By Daniel Morillo, PHD iSharesblog.com
In a recent video post I talked about the correlation that can exist between the active performance of bond fund managers and equities. I pointed out that investors might not realize that core (or, in Morningstar parlance, intermediate term) bondmutual fund managers often take their active positions in the form of equity-like risky assets to achieve alpha.
As my colleague Matt Tucker has also discussed on this blog, taking these active positions means a typical core bond fund manager’s alpha is often positively correlated with the returns of broad equity benchmarks like the S&P 500. This means an investor’s actively managed fixed income holdings may perform more like equities than bonds.
Why is this problematic? Because when this correlation is introduced into a portfolio, every dollar allocated to the active manager results in a larger increase in total risk. To justify the additional risk posed by an active fixed income allocation, an investor would typically expect a higher level of alpha. Just how much extra alpha? Let’s take a look at this chart:
The horizontal axis, shows the correlation of the active manager’s alpha with equity returns for an active manager who has a 2% tracking error (i.e. the standard deviation of active returns around its benchmark is 2%).
The vertical axis shows the amount of alpha, in basis points, needed to get a 50/50 allocation of active and passive within fixed income. (I chose the 50/50 split to replicate a “conservative” portfolio that is only 50% allocated to active management. I chose a 2% tracking error as a nice round number that captures the range of managers – from those whose tracking error is close to 0% because they closely track an index to active mangers whose tracking error can be well above 2%)
The chart shows that an investor who wants to allocate a significant portion of his or her fixed income allocation to a 2%-tracking manager whose alpha is 45% correlated to equities needs to consistently pick managers who deliver at least 25 basis points of alpha after costs.
That 25 basis points number may appear small, but it is actually material in comparison with typical alpha levels from core bond fund managers. In the last 25 years, the median core bond fund manager’s alpha was negative (at around negative 70 basis points) and it was correlated with equities at about 45%. Over the same period, only about 1/3rd of managers, on average, were able to deliver alpha of 25 basis points or more in any one year.
What you can see is that in this example the active allocation is justified only if you, the investor, are confident that you can consistently select managers in the top 1/3rd of manager performance.
But as Matt has already noted on this blog, active management skill is difficult not only to create but also for you, the investor, to identify.
 The chart is the result of solving a reverse mean-variance optimization problem: given the returns, risk and correlations of the passive assets, how much alpha does the active manager need to produce, at a given correlation of active returns, such that the fixed income allocation ends up being split 50/50 between the active and passive components? The chart assumes returns for equities and core fixed-income based on 25 years of data for the Russell 3000 and Barclays Capital US Aggregate Bond Index benchmarks respectively. The chart was computed for a “conservative” portfolio that targets 5.5% annual risk, in this case roughly equivalent to an allocation of around 20% to equities and that the manager’s alpha is not correlated with any of the passive components.
 The data used as inputs to solve the reverse optimization problem is from Bloomberg. For both the Russell 3000 and the Barclays Capital US Aggregate Bond Index the total return index levels were used. Annual returns were constructed from the end of September to the end of September of the following year starting in 1986. To obtain excess returns the yield of the 1-year constant maturity treasury index at the beginning of each year (as provided by the Fed) was subtracted from the returns of each of the two assets. September was used since it is the last available quarter-end of data as of the writing of this note. To solve the allocation problem expected returns were computed as simple averages of the annual excess returns and expected risks and correlations were computed using sample variances and covariances of the excess return data. In particular, for the Russell 3000 excess return is 6.2% with risk of 18.8% and for the Barclays Capital US Aggregate Bond Index return is 2.9% with risk of 4.5%
 Data is from Morningstar. Data on post-cost monthly returns for all mutual fund share classes classified as ‘intermediate bond’ were collected from 1986 to September 2011, including shares classes that were closed or merged. Monthly fund-level data was obtained by taking the median return of all share classes linked to a single fund in any one month. For each fund alpha is computed as the fund’s return minus the return of the Barclays Capital US Aggregate Bond Index in that month. For each fund annual alpha from September-to-September is constructed (to match the benchmark data for the Russell 3000 and the Barclays Capital US Aggregate Bond Index). Each year the median fund’s return across all fund is computed and the average of these across all 25 years is reported as the overall annual median manager’s alpha of negative 70bps.
About Daniel Morillo, PHD
Daniel Morillo, PhD, Managing Director, is the Global Head of Investment Research for iShares. Dr. Morillo’s service with the firm dates back to 2003, including his years with Barclay’s Global Investors (BGI), which merged with BlackRock in 2009. At BGI, he served in a variety of senior research and portfolio management roles including, Head of Global Equities within the Scientific Active Equity group.