It all Depends on Maths

My last post questioned the true meaning of the increasingly popular phrase “evidence-based investing”. All investing should be evidence based. Anything else is just punting (speculation). That said, it looks to me like the term is beginning to be used by some as a marketing label.

Why is this a problem? Because it creates the possibility that people will simply choose “evidence-based investing”without necessarily considering how the evidence might apply to their circumstances or goals. Somewhat ironic, investing in “evidence-based investing” without first considering the evidence, wouldn’t you agree?

This would be a bad thing to do.  No investment strategy works all of the time. Wes Gray made this clear in one of my all-time favourite Alpha Architect posts: Even God would Get Fired as an Active Investor. Its a must-read for anyone that invested in an active (fundamental or quantitative) investment strategy.

Success in investing depends on investing in a strategy that we can stick with. We can’t do that without forming reasonable expectations around the possible risks and rewards involved.  Obviously requires evidence. But it also requires an understanding of the key factors that determine whether the evidence applies to a particular set of circumstances. 

An example might help to illustrate the idea. Are rising interest rates good or bad for equity market performance? On the one hand, a higher discount rate results in lower valuations, which is usually bad for performance.  But on the other hand, higher interest rates may be due to improving economic conditions. In this case the negative valuation impact form higher rates may be positively offset by higher corporate earnings. In other words, the proper interpretation and application of the evidence all depends on the circumstances. 

Let’s apply this idea to making an evidence-based decision on whether or not to invest passively, use a factor-based approach or hire a fundamental active manager. How can we decide which way to invest? A friend and mentor once explained the challenge to me this way:

Friend: What’s the typical institutional fee for a fundamental global equity fund manager?

Me: between 0.5% and 0.75% basis points depending on the strategy.

Friend: OK, lets assume the fee is 0.5%. Let’s also assume they’re skillful, that is they have an information ratio of 0.5 over the long-term and they take a reasonable amount of active risk, for example a tracking error of 5%. How much would you expect them to beat the market by?

Me: With a tracking error of 5% and an information ratio of 0.5, I’d expect them to beat the market by 2.5% over the long-term.

Friend: OK, that sounds fair. What percentage of active global equity fund managers under-perform the market over any one-year, three-year or ten-year period?

Me: It varies, but it’s usually between 60-90%.

Friend: Lets assume it’s 75%. The expected value of your alpha from selecting that manager is expected alpha multiplied by the probability of selecting a manager that out-performs or (5% × 0.5) × (1-0.75) = 0.5%.

In other words, the fund manager has just captured the ENTIRE expected  value of alpha!

What’s the point of this story? The clues are in the maths (Americans say “math”, Australians say “maths”). There are 4 variables:

  1. level of active risk
  2. fee paid
  3. manager skill
  4. your skill in selecting the manager

The decision to invest actively depends on how your circumstances relate to these four variables. It’s as simple as that. Figuring your circumstances out requires some honest self-examination. A good place to start would be to answer questions such as:

  1. How much active risk am I comfortable taking? Can I patiently invest through ups and downs in the market? Will I stick with my chosen strategy even if it under-performs the market for several years?
  2. How much will it cost me to invest? Do I have any negotiating leverage (e.g. a large institutional investor offering seed funding) that can swing the equation in my favour?
  3. Is the manager skilled? Or, is the manager investing in an opportunity set where the competition is weak?
  4. Do I have an edge that shifts the odds of finding a market-beating manager in my favour?

Of the four variables, the fee paid is definitely the most powerful. Its a tautology, the lower the fee paid, the more that’s left for you. It’s also the most reliable. In other, words there’s a one-for-one relationship between what you save and what you get to keep.

One of the best ways I’ve found to lower fees is to avoid paying for risk management (see my earlier post). Admittedly, this is much easier said than done. It can be tough to create the right kind of culture and relationships for this to work.

You’ll have more success with active management if you spend your fee budget on areas where the competition is weaker. For example, would you rather hire an active US investment-grade credit manager or an active emerging markets debt manager? .

This chart from Michael Mauboussin’s must-read paper, Looking for Easy Games,  might help you make up your mind:


Finally, its important to have an edge that helps you improve the odds of finding skilled managers. This is probably the least reliable and most difficult variable to solve in the expected net-of-fee alpha equation.

Unfortunately, there are no easy answers. Here are some ideas I’ve found helpful:

In many cases answering these questions will point towards indexing or investing in a systematic, rules-based strategy designed to target a specific factor such as value or momentum. In some cases, it may point towards selecting a fundamental manager. In either case, you’ll truly be practising evidence based investing.




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