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Position sizing using the Kelly criterion: weighing upside potential against downside risk

One of the bigger worries around thematic investing is that investors may end up mistaking fads for investment themes. An ill-informed thematic investor in 1999 might have been convinced that putting most of their money in Dot com stocks would absolutely future-proof his portfolio, for instance. His or her money would have vanished into thin air.

Our approach is different, as in the model portfolio we generally pick themes that are underpinned by plenty of research and strong and obvious social and economic undercurrents. Things like water scarcity or healthcare innovation, where it is obvious that growing demand for water and healthcare as the world’s population ages and its middle class grows, is not just going to stop from one day to the next.

As a counter example, while we don’t necessarily believe that Blockchain is a fad, for the time being we are holding back from allocating to it as we cannot quite see the end game there yet.

Our approach: Marrying the quantitative to the fundamental

Fundamentally, we are sure that the themes we select are not fads and believe that all themes we invest in have strong return potential above the broader market in the longer run.

But besides being picky as fundamental theme investors, we also believe in marrying the fundamental to the quantitative. Before allocating to any theme, we perform thorough risk analysis on it, and use the output to make informed allocation decisions.

We do this because we know that despite having high conviction on a theme, putting all of our eggs in one basket and getting it wrong (like people got the Dot com bubble wrong), can derail an entire portfolio for the longer run:

  • If you lose -20% in a year, it takes a +25% gain to recover from your loss
  • If you lose -40%, it takes +67%
  • If you lose -60%, it takes +150%
  • If you lose -80%, it takes +400%

To avoid that, we emphasise downside risk management and enforce a position sizing strategy that caps any theme investment at 20%, and further limits that for themes where the downside risks outweigh the upside benefits.

Sound risk management: position sizing using the Kelly criterion

Having a position sizing strategy means setting an objective guideline for the size of every holding in your portfolio. It helps to decide how much to allocate to a certain position (or in our case, theme) and builds a diversified portfolio. That limits the risk of ending up with large and unrecoverable losses.

We apply a custom derivation of the Kelly criterion, a concept from probability theory that has many applications (notably in gambling and trading/investing). The Kelly criterion takes as inputs the win probability and expected returns when winning or losing in order to give you a suggested amount to “bet” on a certain trade. Specifically:

kelly.png

where f* is the suggested allocation, b is the expected return on success, p is the probability of success and q is the probability of losing it all (100%). So in an example where your expected return is 20%, the probability of achieving that is 90% (and the probability of losing it all thus 10%), Kelly would suggest a maximum allocation of 40%.

Typically that amount is then further constrained by setting a maximum allocation on each trade in the portfolio of say 10%, then multiplying that by the Kelly criterion result (the above example would get an allocation of 4%).

At its essence, this is a clever way to distinguish attractive from less attractive investments and allocate accordingly. The Kelly criterion will suggest betting more money on something if:

  • The likelihood of winning is higher
  • The payoff when winning is higher
  • The losses when losing are lower

Our derivation of the Kelly criterion

The above is more of a gambling approach, but there are obvious ways to incorporate it into portfolio management. We take a custom approach and use two analytics from the Bloomberg PORT risk model for every theme:

  • For the expected return in a positive scenario, we take the annualised returns in the 2010-2018 scenario. This was an extremely long-running bull market, and using Bloomberg’s risk model we calculate a hypothetical return based on the portfolio’s factor exposures and factor returns during the period. It should give a decent idea of how well each theme could be expected to do over the longer run, suggesting for instance that our Brexit theme would return some 5.0% annualised, while the Space race theme could earn as much as 16.5%
  • For the expected return in a negative scenario, it takes a similar approach but this time for the years 2008-2009, or the worst global financial crisis that many of us can remember.

We furthermore set the probability (rather subjectively, but uniform for all themes) of the positive scenario occurring at 82.5%, while the negative scenario gets a probability of 17.5%.

For each theme we work with a maximum allocation of 20%, with exception of the core bond and core equity portfolios for which we work with 25% (core bond) and 75% (core equity). All in all that gives us the following sizing function:

Max. position size = 20% *

[ ((82.5% * 2010-2018 return) + (17.5% * 2008-2009 return)) / 2010-2018 return ]

For instance, if the expected payoff on the Space Race theme over 2010-2018 would have been +250% (annualized from December 2009 to March 2018 that makes about 16.5%) and its return in 2008-2009 would have been -50.7%, our rule suggests a maximum allocation of:

20% * [((82.5% * 16.5%) + (17.5% * -50.7%)) / 16.5%] = 20% * 28.7% = 5.7%.

Had the downside loss been cut in half (-25%), we could have put 11.2% in it.

That gives the following maximum figures for the currently covered themes:

CategoryName2008-20092010-2018Max alloc.Kelly % max
Higher RiskHard Brexit-7.7%+49%20.0%11.1%
Lower RiskRising interest rates-8.2%+78%20.0%12.5%
Lower RiskThe next market crash+9.4%+37%20.0%20.0%
Higher RiskTrade wars-5.7%+87%20.0%14.0%
Higher RiskStagflation+2.1%+109%20.0%17.3%
Lower RiskLow volatility high yield-16.8%+158%20.0%11.7%
Higher RiskRobotics / Automation-25.9%+167%20.0%9.4%
Higher RiskWater scarcity-21.2%+140%20.0%9.9%
Higher RiskGlobal tourism-33.7%+192%20.0%8.1%
Higher RiskFrontier Markets-14.8%+142%20.0%11.9%
Higher RiskHealthcare Innovation-10.5%+211%20.0%14.0%
Lower RiskCore Bond-3.4%+11%25.0%9.0%
Higher RiskCore Equity-12.8%+137%75.0%46.7%
Higher RiskBatteries-21.7%+156%20.0%10.2%
Higher RiskBlockchain-24.9%+173%20.0%9.8%
Higher RiskFintech-27.5%+213%20.0%10.1%
Higher RiskSpace Race-50.7%+250%20.0%5.7%
Higher RiskClean Energy-0.2%+101%20.0%16.4%
Higher RiskMillennials-30.9%+167%20.0%8.0%
Higher RiskUrbanisation-12.2%+133%20.0%12.6%
Higher RiskModern Agriculture-13.4%+169%20.0%12.8%
Higher RiskSelf-driving vehicles-13.7%+192%20.0%13.1%
Lower RiskPost Trump Administration-8.7%+50%20.0%10.5%
Higher RiskEmerging Markets-5.1%+110%20.0%14.6%

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