Benchmarking low-volatilty strategies

Low volatility investing and performance measurement — my favorite topic scheme — how could I resist?

The paper

The paper is “Benchmarking Low-Volatility Strategies” by David Blitz and Pim van Vliet.

The problem

They claim that using a low-volatility index as a benchmark for a low-volatility strategy is not a good idea because:

  • All low-volatility indices are essentially just arbitrary low-volatility strategies
  • Some low-volatility indices constrain turnover and hence are path-dependent
  • Many indices are not very transparent in their assumptions
  • A global index can be suitable for at most one home currency

Their solution

Given the problems with a low-volatility index, they essentially suggest just giving up and benchmarking against the capitalization-weighted index.

My take

I agree with them about the problems of benchmarking with a low-volatility index.

They aren’t very explicit about what it would mean to benchmark against the cap-weighted index.  They talk about using the Sharpe ratio or Jensen’s alpha, but don’t say what would be done with those statistics.

Whatever is done, I doubt it’s a good idea.  Using a benchmark that fits the strategy is troublesome enough.  Here we are talking about using a benchmark that is systematically different than the strategy.

I think it would actually be dangerous because it would give the wrong signal.  During a boom the cap-weighted index would outperform the low-volatility strategy.  That would encourage people to switch out of low-volatility at precisely the wrong time.

The first question to ask, I think, is: “What’s the question?”

Do we want to know how our fund is performing relative to other low-volatility possibilities?

Do we want to know how our fund is performing given the path-dependence due to our turnover constraint?

Do we want to know how low-volatility is performing relative to market-like strategies?

Something else?

The paper is not very clear on the question or questions being asked.  My suspicion is that random portfolios will probably have better answers than a benchmark for whatever questions there are.

Epilogue

Red hair and black leather my favourite colour scheme

from “1952 Vincent Black Lightning” by Richard Thompson

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11 Responses to Benchmarking low-volatilty strategies

  1. Pingback: Monday links: second chances | Abnormal Returns

  2. David Blitz says:

    It is true that in our paper we don’t elaborate on what it means to evaluate low-vol strategies against the cap-weighted index using Sharpe ratio or Jensen’s alpha. That’s because we considered this to be pretty straightforward. The whole point of low-vol investing is to get a higher return per unit of risk than the cap-weighted index. If you define risk as volatility this means the aim is to get a higher Sharpe ratio and if you define risk as beta it means the aim is to get a positive Jensen’s alpha. So what could be more natural than evaluating a real-life low-vol strategy using precisely these measures?

    If you want to assess if low-vol strategies did better than the market, simply look at whether their Sharpe was higher (or whether their Jensen’s alpha was positive) compared to the market index. By the way, in this way you specifically prevent switching out of low-vol at precisely the wrong moment, because if low-vol has lower returns than the market during a boom, it may still have the same or even a better Sharpe ratio (or positive Jensen’s alpha). That’s the whole point of using a risk-adjusted performance measure.

    Alternatively, if you want know how your fund is performing relative to other low-vol funds, simply compare their Sharpe ratios or Jensen’s alphas. This way you can assess whether your fund is e.g. a top quartile fund or a bottom quartile fund among the group of low-vol funds that you’re looking at.

    • Pat says:

      David,

      Thanks for the clarification on your proposed benchmarking.

      So now we have two hypotheses about the relative size of Sharpe ratios of low-vol versus cap-weight leading up to a crash. Some data would be useful to see who (if either) is right.

      Another concern of mine about benchmarking is that it is going to be very noisy. Noisy in the sense that a bootstrap of the statistics is going to be wide. I’d guess that bootstrapping differences would often include zero in the distribution.

      It is also noisy in the sense that the cap-weighted statistics will be unduly driven by the behavior of the megacaps — when the assets with the biggest weights do relatively well, cap-weight is really hard to beat.

    • “The whole point of low-vol investing is to get a higher return per unit of risk than the cap-weighted index.”
      I am not sure about that. According to this logic, we can get rid of any benchmarks. Risk-adjusted returns are an investment objective which is independent of the benchmark question. For practical purposes, I would suggest to use peer averages as a benchmark. I consider low-vola investing an investment style or theme, and cap-weighted benchmarks do make sense to evaluate a style because they do still represent a passive, “theme-less”, alternative. I would also consider simple data-driven quant algorithms as a benchmark. Such benchmark may make use of random portfolios (or not).
      I is important to properly consider the implicit or explicit promises of low-volatility strategies. “Low volatility” to me sounds a risk-based strategy, not a risk-adjusted return strategy. Therefore, it might be appropriate to benchmark risks, not returns.

  3. Pat says:

    Andreas,

    You are correct that “low-volatility” sounds like a risk-based strategy. But the key point is that it is really a return-based strategy — the highest volatility assets tend to have low expected returns.

    So comparing the returns of a low-vol strategy with other things really does make sense.

    • Hi Pat, I am well aware of that (did several theoretical and empirical investigations into this). But short-term and long-term relationships are really a “theory”, which cannot be guaranteed. The “low risk” portfolio characteristics, on the other hand, can be managed. Therefore, low-risk strategies might need “risk benchmarks”, not “return benchmarks”. Rgrds, Andreas

  4. Pat says:

    Andreas,

    Well, okay. If we did have risk benchmarks, what would we be gaining?

  5. Pat says:

    Andreas,

    I’m back to what I said in the post: What’s the question?

    And once we have an answer, how does that affect our behavior?

    That is, do you have any specific scenarios in which a risk benchmark would help a fund manager?

    • I remeber a case in which a low risk manager did not perform and subsequently played “double-or-nothing”, i.e. massively increased risk. The discussion was very akward initially because it focused on performance; risk-benchmarks made people remember again the original purpose of the product.
      Another common case are “low risk” portfolios that are managed relative to a constant risk target (for example, VaR). Managers of such portfolios are very often (typically in bull markets) confronted with complaints that they “underperform” relative to some benchmark which is not subject to risk restrictions. Risk-based benchmarks are essential for such managers. On the other hand, clients also need risk-based benchmarks in order to confront managers who use risk limits as an excuse for their underperformance: “I underperformed so much because I was forced to reduce risk”. Random portfolios give very interesting answers in the last situation: they can be used to demonstrate whether a risk limit was binding or not.

  6. Pat says:

    Andreas,

    Thanks. I think random portfolios are a good tool for all of your situations: they give you a distribution rather than a single number, and they can be specialized for the question at hand.

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