# Two amazingly simple rules for making alpha/beta allocations

We review a lot of academic research here at AllAboutAlpha.com.  Some of it can be a little dense and we’re the first to admit that we often can’t follow the mathematical nuance or arcane calculus contained in some of it.  Still, we try to distill these papers down to a simple lesson or two that can be communicated in the 5 minutes or so that you have to read our daily posts.

But occasionally, we come across academic-style articles written by practitioners.  Not surprisingly, these tend to be a little more, well, practicalHere’s a great example

Robert Scott of Schroders Investment Management in London has come up with a simple, yet elegant way to determine if it makes sense to add an alpha source to a portfolio.

Scott laments that the proportions of alpha and beta used by most managers is usually quite arbitrary:

“…91.5% of total investment performance comes from the asset allocation or beta risk, while the remainder of the performance comes from active or alpha risk. This allocation is often considered an exogenous variable, determined at the whim of the investment manager.”

As we have reported on these pages, this allocation isn’t just arbitrary, it’s usually unconscious – determined by the fund’s level of active management.

But let’s say the active/passive balance of a fund is explicitly determined by a manager and is expressed in the form of allocations to alpha and beta risk.  What is the optimal proportion of both – the proportion that yields the highest risk-adjusted returns?

Scott argues that the information ratio (excess returns over the standard deviation of those excess returns) “has failed us” since it does not capture the correlation (or lack thereof) of those excess returns.  As he points out, the information ratio would reward a manger for simply leveraging the benchmark in good times.  As he writes:

“If a manager is delivering uncorrelated alpha, this should be better rewarded than a manager who delivers perfectly correlated alpha (i.e. beta)…”

Rule #1

By simply manipulating the formulas for the information ratio and standard deviation (thankfully, in the paper’s appendix) he shows that a new asset should be added to a portfolio if the ratio of it’s information ratio to the portfolio’s Sharpe ratio is larger than its correlation to that portfolio.

The intuition behind this is a little obfuscated by the complexity of the formulas involved.  But think of it this way:  If the correlation between a possible new investment and the existing portfolio is one (for example, if the new investment is simply a levered version of the existing portfolio) then the new investment would have to deliver an information ratio that is higher than the Sharpe ratio.  In other words, it would simply have to be a better investment, with better risk-adjusted returns (which would, by definition, be impossible anyway).

If, on the other hand, the correlation between the possible new investment and the existing portfolio were, say, zero, then the information ratio of that new investment would simply have to be positive in order for it to add value.

Finally, if the correlation was negative, then the information ratio of the new investment could be negative and still add value.

This rule can be particularly helpful, of course, when the correlation between a possible new investment and the existing portfolio is somewhere between 0 and 1.

Rule #2

Using similar algebraic manipulation, Scott argues that the of alpha and beta is simply the ratio of the alpha source’s IR and the portfolio’s Sharpe ratio – assuming the alpha source has a zero correlation to the portfolio.

If, on the other hand, the alpha sources has a non-zero correlation to the existing portfolio (which is almost always the case), then the optimal allocation would be:

Where “I” is the information ratio, “S” is the Sharpe ratio and rho is the correlation between the alpha source and the existing portfolio.

Scott concludes by echoing Robert Litterman’s “active risk puzzle” (related post):

“Traditional asset management mandates typically consume the largest component of risk in a benchmark and only a residual amount of risk in the active component…”

In our view, the growing realization of the importance of active risk is what is fueling the popularity of alternative investments.  Tools like Scott’s are valuable ways of quickly seeing the value of these uncorrelated asset classes.

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