Portfolio construction can have a profound impact on investment results. True diversification is difficult to measure and even harder to implement. Our proprietary approach to managing portfolio dimensionality is designed with the aim of delivering more stable outcomes for clients.
Successful active investing requires two main ingredients. First and foremost, we need good investment ideas. With skill in selecting the appropriate portfolio exposures (whether they be stocks, bonds, macro instruments, illiquid assets or individual managers) there is a strong incentive to pursue active investment management. Secondly, the importance of expert portfolio construction, which can often be underestimated. It is true that portfolio construction by itself cannot turn bad investment ideas into good ones. However, by spreading capital allocations more or less efficiently, it can still have a profound impact on investment results.pcoming election and expect volatility could provide good buying opportunities.
Outcome oriented portfolio construction
Outcome oriented portfolio construction aims to balance the exposure to investment ideas and maximize the likelihood of achieving the portfolio investment objective. Since the seminal paper on mean-variance optimisation by Markowitz (1952), this process is often implemented as a quantitative approach to maximising expected returns for a given level of risk, or vice versa, minimising portfolio risk for a given level of expected return. Often we cannot simply predict future returns with enough confidence to have portfolio weights directly depend on them in a simple quantitative optimisation. Recognising these practical difficulties of working with expected returns in an optimization setting, more recent research has focussed on risk diversification as a central portfolio construction concept. This approach aims to spread capital allocations in a portfolio such that the included investment ideas contribute to overall risk in a similar manner.
While the concept of risk diversification has become central to modern portfolio construction, the industry has not reached consensus on the ‘right approach.’ In fact, there is not even agreement on what exactly should be achieved in terms of the portfolio outcome. Most practitioners implicitly or explicitly focus on portfolio volatility reduction. This is seldom an appropriate objective on its own and can in fact encourage portfolio managers to reduce volatility by holding more cash or hedging exposures. However, clients expect active managers to maximize exposure to their investment skill in selecting suitable exposures, not to dilute their investments by investing less or in mutually offsetting ideas. At the same time, clients expect protection from losses as much as possible. This is exactly what we seek to do, and much of our research efforts has been focussed on finding the best and most robust way of doing so.
Diversification: easy to understand, difficult to measure and harder to implement
The old adage says not to put all your eggs in one basket. An easy enough concept to grasp, but one that is hard to quantify in detail, let alone leverage to your advantage in practical investment decision making. What do we consider to be baskets and how do we count our eggs in the portfolio context? Spreading risk appears sensible, but how to measure it and how do we attribute it to portfolio components?
The difficulties start in making ‘risk’ a precise statistical concept in a way that reflects asset owner’s perceptions. Volatility is the predominant measure used to characterise the uncertainty of returns on financial investments (at least in liquid public markets). It is convenient and simple to use, as the mathematics offer easily identifiable solutions. However, it is in many ways a flawed measure of uncertainty. It does not distinguish between upside uncertainty (which few investors mind) and downside uncertainty nor does it adequately reflect the potential of more extreme events. Most importantly, in our experience people care much less about volatility, than they care about real losses.
Much of the focus on volatility comes from the fact that it is an operationally convenient measure. However, this convenience comes at the price that it is only an appropriate measure for potential portfolio losses if portfolio returns are normally distributed to start with. Our lives would be much easier if this were to be the case. All investment uncertainties would reduce to a simple covariance matrix. Our main problem would become one of measuring volatility (and correlations) as precisely as possible.
Individual asset returns are rarely as well behaved as we would want them to be. The risk of unexpected large losses is embedded in all risky instruments. That is, they tend to have skewed and fat-tailed distributions. We would be negligent if we did not take this into account in portfolio construction. Diversification is the mechanism that helps us manage these risks. We can allocate to our portfolio components so that the overall outcome is increasingly similar to a normally distributed return series. This makes it easier to measure, predict and control than the individual components. We even have a precise recipe for doing so. The Central Limit Theorem is one of the fundamental tenets of statistical theory which tells us that equally allocating risk to independent return streams (or investment dimensions as we call them) in the portfolio will lead to maximum diversification.
Taking this approach allows us to quantify our portfolio expectations in a clear way. Chart 1 illustrates this for a stylized example in which we have assumed return streams with fat tails and Sharpe ratios calibrated to real world observations. The probability of loss is halved as the number of dimensions rises from one to four. More importantly, the average scale of loss, if one occurs (conditional loss, red line) also reduces from over -8% to under -4%. The result is a more than doubling in the probability of achieving a Sharpe Ratio of more than 0.75, from 30% to 75%.
Diversification is the mechanism that helps us manage these risks.
Chart 1: Diversification improves risk-adjusted returns and decreases portfolio lossesSource: internal calculation; Aberdeen Standard Investments (as of April 2019)
These results can only be achieved if we have sufficient truly independent return streams to construct portfolios from. These are challenging to find. Investments are interlinked in complex ways reflecting the shifting preferences of multiple investor types with differing outlooks and beliefs. Similar broad macroeconomic drivers influence a number of markets, instruments and strategies. As a result they may experience losses in similar economic scenarios. For example, they may all contain some measure of broad equity market risk. Importantly, they may also offset one another – good for reducing volatility, but not useful in also generating a return! As a result, we need to recognize and evaluate these common underlying risk drivers. We can then size and group positions that reflect and isolate genuinely independent return streams that are available in our portfolio universe.
Put simply, our task as active managers is three fold. First, find as many good investment ideas as we can. Secondly, deal with the real-world limitation of overlapping underlying risks by identifying independent return streams available to a portfolio. Last, we must then size each one of them in line with the investment objective.
Measuring diversification: effective portfolio dimensionality
Measuring independent return streams within an investment universe is challenging and we have made significant research efforts to make this idea operational. We have developed a unique statistical approach, which allows us to precisely capture the notion of diversification in a metric we call effective portfolio dimensionality. Armed with this tool, we can measure the number of independent return streams in portfolios on a like-for-like basis and use it to understand likely portfolio outcomes better.
Effective portfolio dimensionality = the number of
equally sized independent return streams in a portfolio
To illustrate, we consider the example of a typical US institutional multi-asset allocation (see Chart 2). At first sight this portfolio is highly diversified. It contains a bit of everything: developed markets, emerging markets, bonds, loans, equities, etc. When we measure the dimensionality of this portfolio though, we find it contains 1.6 independent return streams. Many of the positions in the portfolio capture equity-like returns, which is the first investment dimension present. The remaining (partial) investment dimension corresponds to duration-like risk and some lesser diversifying return streams such as credit spreads. As a result, the likelihood of losses in the portfolio is driven by the equity-like investment dimension, and its associated risks of large drawdowns.
Chart 2: Typical US institutional multi-asset investment universeSource: internal estimtes; Aberdeen Standard Investments (as of April 2019)
Could we improve diversification for this portfolio? An obvious first step would be to size the duration component so that its overall risk impact is more equal to equities. Doing so would increase the effective portfolio dimensionality to nearly two, making more effective use of the independent return streams available. To go beyond educated guesses we need a more rigorous approach to managing portfolio dimensionality.
Managing portfolio dimensionality
To actively manage diversification levels in portfolios we need to design rules that assign portfolio weights to investment positions that result in the desired effective portfolio dimensionality. The portfolio construction approach we have developed to manage portfolio dimensionality consists of the following steps:
- Analyse your investment universe to understand diversification potential and find the available independent investment dimensions (we use a purpose-built ‘unsupervised’ machine learning algorithm to achieve this.)
- Construct sub-portfolios that align with the identified investment dimensions
- Weight these sub-portfolios to achieve the desired level of effective portfolio dimensionality
To bring this to life, we return to the example of the median US multi-asset allocation. We can compare the results of applying our portfolio construction approach to the same investment universe (on a rolling real-time basis). The resulting portfolio has an effective portfolio dimensionality of 2.6. This compares to the 1.6 we saw for the original median allocations and results in a much improved investment outcome.
Chart 3: Optimizing dimensionality of the median US multi-asset portfolioSource: ThomsonReutres DataStream, Bloomberg, internal calculations Aberdeen Standard Investments (as of April 2019)
We make two main observations. The risk-adjusted excess return ratio of the optimized dimensionality portfolio is nearly 40% larger than the ratio of the original allocation (average excess returns versus volatility stand at 0.7 and 0.5 respectively). Admittedly, it also has lower returns (5.2% versus 7.0%), but this could be addressed through deployment of leverage if needed. More importantly though, the risk of outsized losses is much lower for the optimized dimensionality portfolio. Downside risk measures have improved: for example the annualised expected shortfall has reduced from 19.2% to 8.6%.
Active investing needs good investment ideas and a clear portfolio construction philosophy. In our opinion, there are many valid routes to successful idea generation, including different flavours of fundamental analysis as well as data-driven systematic approaches. The same is not true for portfolio construction. There are a few common underlying diversification principles that apply to any portfolio. We believe managing portfolio dimensionality is a coherent and robust way to understand and implement these principles. In a world where risk assets have become increasingly correlated through globalization and financial policy, finding true diversification is increasingly challenging. Doing so is paramount to achieving long-term investment success.
Diversification is the mechanism that helps us manage these risks.