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Summary­

• Few investors hold explicit shorts in their portfolio, but all active investors hold them
• We (re-)introduce the simple framework of thinking about an active portfolio as a combination of a passive benchmark plus a long/short portfolio.
• This decomposition provides greater clarity into the often confusing role of terms like active bets, active share, and active risk.
• We see that while active share defines the quantity of our active exposure, the active bets themselves define the quality.

Ask the average investor if they employ shorting in their portfolios and “no” is likely the answer.

Examine the average portfolio, however, and shorts abound.  Perhaps not explicitly, but certainly implicitly.  But what in the world is an implicit short?

As investors, if we held no particular views about the market, our default position would be a market-capitalization weighted portfolio.  Any deviation from market-capitalization weighted, then, expresses some sort of view (intentional or not).

For example, if we hold a portfolio of 40 blue-chip stocks instead of a total equity market index, we have expressed a view.  That view is in part determined by what we hold, but equally important is what we do not.

In fact, we can capture this view – our active bets ­– by looking at the difference between what we hold in our portfolio and the market-capitalization weighted index.  And we quite literally mean the difference.  If we take the weights of our portfolio and subtract the weights of the index, we will be left with a dollar-neutral long/short portfolio.  The long side will express those positions that we are overweight relative to the index, and the short side will express those positions we are underweight.

Below is a simple example of this idea.

“Dollar-neutral” simply means that the long and short legs will be of notional equal size (e.g. in the above example they are both 25%).

While our portfolio may appear to be long only, in reality it expresses a view that is captured by a long/short portfolio.  As it turns out, our portfolio has an implicit short.

This framework is important because it allows us to go beyond evaluating what we hold and instead evaluate both the bets we are taking and the scale of those bets.  Generically speaking, we can say:

Portfolio = Benchmark + b x Long/Short

Here, the legs of the Long/Short portfolio are assumed to have 100% notional exposure.  Using the example above, this would mean that the long/short is 100% long Stock B, 100% short Stock A, and b is equal to 25%.

This step is important because it allows us to disentangle quantity from quality.  A portfolio that is very overweight AAPL and a portfolio that is slightly overweight AAPL are expressing the same bet: it is simply the magnitude of that bet that is different.

So while the Long/Short portfolio captures our active bets, b measures our active share.  In the context of this framework, it is easy to see that all active share determines is how exposed our portfolio is to our active bets.

We often hear a good deal of confusion about active share.  Is more active share a good thing?  A bad thing?  Should we pay up for active share?  Is active share correlated with alpha?  This framework helps illuminate the answers.

Let’s slightly re-write our equation to more explicitly highlight the difference between our portfolio and the benchmark.

Portfolio – Benchmark = b x Long/Short

This means that the difference in returns between the portfolio and the benchmark will be entirely due to the return generated by the Long/Short portfolio of our active bets and how exposed we are to the active bets.

R_Portfolio – R_Benchmark = b x R_Long/Short

Our expected excess return is then quite easy to think about: it is quite simply the expected return of our active bets (the Long/Short portfolio) scaled by how exposed we are to them (i.e. our active share):

E[R_Portfolio – R_Benchmark] = b x E[R_Long/Short]

Active risk (also known as “tracking error”) also becomes quite easy to conceptualize.  Active risk is simply the standard deviation of differences in returns between our Portfolio and the Benchmark.  Or, as our framework shows us, it is just the volatility of our active bets scaled by how exposed we are to them.

s[R_Portfolio – R_Benchmark] = b x s[R_Long/Short]

We can see that in all of these cases, both our active bets as well as our active share play a critical role.  A higher active share means that the fee we are paying provides us more access to the active bets.  It does not mean, however, that those active bets are necessarily any good.  More is not always better.

Active share simply defines the quantity.  The active bets, expressed in the long/short portfolio, will determine the quality.  That quality is often captured by the Information Ratio, which is the expected excess return of our portfolio versus the benchmark divided by how much tracking error we have to take to generate that return.

IR = E[R_Portfolio – R_Benchmark] / s[R_Portfolio – R_Benchmark]

Re-writing these terms, we have:

IR = E[R_Long/Short] / s[R_Long/Short]

Note that the active share component cancels out.  The information ratio provides us a pure measure of the quality of our active bets and ignores how much exposure our portfolio actually has to those bets.

Both quantity and quality are ultimately important in determining whether the portfolio will be able to overcome the hurdle rate set by the portfolio’s fee.

b x E[R_Long/Short] > Fee_Portfolio – Fee_Benchmark

The lower our active share, the higher our expectation for our active bets needs to be to overcome the fee spread.  For example, if the spread in fee between our portfolio and the benchmark is 1% and our active share is just 25%, then we have to believe that our active bets can generate a return in excess of 4% to justify paying the fee spread.  If, however, our active share is 75%, then the return needed falls to 1.33%.

Through this equation we can also understand the implications of fee pressure.  If the cost of the active portfolio and the cost of the benchmark are equivalent, there is zero hurdle rate to overcome.  We would choose active so long as we expect a positive return from our active bets.[1]

However, through its organizational structure and growth, Vanguard has been able to continually lower the fee of the passive benchmark over the last several decades.  All else held equal, this means that the hurdle rate for active managers goes up.

Thus as the cost of passive goes down, active managers must lower their fee in a commensurate manner or boost the quality of their active bets.

Conclusion

For long-only “smart beta” and factor portfolios, we often see a focus on what the portfolio holds.  While this is important, it is only a piece of the overall picture.  Just as important in determining performance relative to a benchmark is what the portfolio does not hold.

In this piece, we explicitly calculate active bets as the difference between the active portfolio and its benchmark.  This framework helps illuminate that our active return will be a function both of the quality of our active bets as well as the quantity of our exposure to them.

Finally, we can see that if our aim is to outperform the benchmark, we must first overcome the fee we are paying.  The ability to overcome that fee will be a function of both quality and quantity.  By scaling the fee by the portfolio’s active share, we can identify the hurdle rate that our active bets must overcome.

[1] More technically, theory tells us we would need a positive marginal expected utility from the investment in the context of our overall portfolio.

Corey Hoffstein

Corey is co-founder and Chief Investment Officer of Newfound Research. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.