As I’ve noted before on this blog, no matter the strength of historical observation, I am often asked by clients whether minimum volatility (MV) portfolios can continue to perform as they have in the past. In my last blog I answered that question by looking at a “behavioral” explanation – the “favorite/long-shot bias”– as a potential source for the performance of minimum volatility portfolios.
But it’s worth noting that the case for MV portfolios does not rely purely on arguments about behavioral biases. There’s also an interesting argument around what is known as “limits to arbitrage” that may lead to an outperformance of low-beta stocks.
“Limits to arbitrage” refers to situations where investors operate under restrictions that shape their investment behavior — even if they are not subject to behavioral biases. One such “limits to arbitrage” explanation for the outperformance of low-beta stocks is linked to the widespread use of index benchmarks as a mechanism to evaluate active managers[1].
When an active manager is given the mandate to beat a benchmark, he or she is effectively told to care only about the tradeoff between returns in excess of the benchmark and similarly to care only about the active or relative risk against that benchmark. This means that the manager is unconcerned with the tradeoff between total returns and total risk because they will only get paid on the basis of relative performance against the benchmark.
Why does this matter?
Imagine an active manager that operates under such a mandate who has two stocks that he believes are similarly undervalued and thus have the same expected “alpha”. This manager expects to obtain total returns equal to each stocks’ exposure to the market (or the “beta” component of the return) plus an additional positive alpha arising from his or her expertise in stock-selection (or the “alpha” component of the return).
Let’s say these two stocks have a beta of 0.75 and 1.25. The manager expects higher total returns for the high-beta stock because it has the same alpha as the low-beta stock, but it is levered to the positive expected returns of the market. But he also understands that this stock has higher total risk since its high beta “amplifies” the return variation of the market. The two stocks end up with comparable levels of total return per unit of total risk. If the manager cared about total return and total risk, he or she would therefore want to hold a similar, if not larger, amount of the low-beta stock compared with the high beta stock.
In this case, however, the active manager cares only about active risk so he ends up with a significant preference for the high-beta stock. That is because it induces the same amount of active risk as the low-beta stock (both stocks deviate equally from a beta of 1) but it also offers the benefit of being levered to the positive returns of the market and offers higher expected active returns . In short, the ratio of active return to active risk is much better for the high-beta stock.
The upshot is that if there is a sufficiently large number of managers who operate under this sort of active mandate, high-beta stocks can end up being “overbought” — leading to their future underperformance — while low beta stocks can end up being “oversold” — leading to their future outperformance.
What does this mean for minimum volatility portfolios? They are able to take advantage of this stock picking behavior by overweighting low-beta stocks and underweighting high-beta stocks.
Daniel Morillo, PhD is the iShares Head of Investment Research and a regular contributor to the iShares Blog. You can find more of his posts here.
[1] See, for example, Malcom Baker, Brendan Bradley and Jeffrey Wurgler “Benchmarks as limits to arbitrage: understanding the low risk anomaly”. Financial Analysts Journal. 2001. Volume 67 Number 1.
Mr. Morillo,
I’m not sure I understand the distinction here between total risk+return and active/relative risk+return.
Returning to those two stocks with different betas:
The manager theoretically prefers the higher beta selection because he expects its excess return to be higher? Even though both stocks have the same return/risk level?
Thanks,
Ravi
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Dan M: Thanks for the question Ravi. Active or relative risk is measured as the standard deviation of the difference in returns between a security (or fund) and the benchmark. For example, the total risk of an individual security could be 15% per year, but have only a small active risk, say 2%, as measured against the S&P 500. Key to this is the idea that the bigger the difference between a security’s beta and 1, the larger its active risk.
On the second question, the stock that has higher beta has “leverage” to the market returns. A beta of 1.25 means that if the market is up by, say, 10% this high-beta security would be expected to be up more than the market at 12.5%. Insofar as over long periods of time the market is expected to have a positive return, this higher leverage makes it preferable for active managers who see the higher expected return given that its active risk is the same as that of the low-beta stock.
As more money flows into minimum variance portfolios, won’t low beta stocks become less “oversold”, driving up their valuations and thus reducing future returns?
Thanks for the question Mike. Yes, this is true with any risk premia or, for that matter, market inefficiency. For example, as more money flows into ‘value’ or ‘momentum’ stocks those effects would also reduce the future returns associated with such characteristics. The key issue is how likely is it that there will be sufficiently large flows to reduce or eliminate the effect in the near to medium term. Given that part of the minimum-variance effect may be related to an institutional constraint that induces a large segment of the investment population (active managers paid on the basis of relative return) to ignore the total-return/total-risk relationship, it is difficult to envision that behavior would rapidly change and eliminate the effect in the near- to medium-term.
- Dan