that active fixed-income has fared better in non-crisis periods. The worst years for active equity were precisely the years where the equity market performed best: 1994-99. The best years for active equity were those where equity prices collapsed: 2000-02 and recently. Meanwhile, for fixed-income sectors, the presence of positive alpha is generally steady over both the bull and bear markets of 1989-2006. However, the singularly severe crisis of 2007-08 succeeded in ruining fixed-income alpha in a way that preceding credit crises over 1989-2006 failed to do.
Even if the averages for 1989-2008 are taken to be most representative of future market conditions, the details of the various market environments are still important. These details suggest that active equity fares best as a defensive tactic, better suited to stemming declines in a bear market than reliably enhancing returns during a bull market. Therefore, the tactic of active equity/passive fixed-income would appear to work best as a hedge against future downside risks—that is, a way of reducing downside risks should recession and bear markets linger, but not an effective way of enhancing upside potential should markets rebound.
Optimizing Active Management Allocations
Asset allocation is a strategic decision, and the aggregate of the benchmarks comprising that allocation represents a minimum-risk strategic deployment. Active management is an effort to enhance returns above those of the minimum-risk, passive deployment. The asset allocation itself should be efficient: no other allocation should be able to deliver higher expected returns unless it delivers higher risk or volatility. The active management allocation should be similarly efficient. No other active allocation should offer higher aggregate expected returns unless it also features higher risk/volatility against the aggregate benchmark, that is, higher tracking error. Another way of stating this is that an efficient active allocation has maximum information ratio: maximum ratio of expected alpha to aggregate tracking error.
The return from active management is just the sum of alphas across managers. The aggregate tracking error of active management from the aggregate benchmark of the allocation is merely an amalgam of the tracking errors of individual managers. Maximum information ratio for an active allocation is achieved by directing active management toward those sectors featuring the highest information ratios. In fact, it can be easily shown that if the alphas of various sectors are uncorrelated, then active management should be allocated across sectors in proportion to the squares of the information ratios of those sectors, with higher information-ratio sectors receiving much higher active allocation and vice versa.1
This implies that active management should be confined to a single sector only if that sector alone can be expected to provide positive alpha. Any sector that can be expected to provide positive alpha should receive some allocation of active management. This is in line with the general principle of diversification. Just as it is risk-efficient to diversify any time there are two or more assets with positive expected returns that are not perfectly correlated, any time a number of sectors offer the expectation of positive alpha, an efficient active allocation would invest in all of those sectors to at least some extent.
In summary, the issue of whether or not to confine active management to equities should revolve around the question of whether equities and equities only offer the expectation of positive alpha. Information ratios for active equity management should be statistically significant, and information ratios for active fixed-income should be uniformly insignificant throughout fixed-income sectors in order to validate an active stocks/passive bonds allocation. Needless to say, information ratios for equities should be much larger than those for fixed-income in order for this to be true. This is the “thorough dominance” referred to above.
Setting Up The Empirical Results
Investworks compiles manager universes for a wide range of market aggregates. The analysis here focuses on the Investworks universes of large-cap equity, core and core plus fixed-income, and long-duration fixed-income. Benchmarks for these universes are the S&P 500, Barclays Capital U.S. Aggregate Bond Index (twice), and Barclays Capital U.S, Long Government/Credit Bond Index, respectively.
Annual holding period returns were calculated for each manager in the respective universes, and annual alphas were calculated as the compound differences between each manager’s total returns and those for the respective benchmarks. For each sample period considered, the analysis summarized in Exhibit 1 was confined to those managers reporting full-year returns for each year in that sample period. Summary measures of manager alpha for each universe and each sample period are reported in the exhibit. The count of managers for each universe and sample period is shown in the first line of each subsection of the table.
The rest of the results in Exhibit 1 describe the distributions of compound (logarithmic) annual alphas for individual managers within each universe. For each manager in a sample period, alpha will have a mean, tracking error (volatility), information ratio (ratio of mean to tracking error) and correlation with its benchmark. The table shows the median levels of these statistics across the relevant universe of managers.
For example, over the 1989-2008 sample, each of the 45 reporting equity managers had an average alpha for that 20-year period, and the median across managers of these average alphas was 75 basis points per year (bpsy). The other medians reported were derived comparably. Also shown is the range of values occurring across managers. Thus, for the 45 equity managers in the 1989-2008 sample, average alphas ranged from -115 bpsy to +373 bpsy. Results for other samples and other universes are presented similarly.
The 1989-2008, 1994-2008 and 1999-2008 sample periods show 20-, 15- and 10-year results respectively. Sample periods 1989-2006, 1994-2006 and 1999-2006 show how the results for those respective sample periods vary when 2007 and 2008 are excluded. 1992-2006 and 1997-2006 show 15- and 10-year results for periods not including the current financial crisis. Periods shaded in blue include the current crisis; gray-shaded periods do not. Results across manager universes within a particular sample period can be compared by moving down the appropriate column. The same universe across sample periods can be compared by moving across the appropriate row.
Keep in mind also that while the results here describe all managers within a particular universe reporting to Investworks, they do not include all investors nor even all managers. It is possible that there is reporting and survivorship bias within these findings, so the results cannot be taken as definitive statistical evidence of the existence or non-existence of significant alpha in any particular universe. However, there is no reason to believe that any reporting or survivorship biases in the data taint comparisons of one universe to another or of any universe over time, and it is these latter comparisons that are of prime interest here.
Finally, the last line of the table shows critical values that information ratios should surpass in order to exhibit statistical significance. Information ratios above these critical levels would be a definitive indication that a manager’s alpha is real and not merely luck of the draw.2
Review of Empirical Results
As seen in Exhibit 1, median average alphas were generally positive in most universes. The exceptions occurred in fixed-income sectors over sample periods including 2007-08, especially in sample periods such as the last 10 years, where the 2007-08 results were most dominant.
For the longest sample period, 1989-2008, median average alpha was a bit higher in the equity universe than in the (admittedly small) long-duration universe and a good bit higher than in core fixed-income universes. Notice, though, that even in the 1989-2008 period, median information ratios were generally unimpressive and uniformly insignificant. Over 1989-2008, no equity manager achieved significant alpha. (The top value of the range, 0.27, is below the 0.39 critical value for that sample.) Only a handful of fixed-income managers did, and these were within universes with lower median alphas than equities’.
The results are much the same over the shorter periods including 2007-08. While median average alphas and information ratios are higher for equities than for fixed-income sectors, median information ratios for equities are not significant, nor are they significantly better than those for fixed-income.
Furthermore, the results change substantially when the sample periods are truncated to exclude the current financial crisis. Over 18-, 13-, 8-, 15- and 10-year sample periods ending in 2006, there is little or nothing in the size of median average equity alphas to distinguish them from those for fixed-income sectors. More importantly, the information ratios of fixed-income are generally higher than those for equities, though here also, median information ratios fall short of statistically significant thresholds.
The one sample period ending in 2006 with any difference in results is that of 1999-2006, an 8-year period excluding both the current crisis and most of the late-1990s’ bull market. Active equity shines most in this non-bull, non-crisis environment. The median average alpha of 123 bpsy is well above that for any fixed-income universe, and the median information ratio of 0.42 for equity managers is similarly higher than that for any fixed-income sector (though still falling short of statistical significance).
Manager Alpha Over Time
In general, active equity fared best relative to active fixed-income in sample periods including the last two years of financial crisis, and particularly for the sample period also excluding most of the 1990s’ bull market: 1999-2008. To shed light on whether there is a pattern here, we can look at time series data on median manager alphas across the universes. For this analysis, rather than restricting consideration to those managers reporting results across a particular sample, we look at the median alpha in each year for all managers reporting full-year results. For each manager universe, Exhibits 2-5 chart median alphas for each year versus corresponding benchmark returns.
For the equity universe (Exhibit 2), median alphas were strikingly different during the late-1990s’ bull market than in other years. Apparently, continuous, rapid increases in equity prices were a far greater challenge for equity manager alpha than the pernicious bear markets of 2000-02 and 2007-08.
In contrast, within fixed-income, there is little to distinguish one year from another over 1989-2007, but 2008 was a big sore thumb for all three. Notice also that in contrast to the credit market sell-offs in 1994 and 1999—but similar to that of 2002-03—fixed-income benchmark returns in 2007-08 were decent, thanks to the Treasury rally, even while credit spreads blew out. However, fixed-income managers were generally able to achieve either positive or only modestly small negative alpha in 1994, 1999 and 2003-2004. The active fixed-income washout of 2008 is testament to the severity of recent market stress.
It seems fair to say that active fixed-income stands a decent chance of outperforming its benchmark in all but the most extremely perverse environments (i.e., 2007-08). Active equity fared markedly better in distressed market environments—even severely distressed ones—and faced its toughest sledding during very strong, sustained bull markets.
The results in Exhibit 1 indicate that in all the universes, manager alpha was generally not positively correlated with the corresponding benchmark. If alpha were positively correlated with the benchmark, that would suggest that managers largely leveraged their benchmarks, so alpha would rise and fall with general market performance. In active equity, alpha is typically negatively correlated with the benchmark, apparently reflecting a tendency of active equity managers to be short high-beta or pro-cyclical sectors (or long cash). This would seem to be the reason active equity fared well as a defensive tactic, underperforming during the big bull market but outperforming during bear and mediocre markets.
In contrast, fixed-income managers’ alpha was generally uncorrelated with their benchmarks. There was no apparent tendency to outperform in one environment or the other. Again, the extreme underperformance in fixed-income in 2008 is quite an outlier from the experience of the rest of the period and would not appear to be indicative of future behavior (unless future markets are typically equally distressed).
Only in long duration was there a tendency for alpha to be positively correlated with the benchmark, although even the correlations in this universe fall short of statistical significance. Still, as the long duration investor universe is dominated by defined-benefit pension plans, usually with LDI mandates, a positive correlation of alpha with benchmark is not undesirable here, as it would work to reduce surplus volatility for the overall plan, provided some share of DB assets were invested in sectors other than long duration.
Confining fixed-income allocations to passive mandates and leaving equity allocations actively managed should stem from a conviction that information ratios in the equity space thoroughly dominate those in fixed-income. There is no evidence in the Investworks universe of manager returns over 1989-2008 to support such a conviction. While active equity alphas and information ratios over the last 20 years are higher than those for most active fixed-income sectors, the magnitude of this outperformance does not rise to the level of thorough domination that such an extreme decision would require.
Furthermore, these 20-year results are very dependent on the experience of the last two years (or maybe just last year). Over almost any sample period ending before 2008, information ratios for active fixed-income dominate those for active equities, rather than vice versa, and it is not even the case that the levels of alpha in active equity are appreciably higher than those in active fixed-income.
Even if an investor were to consider the results including 2008 as definitive and/or most representative of market environments to come, it would still seem prudent to take account of how active equity and fixed-income results have varied across market environments. These results strongly suggest that active equity is best deployed as a defensive tactic, a way of stemming losses during adverse market environments rather than a means of enhancing results during favorable market environments. In contrast, active fixed-income would appear to be a reasonable source of alpha in all but the most inhospitable market environments.
None of these results indicate that positive alpha is easy to find. Not a single equity manager displayed statistically significant alpha across the full 20-year period we studied. Neither did any core full manager, and nearly half of all core/core full managers failed to achieve any positive alpha over the full 20-year period. Still, in search for positive returns from active management, the historical data do not support confining that search to equities nor to removing fixed-income from consideration.
- In Bazdarich (2006), “Separability and Pension Optimization,” Journal of Fixed Income, winter 2006 edition, it is shown that any efficient investment allocation can be decomposed into a hedge or minimum-risk allocation and an opportunistic allocation to the “optimal overlay” that features the maximum ratio of expected return to volatility. If, in that context, returns across asset classes are uncorrelated, then the asset weights of “optimal overlay” are in direct proportion to the squares of the Sharpe ratios of the individual assets. The present context concerns “assets” that are themselves overlays, since in moving from a passive allocation to an active one, an investor shorts the benchmark in question and longs an active manager who manages against that benchmark, and the expected return and volatility of this overlay are merely the alpha and tracking error of the active manager in question. It is straightforward to extend the results from Bazdarich (2006) to this context. A formal account of this process will be provided upon request.
For the issue of allocating active management across sectors, the relevant criterion is risk budget and not dollar allocation. An institution willing to undergo 200 bps of tracking error against its aggregate benchmark should allocate active management across sectors according to how much of that 200 bps each sector warrants. Higher information ratio sectors should get higher fractions of the risk budget. Paradoxically, the lower the expected return in a particular sector, the higher the dollar allocation of active management should be in order to achieve that given fraction of total tracking error. (Since the sector is assumed to have a higher information ratio, the lower its expected return, the lower its tracking error must be, and so the higher the dollar allocation must be in order to achieve the specified contribution to total active return or to tracking error.)
- These critical values are based on the simplistic hypothesis that IR•N1/2 is distributed as t with N-1 degrees of freedom, where IR is the information ratio and N the sample size. (This in turn is merely a restatement of the test for the significance of average alpha within a sample.) Phillippe Bertrand  (“The Statistics of The Information Ratio,” available online via web search), presents a more refined analysis of the distribution of information ratios. As the median information ratios derived here do not surpass even the simplistic critical values shown here, a more refined analysis of these data would be overkill.