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: excess returns and volatility expressed most commonly by the Sharpe ratio
  • The correlation between different strategies and assets
  • The return distribution characteristics of the different elements of the portfolio


To make things harder and subject to a lot of chance (no excess return without risk), all three metrics fluctuate over time, especially risk-adjusted return can only be guessed at 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 diversification is all about.
As everybody knows about diversification, I imagine that it might be worthwhile to pay close attention to the less commonly known higher moments of return distributions like skew and alternative low- correlated, strategic return sources.


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 it´s own it is of very limited use as we need to know something about the risk we take to get it.
Risk is what we want to avoid*, but we need to take some risk to earn excess returns. How much risk we 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 educated as possible is one of the main reasons for researching intricate details of investing.


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 is, 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 of the time frame it looks at, because realized returns often differ dramatically over different time frames. As it is widely used, it is still the best measure to compare different strategies.
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 (often referred to as the only free lunch in investing), 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 the portfolio often displays 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 overwhelming. I have managed to do that quite efficiently in the past – ending up with a portfolio full of stocks that lose even in the midst of a bull market – and I´m sure I´m not alone in that experience.
Analysing 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 for me.


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 should yield similar returns to a pure equity portfolio, but with half the volatility and drawdowns (which is extremely important, because that is where people start to panic and deviate from their investment plan).


This could be considered sophisticated, but standard practice (used by many robo advisors and money managers), which should lead to a solid performance. 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%?


The actual allocation can vary considerably without having a huge impact, but consider how to weight the different assets. 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 it is also a smart possibility to weight them by volatility: a risk parity portfolio. In practice this leads to a great weight for bonds in the portfolio as their volatility is about one third of equity´s – for the last 30 years that was a great idea, but future expected returns for bonds are very low, as these 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 integrated leverage as typically companies are 2x to 10x leveraged) to juice up returns. This will expose them mainly to equity risk and the main idea of diversifying across uncorrelated assets goes out the window. It is replaced by the reality of investing in equities 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 lever up your asset mix towards that level of volatility. Here is a good tool to combine return expectations for different assets into a portfolio.
This should lift the portfolio sophistication one level higher: widely used, but not common practice.


Because correlations between assets are changing and somewhat unreliable (especially during a crisis they tend to move towards 1), it will likely pay off to incorporate more alternative, strategic return sources with low correlations. This is what a lot of hedge funds do and is termed alternative beta. These strategies target strategic risk premia, which is what I mostly concentrate on in my research.
The main ideas I include or plan to add to my portfolio at the moment are:


  • Factors: long only factor exposure (value, momentum, carry, low beta, quality, etc.) has been added to standard practice in portfolio construction in recent years under the buzzword smart beta. Because they are especially pronounced and robust, I mainly use the value and momentum factors. They display the rare quality of often being negatively correlated, which boosts their combined Sharpe ratio enormously.
    A new avenue I am researching and looking at implementing at least partly via my short option strategy is long/short factor exposure. A domain of hedge funds, this targets the pure returns 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 crisis, but is hard to implement for the individual as it requires shorting a large number of stocks and employing very high levels of leverage around 8x to 10x. It can be accessed at cost through mutual funds.
  • Trend following managed futures: even though relatively widely used, 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 use a big portion of managed futures in my portfolio through mutual funds and ETF, especially 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 WDTI. 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 exaggerated fees.
  • Volatility risk premium and carry: these are highly correlated to each other, but very reliable risk premia in the market. Because of the correlation, I just concentrate on the volatility risk premium: 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. It basically is selling 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 a basic 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 has the downside to be exposed to sudden, large losses in down markets, when volatility is likely to shoot up suddenly. A risk that definitely has to be very strictly controlled. This specific return distribution is called negatively skewed, a property that is shared by many assets and needs to be addressed in detail.


For a holistic view of portfolio construction I concentrate on analyzing the return distribution in more detail – specifically the skew.


Most portfolio measurements (like the Sharpe ratio) and financial models implicitly assume that returns are normally distributed and statistical measurements can quite 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 judged as virtually impossible to happen by standard measures.
Return distributions often show larger and more common occurrences far away from the mean – called fat tails or black swan events – than a normal distribution. If these events are unusual windfall gains, the return distribution is positively skewed and if the black swans are 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 whole portfolio should 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 a kind of holy grail in investing.
Assets offering high risk premia, like equities or volatility, display strongly negatively skewed returns. The more it hurts 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 large losses. The high win rate feels very good and makes long strings of losses less probable. You can even create an income stream that is very constant and reliable 70% to 80% of the time by writing options. A single large, infrequent loss on the other hand can wipe out a long string of wins at once. Owning equities or writing options have been net positive strategies on average, so 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 an adaptive asset allocation plan.
  • Positive skew: you can expect many losses and few, but large winners. Long strings of losses and consequently a lot of time spent in a drawdown are hard to tolerate for any length of time, but this psychological hurdle can easily be mitigated by combining such a strategy with a negatively skewed, constant return stream. The harder part is to find strategies that have a positive expected return at all, because investors greatly value a way to make money in a crisis, without costing an arm and a leg in good times (for example a positively skewed strategy that has historically been very expensive overall is buying protective puts).
    Trend following managed futures to me is the most promising, 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 a larger strategy (for example a strategy that is short volatility the majority of the time), that employs these measures when it perceives massive breakdowns and the market going into full crisis mode. Again that is a role an adaptive asset allocation can play.


I use a matrix that gives me a birds eye view of my portfolio´s basic elements and their place and function in it. From that I can dive into the details.



*„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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