What metrics really count when building a diversified portfolio

The three things I look at in detail whenever I think about adding a new strategy or asset to my portfolio are:


  • The expected risk-adjusted return over the long-term: this is defined by excess returns and volatility, expressed most commonly by the Sharpe ratio
  • The correlation between different strategies and assets, taking a special look at correlations in crisis periods
  • The return distribution characteristics of the different elements of the portfolio


To make things harder and more uncertain, all three metrics fluctuate over time – especially for expected risk-adjusted returns we can only take an educated guess based on historical values.


Each metric adds an additional layer of information. Balancing different characteristics makes the portfolio´s performance more robust to different future scenarios, which is really what the concept of diversification is all about. Optimal diversification is what we should aim for in portfolio construction as it leads to higher returns while taking less risk.

Uncorrelated performance of assets in a portfolio often does not feel very good. Diversification implies that there will always be parts of your portfolio that underperform or even lose while others excel. We take disproportional notice of these laggards and instinctively want to avoid them – the benefit over time (as leaders and laggards continuously change) is very abstract and counterintuitive as it isn’t visible in daily portfolio performance.

As just about everybody knows about diversification being the only free lunch in finance, I think that it is worthwhile to pay close attention to the less commonly known higher moments of return distributions, for example the skew, and to integrate alternative, uncorrelated return sources in our portfolio.


It is a bit like peeling back the layers of an onion
Return is our goal, the reason for investing in the first place. But on its own it is of very limited use as we need to know what risk we are taking to reach it.
Risk is what we want to avoid*, but we need to take risk to earn excess returns. Just how much risk you are willing to take is a key question every investor needs to answer. As the future is unknown, we can at best take an educated guess as to how much risk we are actually taking – to make that guess as good as possible is one of the main reasons for researching the intricate details of investing.


Risk-adjusted Return
Combining return and risk gives us the risk-adjusted return. If we divide excess return by volatility (as an expression of risk) we get the Sharpe ratio. In general the higher its Sharpe ratio, the better the strategy or portfolio is.
As the Sharpe ratio depends on the assumption of returns being independent of each other and normally distributed, which poorly reflects the properties of real markets, it always has to be taken with a grain of salt. It is also very sensitive to the time period it looks at, because realized returns often differ dramatically over different periods in history. As it is widely used, it is still the best measure to compare different strategies when our information comes from different resources.


Correlation and Diversification

Individual asset classes on their own have a fairly similar long-term Sharpe ratio between 0,2 and 0,4.

Diversifying across different asset classes with low correlation to each other, raises the portfolio´s Sharpe ratio – that is investing 101, but it is amazing how concentrated many individual investors´ portfolios are.

Often the bottom-up approach many investors take is the reason they end up with an unbalanced portfolio with a suboptimal expected risk-adjusted return. Security selection concentrates in areas of personal preferences, expertise and media attention. So portfolios commonly display a sector bias (stocks that are en vogue or exceptionally cheap or connected to an industry we know a lot about), in our home country, towards equities. Typically winners are sold quickly and losers kept until their loss levels become unbearable. I have managed to do that quite efficiently in the past – ending up with a portfolio full of individual stocks that manage to lose even in the midst of a bull market – and I´m sure I´m not the only one with that particular experience.
Analyzing my portfolio from a top-down perspective before taking on new positions or implementing a new systematic strategy has turned out to be a great solution to the problem of holding an unsystematic tangle of securities.
I have even gone so far as to free myself from the idea of having to select individual stocks altogether to beat the market – the chance of picking outperformers is simply too small as about 65% of stocks underperform their market average and a small percentage of extraordinary performers carry the majority of market gains. I simply invest in broader market ETF, which makes it much easier to structure a portfolio.

Global Asset Allocation

The key to diversification is the correlation between assets, because uncorrelated assets in combination will achieve higher risk-adjusted returns.
Basic asset classes are: equities, bonds, real assets and cash (an open option with a Sharpe ratio of about 0). These can be combined into a Global Asset Allocation portfolio** that can be expected to perform well in very different market environments. It yields similar returns to a pure equity portfolio, but with half its volatility and drawdowns historically (which is extremely important, because when drawdowns become too large investors start to panic and deviate from their investment plan – usually bringing down returns).


A balanced global asset allocation can be considered a sophisticated portfolio for an individual investor, but it is standard professional practice (used by many digital advisors and money managers) and should lead to a solid performance. In practice the key are low fees – a standard portfolio should not cost much to implement: 0,5% to 1% is a good rule of thumb, but it can be done even cheaper. How about 0,06%?

Risk Parity and Leverage

The actual allocation can vary considerably without having a huge impact on returns, but it is still an important consideration how to weight the different asset classes. Because Sharpe ratios are similar it would make sense to equal weight all asset classes to get the most correlation benefit. As volatility of different assets is vastly different another smart possibility is to weight them by volatility: a risk parity portfolio. In practice this leads to a greater weight for bonds in the portfolio as their volatility is about one third of equity volatility. For the last 30 years that was a great idea, but future expected returns for bonds are very low – they can be estimated by the current yield. A large weight of low volatility, low return assets will be good for the portfolio´s stability, but yield rather low expected returns.
Because of common leverage constraints, investors will tend to overweight equities (these have some internal leverage as typically companies are 2x to 10x leveraged by debt) to juice up returns. This will expose them mainly to equity risk and the main idea of diversifying across the risk factors of uncorrelated assets goes out the window. It is replaced by being invested primarily in equities to all intents and purposes and adding some small diversifiers to feather the drawdowns.
Better would be the following approach: first determine your optimal asset allocation, estimate the returns and volatility of that mix. Then determine your risk tolerance and leverage your asset mix targeting a level of volatility that fits your risk tolerance. Research Affiliates has developed excellent tools, freely available for anyone, to combine return expectations for different assets into a portfolio.
This process should lift the portfolio´s sophistication one level higher: widely used, but not common practice.


Added Diversification from Alternative Return Sources
Because correlations between asset classes are constantly changing and somewhat unreliable (especially during a crisis they tend to move towards 1, which means they can be completely correlated at the worst possible time), it will pay off to incorporate alternative, systematic return sources with low correlation to other asset classes. This is what a lot of hedge funds do – termed “alternative beta”. These strategies target systematic risk premia, which is what I mostly concentrate on in my research.
The main ideas I include in my portfolio are:


  • Return Factors: long-only factor exposure (value, momentum, carry, low beta, quality, etc.) has been added to he standard toolbox for portfolio construction in recent years under the buzzword “Smart Beta”.
    Selecting securities according to these return factors has historically outperformed a market cap weighted portfolio.
    Because they are especially pronounced and robust, I mainly integrate the value and momentum factors in my portfolio. These two factors display the rare quality of often being negatively correlated, which boosts their combined Sharpe ratio enormously. Whenever value lags, momentum usually outperforms and vice versa – which leads to a much smoother equity curve as each factor can underperform the market for years on end.
    A new avenue I am researching and looking at implementing at least partly via a short option strategy is long/short factor exposure. A domain of hedge funds, this method targets the pure outperformance of factors by going long the stocks displaying the factor most strongly and simultaneously going short the stocks showing the factor most weakly. This yields great Sharpe ratios and a low correlation to other assets specifically during a crisis, because it is independent of market direction. But is very hard to implement for the individual investor as it requires shorting a large number of stocks and employing very high levels of leverage (around 8x to 10x). It can be accessed through mutual funds – usually for substantial fees.
  • Trend-following Managed Futures: even though relatively widely used as a tiny part of institutional portfolios, this strategy is still under the radar for most individual investors, because it is difficult and expensive to implement. It has shown to be one of the best diversifiers in the past, because of its propensity to deliver positive returns in times of crisis – termed crisis alpha. I have a considerable allocation to managed futures in my portfolio (between 15% and 40% depending on the market environment). Until the end of 2017 I accessed the strategy exclusively through mutual funds and ETF, increasing the allocation continuously as the equity bull market is getting longer and managed futures have underperformed in recent years. Both are likely to regress to their mean returns in the future. One ETF that looks good in theory (but unfortunately has not yet performed well) is WisdomTree Managed Futures Strategy ETF WTMF. Mutual funds are specific to the part of the world you reside in, but in general large CTAs have proven to be effective. In Europe it is fairly easy to access the MAN AHL, Winton or Transtrend programs via UCITS funds, if you are willing to pay the high fees.
    Starting in 2018, I have begun to trade my own managed futures strategy, finally overcoming numerous practical hurdles – e.g. the high amount of capital required to run it at a tolerable risk level. This was a very important step for me, as the history of the strategy gives me confidence that I will be able to generate positive returns in a market crisis.
  • Volatility risk premium and carry: these are highly correlated to each other, but both offer very substantial, reliable alternative risk premia. Because of their correlation, I mostly concentrate on the volatility risk premium – I have found it to be a superior source of outsized returns: the expected (implied) volatility is – on average – consistently higher than the volatility that actually materializes in the market´s movements (realized volatility). The premium is the spread between the two which is positive on average. Its basic concept is to sell catastrophe insurance to other investors for a premium. The strategy is rising in popularity (and therefore crowdedness) because it has recently had very high Sharpe ratios (above 5 for many strategies), but is not (yet) considered an independent asset class. It can capture reliable income streams in sideways- (that´s great, because these are often frustrating and test investor´s patience) and up- markets, but is exposed to rare, but large losses in down markets, when volatility is likely to shoot up suddenly. This risk definitely has to be very strictly controlled. Such a return distribution is called negatively skewed, a property that is shared by many asset classes and strategies. Being essential for portfolio construction return distribution needs to be addressed in detail.


Return Distribution: Skew
For a holistic view of portfolio construction I analyze the typical return distribution of different strategies in more detail – specifically their skew: at what times and how strongly are they likely to out- or underperform.
Most portfolio measurements (for example the Sharpe ratio) and financial models implicitly assume that returns are normally distributed and that statistical measurements are able to accurately estimate how likely the deviations from the mean return are (99.7% of all variations fall within three standard deviations of the mean).
Unfortunately reality doesn’t seem to behave so predictably – for example the 1987 crash or the 2010 flash crash deviated so far from the norm as to be virtually impossible by standard measures.
Actual return distributions often show larger and more common occurrences far away from the mean – often called fat tails or black swan events – than a normal distribution. If more of these events tend to be unusual windfall gains, the return distribution is positively skewed and if there is a majority of black swans with improbably large losses, the distribution is negatively skewed.
Both skews have some properties that are very desirable and others that are decidedly uncool. Combining strategies with different skew properties will diversify away some of the bad characteristics while preserving most of the good. The aim for the portfolio as a whole is to be as neutral as possible or even a bit positively skewed, so that surprises are more likely to happen to the upside. The problem is that negatively skewed asset classes and strategies are plentiful, while positively skewed strategies that have a positive return expectation are very hard to find – they are the holy grail in investing.
Asset classes and strategies offering unusually high risk premia, e.g. equities or short volatility strategies, display strongly negatively skewed returns. The more losses hurt when times are bad, the more investors demand to get paid for putting their money at risk. This skew is reflected in an unrealistically elevated Sharpe ratio.


This is how the return distribution will affect your portfolio in practice:
  • Negative skew: you can expect many small wins and few, but very large losses. The high win rate feels very good and makes long strings of losses less probable. It is possible create an income stream that is very constant and reliable 70% to 80% of the time by writing options, for example. A single large, infrequent loss on the other hand can wipe out a long string of winners at once. Owning equities or writing options have been net positive strategies on average, but you have to make sure you can survive the drawdowns without abandoning the strategy. A way to actively handle the risk and exploit these strategies in good times, while reducing or shutting them down in bad times might be to use an adaptive asset allocation and to balance them with positively skewed portfolio elements.
  • Positive skew: you can expect many small losses and few, but large winners. The very real possibility of experiencing long strings of losses and consequently spending a lot of time in a drawdown are hard to tolerate for any length of time, but this psychological hurdle can be mitigated by combining such a strategy with a negatively skewed, constant return stream. The harder part is to find such strategies, that have a positive expected return at all – the rare winners have to be bigger than the accumulated small losses.
    Investors greatly value a way to make money in a crisis, that doesn’t cost them an arm and a leg in good times. For example, a positively skewed strategy that has historically been very expensive, with negative average returns, is buying protective puts for a portfolio. It still is attractive for many investors, because it provides a certain protection against deep drawdowns in bad times.
    Trend-following managed futures to me is the most promising positively skewed strategy and it has a high allocation in my portfolio, but I also hedge my portfolio through asymetric bets by buying far out of the money puts in areas of the market that show weakness or extreme overvaluation. Explicitly going long volatility, either through protective puts or using volatility instruments directly usually has very low odds and doesn’t pass my strategy criteria, unless it is part of an overall positive strategy (for example a strategy that is short volatility the majority of the time), that employs these protective measures only when it perceives massive breakdowns with the market going into full crisis mode. Again that is a role an adaptive asset allocation can play.


Diversification Matrix
I use a matrix that gives me a birds eye view of my portfolio´s basic elements and their place and function in it. With that in mind I can dive into the details of balancing them.
In “A Barbell Portfolio Strategy” I dive deeper into the benefits of balancing extreme strategies for less risk and high return.



*„Against the Gods“ by Peter L. Bernstein delves deep into the complexities and history of risk


**A good place to start and a quick read is the book „Global Asset Allocation“ by Meb Faber.


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