Adding Value by Truly Integrating Asset Allocation in a Coherent Investment Framework

The importance of getting the correlations right

By Erik L. van Dijk (LMG Emerge)1

1. Introduction

Brinson, Hood & Beebower (BHB) wrote a seminal paper in 1986 in which they derived that the bulk (80-90 percent) of overall investment performance is the result of asset allocation decisions. The paper almost became a gospel in the academic world, but in the practitioner world it was often mentioned in research publications by large investment management firms but it was hard to find out to what extent they had changed their investment approach as a result of it.

BHB used a time-series approach and later work by Ibbotson & Kaplan (2000) and Xiong, Ibbotson, Idzorek & Chen (2010) showed that the BHB conclusions were to a large extent related to the use of this approach. Overall market movements dominate total return time series. But investors can and should also be compared cross-sectionally. Ibbotson & Kaplan (2000) and Xiong et al (2010) derive that the relative importance of asset allocation decisions doesn’t come anywhere close to the 80-90 percent suggested by BHB and their addicts. It is ‘at best’ 50 percent.

Is this a downgrading of the importance? We don’t think so. Look carefully at what has been done here in the newer studies. The newer studies look at the overall investment process – both top-down and bottom-up – of investors in an integrated manner, whereas BHB looked at just one aspect. We believe that the result of the integrated studies and correct derivation of asset allocation importance will just do that: make asset allocation more important in a truly integrated, active framework.

In paragraph 2 we will look at this integrated framework in an ‘ideal’, rational world and show how problems with the important correlation factor led to so many disappointments and even catastrophes witnessed in practice. And that is already before taking into account the existence of irrationalities and other behavioral factors, a topic we will address in a future piece. Paragraph 3 concludes.

2. Integrated Asset Allocation in an ‘ideal’ world

At any point in time we have to take portfolio decisions (not doing anything is also a portfolio decision!) based on historical information and expectations about the future. Quantitative investors use some kind of ‘model’, which is always ‘just’ and approximation of reality. Fundamental investors do often seem to look down on ‘quants’ every time the latter have gone through some kind of bad period for their style, explaining everyone that you cannot capture the world in a model. However: they seem to forget that they are also using a model, albeit one that is far less explicit. Sometimes this lower amount of rigor works to their advantage in that the fundamentalists seem to be able to cope with regime shifts quicker

1 Erik L. van Dijk is principal at Dutch institutional investment consultant LMG Emerge. LMG specializes in Asset Allocation, Manager Selection and Emerging Markets studies. LMG’s asset allocation framework has benefited from joint work with Noble Prize Laureate Dr H Markowitz and other scholars.

and better. And that attention given to potential regime-shifts is important as we will see later in this article.

On the other hand: without a rigorous and transparent analysis of your own mistakes it is hard to gradually adjust your investment process and approach over time. In other words: both approaches do have a certain appeal and both have certain flaws. One is good in picking up the major shifts that happen once in a while, whereas the other is better in adjusting to long series of smaller adjustments of markets. Whenever your portfolio size does allow you the incorporation of more than one manager for a certain sub-component of it, it might be wise to diversify between the two investment styles.

The overall ‘ideal’ asset allocation and portfolio composition are a function of:

Expected Returns

Expected Risks

Expected Correlations between portfolio components

The investor’s Risk Profile

Guidelines provided by the investor’s ALM study

We will not address the issue of ALM and Risk Profile in this paper and assume that they have been tackled by the investor. But research about Pension Fund Governance and risk profiles of Boards of Trustees – as opposed to that of individual decision takers – show that this is already quite an issue in-and-of-itself. And even when getting the numbers right when it comes to the translation of individual to collective risk profiles, one is still faced with the problem that recent research has confirmed what we did already know: risk preferences do contain all kinds of linkages – both linear and non-linear – to variables like gender, age, wealth, income, education and culture. But let’s for now assume that all of this has been tackled and that there is agreement on the ALM and risk preference.

When looking at Return and Risk we need to distinguish between short-term and long-term expectations and bullish versus bearish market climates. Depending on the asset class we are considering, outcomes will be more or less sensitive to these distinctions. And when it comes to Risk, we also need to distinguish between various types of Risk. The ‘ideal’ framework would incorporate all these elements and then, using information about correlations between securities / asset classes assign to them the optimal portfolio weights. It may already sound like a lot of work, but technically it can be done and most professional organizations do at least have some kind of more or less structural framework to do it (which is not the same as saying that they are adding much value by doing it, because in the end it is not just about the framework, but also about the numbers that you plug into it).

The next step would then simply be to make use of the ‘only free lunch in investing’: proper diversification based on incorporation of the right correlation coefficients within the framework. Markowitz (1952) received the Nobel Prize in Economics (1990) for his work on the framework. And the fact that it took so long – and even longer – for many practitioners to really start using it was related to the fact that Markowitz (1952) only provided rough guidelines for the various necessary steps discussed above. Markowitz used standard deviation or volatility as his risk measure, but knew that semi-variance might be at least as interesting when market returns are not normally distributed. In other words: he

described the mean-variance system understanding that it was not the whole thing. Yes, it was the whole thing in terms of approach, but the proof of the pudding is in the eating and the cook (read: investor) did still need to add some additional flavors and/or change the topping. Another problem: there are far more asset classes/country(or region) combinations than today’s computer power can handle in a true mean-variance optimization. Markowitz-van Dijk (2003) derived a heuristic labeled ‘near optimization’ that according to Monte Carlo tests by Kritzman et al. (2007) does a good job. The optimization technique outperforms known alternatives (e.g. ‘rules of thumb’-based decision techniques) for large numbers of investment opportunities and comes extremely close to a ‘real’ optimization when the numbers of investment alternatives is small enough to do a real one and compare things.

What does that mean? In terms of framework the ‘ideal’ is there. But real-life investors have made terrible mistakes when plugging in the numbers. Take for instance correlation coefficients. Correlation coefficients are not stable between asset classes. Even more so: they are not stable when looking at securities within an asset class! Correlations tend to move toward one in turbulent periods. This translates into huge diversification problems, especially in periods when it is needed most. Longin and Solnik (1995, 2001) have found that correlations are highest in turbulent, high volatility periods. If we add to this that correlation coefficients are creeping upward due to ongoing globalization, we need to do something if we want to create optimal portfolios with the return-risk ratios that we are looking for. And this is especially important at a time when demographic factors are working against some of the largest institutional investors: Western pension plans that represent an overall value of more than $ 13,000 trillion in assets under management.

So what to do? Give up? Resign? Of course not: three ‘solutions’ will help. First of all, the importance of Alternatives within the overall portfolio and asset allocation will increase. Long/short style portfolios will help mitigate the risk of increased diversification opportunities. But they will only do so when investors will learn that long/short and other hedge fund managers are no geniuses in general. Just like in any other asset class proper due diligence is important. I.e. a due diligence that incorporates asset class returns in a screening framework so as to distinguish between ‘true skill’ (as a result of selection), ‘technique’ (performance due to their going long and short) and ‘luck’.

Second, work by Bernhart, Hochst, Neugebauer, Neumann & Zagst (2009) shows that working with a so-called regime shift model does improve returns while reducing overall portfolio risks. In this approach – also integrated in the LMG asset allocation model – returns, risks and correlations are separately calculated for high volatility and low volatility environments. One can use the Chicago Board of Options Exchange VIX index to distinguish between the two environments. Relevant factor weights and return, risk and correlation forecasts are based only on the historical observations of the regime that one is studying. In other words: instead of one model with weights based on the overall historical sample you have two sub-models2. Based on what is going on with the VIX you can then decide which one of the two

2 When we talk about ‘model’ here we mean the investment approach chosen for the integrated framework including asset allocation. Fundamental approaches do also fit this description, albeit that their idea of a ‘model’ is less tangible.

derived forecast sets and accompanying asset allocation you will use. Table 1 shows the estimated added value of the regime-shift approach vis-à-vis the static framework.

Table 1; The Value of Incorporating Regime Shifts in an Asset Allocation Framework

It is remarkable to see how the regime-shift model found the following ‘high volatility, turbulent’ regimes and how it adjusted its allocation based on that fact:

1987 The Black Monday crash and its aftermath

1990 The Gulf War and its aftermath

1998 The Russian Ruble Crisis

2000-2003 The Burst of the .com Bubble

2007-2009 Global Financial Crisis

(not for the US but captured for Europe) 1997 Asian Financial Crisis

And of course, this approach is not magic but it helps a lot. ‘Found’ does not mean that you shift from bullish to bearish exactly at the time of the big negative event. Most of the time shifts were made too early, because volatility levels creep up before the big clash. But it is definitely a considerable improvement. The low-risk investor does probably improve his returns by around 0.5% annually and the high-risk investor by somewhere close to 1.5%. And this improvement is accompanied by lower risk levels.

But it is not only these missed regime shifts that went wrong when looking at standard investor’s approaches to their overall allocation of assets and the extent to which this could be attributed to correlation coefficients. There is a third factor that one could incorporate to improve on existing approaches. Haber & Braunstein (2009) have shown that the practice of using longer-term, allegedly stable correlations in optimization frameworks does also lead to another problem irrespective of

underlying volatility regimes. Correlation coefficients are often presented by taking some longer, historical period with return and risk figures often presented over a set of shorter (sub-)intervals as well. However: what investors really care about is future correlations. The authors analyze random (!) samples of 180 monthly return observations to simulate 15 years of return patterns. Low or no correlation between two asset classes over a longer period of time might be the result of a negative correlation in good periods (bull markets) and a positive correlation in bad periods (bear markets) or vice versa. The average correlation is indeed low: but we will never be happy with the results when managing an overall portfolio on this basis when going forward knowing that we will be monitored over relatively shorter time intervals as well! Therefore: we should pay attention to sub-periods and that is exactly what the regime shift approach is doing based on a linkage with volatility. But correlation patterns might also be linked to other factors.

In chart 1 we present Haber & Braunstein’s results of an experiment in which they calculated the 3-, 2- and 1-year correlations between their 180-observation series of monthly random returns. They repeated the experiment 100 times and the results are shocking.

Chart 1: Significant Correlations do even play a role in Random Long-Term Patterns!

If we then keep in mind that shorter-term, more recent correlations are probably more relevant than longer term information about let’s say the correlation 15 years ago in a setting that is not truly random,

we see that the standard approach can also go terribly wrong even when we are not in a regime-shifting situation where we go from high to low volatility environments or vice versa. An alternative approach in which we use time-weighted correlation estimates with time-weights derived in such a way that recent period estimates get a higher weight might further help improve results.

Evaluation

The standard framework for rational decision taking within the context of asset allocation is more or less there. However, as always, it is garbage-in, garbage-out when you do not get your numbers right. Just like investors have always spent more time on bottom-up security selection and manager picking than on top-down asset allocation, they have also spent more time on return predictions than on risk management and measurement. The latter includes correlation analysis. Within a proper asset allocation framework correlation analysis is not less important than return, beta, volatility or currency risk. Especially now that we are moving into a world that – through globalization – will make free lunches less easy to find, it is important that investors start taking correlation a bit more seriously. In this little article we presented some thoughts on what can already be done in terms of future as well as current research. The Markowitz-van Dijk (2003) heuristic shows that an integrated approach in which the various components of an optimization are incorporated in a pragmatic way can add tremendous value. It is our belief that correlation analysis is probably the first area that investors should look at when trying to improve their asset allocation decisions. By doing so, they can improve their return-risk trade-off substantially: depending on your risk profile incremental returns of 0.5-1.5 percent per annum seem to be realistic. Another area is related to non-rationality in international asset allocation decisions. Research has shown that cultural factors have lead to home and foreign biases. With the quest for new opportunities in a globalizing world - characterized also by increasing importance of Emerging and Frontier economies – being much more international than ever before, we will address that aspect in our next contribution.

Literature:

Bernhart, G., S. Hochst, M. Neugebauer, M. Neumann & R. Zagst, Asset Correlations in Turbulent Markets and their Implications on Asset Management, Working Paper TU Munich, 2009

Brinson, G., L.R. Hood & G.L. Beebower, Determinants of Portfolio Performance, Financial Analysts Journal, 1986

Haber, J, & A. Braunstein, Correlation of Uncorrelated Assets: Near-term Issues, Working Paper Allied Academies International Internet Conference, 2009

Ibbotson & Kaplan, Does Asset Allocation Policy Explain 40, 90 or 100 Percent of Performance?, Financial Analysts Journal, 2000

Kritzman M, S. Page & S. Myrgren, Portfolio Rebalancing: A Test of the Markowitz-van Dijk Heuristic, MIT Working Paper series 2007

Longin, F. & B. Solnik, Is the Correlation in International Equity Returns Constant?, Journal of International Money and Finance, 1995

Longin, F. & B. Solnik, Extreme Correlation of International Equity Markets, Journal of Finance, 2001

Markowitz, H.M., Portfolio Selection, Journal of Finance 1952

Markowitz, H.M. & E.L. van Dijk, Single-period Mean-Variance Analysis in a Changing World, Financial Analysts Journal, 2003

Xiong, J.X., R. Ibbotson, T.M. Idziorek & P. Chen, The Equal Importance of Asset Allocation and Active Management, Financial Analysts Journal, 2010