The integration of alpha and beta
In recent years there is less belief in efficient markets for a couple of reasons.Professional investors are increasingly confident that they have access to sources of excess return, alpha.
This turns upside down the classic world in which strategic choices for asset classes (beta’s, systematic risks) and the tactical choices for temporary deviations from these strategic choices were completely independent from each other. In the new world beta and alpha risks and returns are explicitly balanced. Both worlds are connected by the information ratio an investor thinks he can realise.
Even when information ratios are low it often pays off to exchange beta risks for alpha risks. In addition, the expected information ratio can be increased strongly if a number of independent alpha sources are combined.
This article is an introduction to alpha and beta risks. It consists of four parts:
1) Recent developments in capital management;
2) Introduction to beta and alpha risks;
3) Alpha and beta investing in the Netherlands;
4) Practical matters and challenges.
Part one: Recent developments in capital management
The last two decades up to 2000 were characterised by a stable recipe for a responsible way of investing, which can be described as follows:
o Assess the maximum risk tolerance of the client and;
o Translate this into a maximum allocation to equities.
Institutional investors were ahead of the private investment world in this way of thinking. The central instrument used was ALM study. In the nineties the private world followed, by using interviews and questionnaires to assess the maximum risk capacity of the client.
In fact this approach of organising the asset mix solely emphasises the risk. The approach was based on assumptions that were hardly questioned because the returns on equity investments constantly surpassed expectations. Though a little exaggerated, the following assumptions were prevalent:
o Markets are efficient;
o Efficient markets always incorporate a sound risk premium for equities;
o Therefore an analysis of the underlying economical phenomena or the valuation is unnecessary.
vIndeed share returns are unpredictable in the short term, but in the long term we receive a risk premium of about 5% for equities as a reward for the risk we are prepared to take;
o Every deviation from the strategic asset mix that results from the ALM study is a serious risk that will probably not be rewarded by return. This is an important reason to invest passively or close to the strategic benchmark.
Because these basic assumptions formed a collective truth, the change of trend on the equity markets was so significant: as the economic environment became more difficult, belief in the basic assumptions diminished. The enormous downturn of the equity markets in 2000-20002 formed a catalyst to reconsider old truths. There was a lot of disappointment with equities, which led to a collective search for a new good and stable approach towards investing.
The disappointment in equities has led to a new worldview for investors, which I named the “new subjective efficient frontier” (or the “low return environment”). This line is a starting point for the analysis of current developments.
The “subjective efficient frontier” has come down in recent years. When we look at the diagram above, we see that the new line lies substantially lower and is much flatter than it was perceived to be five or 10 years ago. In other words, the expected risk premium for equities has - at least in the mind of investors - decreased seriously. In the view of many investors the line has also moved to the right: asset mixes that were sound five years ago, now feel much riskier.
Policy consequences of the new subjective efficient frontier
The change of trend in equity markets led to different incentives for different parties. Supervisors and many investors concluded that they underestimated the risk, and have a lower risk tolerance than before. This led to tightly formulated requirements for the solvency ratio and the risk of not meeting the minimum solvency ratio.
In recent years the returns of institutional investors aimed at have also increased. In addition to the yearly increase in liabilities that have to be fulfilled, the solvency ratio has to rise.
Institutional investors therefore have a problem: the people they are investing for and the supervisors do certainly not allow an increase of risk. A higher risk would also not be logical in light of the flat subjective efficient frontier, because this flat line implies low added return per unit risk.
As a result investors have to find ways of increasing return per unit risk to reach the return objectives.
Current developments in the investment world.
In the Netherlands - but also abroad - the following developments are noticeable as a result of these pressures:
o The primacy of efficient market thinking has ended;
o The primacy of relative risk thinking has ended;
o Fundamental thinking has returned;
o Wide acceptance and maturing of new instruments and products;
o More attention for risk governance on the short-term.
The primacy of efficient market thinking has ended
In the 1880s and 1890s - especially in the institutional world - efficient market thinking was dominant. Large amounts of money flowed to index investments. Many studies showed that the markets were efficient and that active management only costs money. This thinking has pretty much been left behind.
The theoretical foundations for the end of efficient market thinking lay in behavioural finance, where it has been shown that investors do not behave as rationally as the idea of efficient markets supposes.
In practice there were two important developments. On one side a category of investors arose who, within strict boundaries of risk management, developed investment strategies that beat passive investment with a fairly good chance of success (enhanced indexing).
On the other side there are the attractive returns of the alternative and absolute return strategies. These investments stand out for their relative stability and their historically high returns. Because the new subjective efficient frontier is so much lower than in the past, the returns acquired with these strategies seem to surpass the line generously, even after correction for the considerable shortcomings of the available indices. The strategies are promising because they are skill-based and thus independent of the index. We will return to this in part two.
In recent years, the acceptance of absolute return strategies has grown fast in the institutional world. These strategies also fit into the following trend.
The primacy of relative risk thinking has ended
In the nineties of the last century relative risk thinking was dominating. The strategic asset mix, and the resulting risk was not a subject of concern. This risk followed from the ALM study that fell within the responsibility of the pension fund board and outside the responsibilities of the investors.
Consequently, investors – especially institutional investors - were almost completely focussed on the small part of risk relative to the strategic benchmark, the relative risk and on the related relative return that could be earned compared to the strategic mix.
Currently this focus on relative returns has been replaced by the concern if absolute returns reach the required levels: “you can’t eat relative return”.
Fundamental thinking has returned
Strongly related to the abandonment of the idea that markets are efficient, is the return of fundamental thinking, thinking about the relationship between the price currently paid and the expected return given economic fundamentals. Consequently, one has to dismiss the presumed objectivity and value-freeness of the ALM study, which followed from the idea that there is a known, more or less normally distributed probability distribution of risk premiums independent of valuation or economic environment. It follows that it has to be studied which return expectations may be linked to the combination of current valuation and expected (economic) developments.
Wide acceptance and maturing of new instruments and products
As a result of the negative equity returns and the maturation of derivative markets it is accepted on a broader front and broader to include derivatives as an important part of the asset-mix. This brings within reach new strategies, such as portable-alpha strategies and the leverage of skill based strategies. The total portfolio now looks more and more like a modular construction of specific elements that can be moulded precisely to the wishes of the investor.
More attention for risk governance on the short-term
In the Netherlands, pension funds had been focussing on equities in the nineties and were hit hard by dropping equity markets and resulting pension shortages. This was the reason for the supervisor to tighten the solvency ratio requirements . These requirements leave pension funds less flexible in taking risk. Now the trick is to minimise the risk of deviations of assets compared to liabilities.
In addition there is the coming market value valuation of pension fund liabilities in 2006. A logical approach is reducing risk by matching expected cash out flows as much as possible with cashflows from the investment
portfolio. Instruments used can
be nominal (bonds, swaps) as
well as inflation linked inflation. The focus will shift from managing the expected value in the future
to managing the mismatch risk between the marked-to-market present value of assets and
Part two: Introduction to beta and alpha risks
An important aid in organising an investment portfolio is distinguishing between beta and alpha risks. The trends described earlier lead to an important new development. There is a wish to bring alpha and beta risks together in one common framework to be able to coordinate and direct all sources of risk and return in the portfolio.
Starting point for thinking about beta risk is a world in which investment markets are completely in equilibrium. All relevant information has been accounted for in the prices and everybody agrees on this.
In this world there is still a reward for investing. Investing in government bonds is rewarded with the corresponding market rate. Investing in credits comes with an additional reward because of the credit risk one takes and investing in equities is expected to be rewarded with a risk premium compared to bonds.
In this equilibrium world all markets mentioned are priced such that the expected risk rewards will be included. These expected returns are beta returns, the returns that, at that moment, form the price for different systematic risks in the world. The corresponding risks are beta risks.
The expectations for the reward for these sources of risk may vary in the course of time, but even if everybody trades in them and believes in them they continue to exist. This is because there are suppliers of these risks who want to place them in the market against a reward. The government has to finance its debts; the entrepreneur has to finance his company.
Because these suppliers exist, the supply of beta risk is in principal large.
Beta risks are typically found in a widely diversified index. And this (total return) index will rise in the long term; otherwise we would not deal with rewarded (=systematic) risks. The efficient frontier consists completely of beta risks.
One does not have to be smart or work hard to be rewarded for beta risk in the long-term. The only thing to be done is to participate in the respective market. And that is simple. This is why beta risk is a commodity.
Efficient market thinkers believe that the world is always in equilibrium. That’s why in their opinion, (expected) alpha does not exist. Classical ALM thinking is typical beta thinking: moving along the (given) efficient frontier to find the combination of risk and return that suits you.
The expected reward for one unit beta risk varies between approximately 0.4 % and 1% per annum per per cent risk. The bond-index yield at the moment is about 4% for a risk of the same order. Per unit risk the expected reward will thus be roughly 4%/4% = 1. For equities a reward of 6-8 % is expected for a risk of 15-20 %. Per unit risk the expected reward will then be 0.4. In the mid-range of the efficient frontier, where most investors are positioned, the expected reward per unit risk lies between 0.4 and 1%.
An alpha is an extra return compared to the strategic benchmark. This can only be acquired by a (temporary) deviation from this benchmark. That can be one in may ways: tactical asses allocation, geographical asset-mix, equity selection, credit selection etc.
Deviating from the benchmark is only useful in a world that is temporarily or partly not in balance. By taking advantage of these disequilibria one buys what is undervalued and sells what is overvalued. This will restore the balance.
In the alpha world one winner means one loser: the total amount of available return is defined by the available return on the (market value weighed) benchmark. So, if one person has taken an underweight position per definition someone else has an taken an overweight position. If one wins, the other loses.
Therefore the world of alpha is a Darwinistic one. Rational investors only play the alpha game if they think they have a competitive advantage to harvest alpha: you have to be smarter or work harder than others. Or you have to be able to operate cheaper. And if you’re successful, in general others are quick to join the feast. With the result that every unbalanced situation is in principle temporary.
In a world that is reasonably efficient, like most investors assume, the supply of potential alpha is not infinite. In addition, it is often expensive to harvest the available alpha: equity selection within small caps often has added value, but one has to work hard to discover this by visiting companies etc. Therefore, an important part of the gross alpha is lost on costs.
In contrast to beta, alpha is definitely not a commodity. Hard work and scarce talent is needed to harvest. This has to be paid for. For expected alpha a high price has to be paid.
Price differences between alpha and beta risks
The costs of participating in wide markets (beta risk) are extremely low. An index investment can be realised for 0.1% per annum or less, independent on the expected reward per unit of risk.
A unit of expected alpha is considerably more expensive. A rough price indication is that the price paid by professional buyers amounts to 30-40% of the expected alpha, as shown in the following examples:
1. Enhanced equities strategy
Tracking error 1.50%
Expected information ratio 0.40%
Expected alpha 0.60%
Management fee 0.25%
As % of the expected alpha 40.00%
At a (commonly) expected information ratio1 of 0.4 an enhanced equity strategy with an active risk of 1.5% generates an expected return (an alpha) of approximately 0.6%. The fee for this is about 0.25% Around 40% of the expected alpha is thus absorbed by costs.
2. Active Small Cap Mandate
Tracking error 8.0%
Expected information ratio 0.4%
Expected alpha 3.2%
Management fee 1.0%
As % of the expected alpha 30.0%
An active small-cap strategy with a tracking error of 8%, and an expected Information Ratio (1) of 0.5%, will in general ask for a management fee of 1%. Here the price per unit expected alpha would amount to between a quarter and a third of the expected added value.
3. Skill based hedge fund
Tracking error 10.0%
Expected information ratio 0.8
Expected alpha 8.0%
Management fee 2.5%
As % of the expected alpha 30.0%
Absolute-return strategies from the alternative circuit often have a fee structure with a fixed (1-2% or more) and a variable component (10-20%) of the returns above a (low) threshold) The average total fee than amounts to 2-3% at an gross added value of about 8%. At least, that is the added return that could be derived from the average historical return figures. Again, roughly 30% of the expected alpha is consumed by fees.
Although the examples are taken from very diverse investment domains, it becomes clear that the price per unit expected alpha is fairly constant and absorbs a considerable part of the expected added value of a strategy.
Strong incentive: sell beta for alpha
The supplier of investment strategies therefore, has a strong incentive to emphasise the alpha character of its strategies. The other way around, the potential buyer should investigate if he does not implicitly pay for betas that the supplier tries to sell as alphas. In avoiding this, one can save considerably on managing costs!
Skill in alternative investments?
Alternative investments, including skill based investments and hedge funds are gaining importance within investment portfolios. On a world scale they are still small: worldwide investments in hedge funds amount to E800bn, not even 2% of the total market value of equities world wide.
The largest Dutch pension funds have in the meantime taken concrete steps in this direction and defend their positions passionately. Professor Tom Steenkamp, head of Research ABP Investments, recently wrote in Pensioen Bestuur & Management: “Alternative investments have a surplus value in the strategic portfolio of institutional investors. Diversification over different investment categories leads to more efficient portfolios, to more return per unit risk.”
It was already clear that there is an incentive for suppliers to sell beta disguised as alpha. Our analysis shows that the average hedge fund indeed sells a significant amount of beta risk. This is in itself not a problem, as long as the buyer is aware of it and does not pay alpha fees for beta risks.
In our analysis we studied to what extent there are significant links between the CFSB Tremont Hedge Fund Index, an important and widely diversified hedge fund index, and the most important beta risks: the worldwide equity markets and the (US) bond market. Significant links appear to exist with the equity as well as the fixed income index: Every per cent increase or decrease of the worldwide equity market in the last 10 years resulted in an increase of the hedge fund index of 0.3%. Every per cent decrease or increase in the bond market led to a decrease or increase of 0.4% of the hedge fund index.
In the diagram above one can see the development of the hedge fund index, and the same development, corrected for beta risks of equities and bonds. Because of the correction, the average return fell from 11% (after fees) to about 7%. This means good and bad news.
The bad news is: in many cases a high fee is paid for this implicit participation in the equity and bond markets (on average over 4% of 11% return). In a maturing hedge fund world client and supplier should have some serious discussion about this.
The good news: after correction for equity and bond returns, on average there still remained something - in the past 10 years, after fees - compared to the risk-free foot. Something that, if it continues to exist in the future, justifies a role in portfolios, even if when an additional correction is made for a the difficulties that are known to be attached to the hedge fund indices.
Efficient markets revisited.
The fact that on average there remains a pure alpha after corrections supports the idea that markets are a little less efficient than people believed them to be in the 1980s and 1990s.
As a consequence, it makes sense to compare the expected returns of alpha and beta risks. They can no longer be treated independently. This asks for a framework in which their contribution to the portfolio can be analysed explicitly and systematically.
Part three: Alpha and beta investing in the Netherlands
Chart 3, shown below, is a stylised account of the ‘average’ Dutch institutional investment portfolio. A typical portfolio knows a distribution of fixed income : equities of about 60:40. Our observation is that a typical tracking error around this strategic benchmark amounts around 1.5%. The total risk (standard deviation on a yearly basis) of such a portfolio amounts to approximately 8%.
The proportion of beta risk (7.9%) to alpha risk (1.5%) amounts to 5:1.
With an estimated information ratio of 0.4 after costs the long-term expected return of this portfolio would amount to 5.8% based on the aforementioned new subjective efficient frontier. Of the total, 5.2% is generated by the beta risks (fixed income and equities) and 0.6% by the alpha risks (0.6% =1.5% tracking error times 0.4 IR).
The question is if this stylised fund can do better, considering the expected IR of 0.4. By way of an experiment the beta risk is reduced by investing less in equities (30%) and more in bonds (70%). On the subjective efficient frontier the resulting decrease in return is small, because it is so flat.
If the total risk of the portfolio remains constant, the alpha risk is allowed to rise substantially, because the alpha and beta risk are by definition uncorrelated. It turns out that now 4.9% alpha risk can be taken, to keep the total portfolio risk constant at 8.1%.
If this alpha risk is rewarded with an IR of 0.4%, this risk is expected to return around 2%. A significant improvement of the total portfolio return: At the same total risk of 8% the expected portfolio return now amounts to 7% instead of the original 6%.
This experiment changed the alpha/beta risk ratio from 5:1 to approximately 1.3:1 the expected return per unit risk rose with almost 20%. In chart 4, above, we see a potential solution for the challenges of the lowered efficient frontier.
Beta risks as well as alpha risks are expressed as a standard diviation on a yearly basis. The total risk of the portfolio can be calculated as follows: (portfolio risk)2 = (beta risk)2 + (alpha risk) 2 .
The optimal ration between alpha ad beta risk
An important question in this respect is how an investor reaches a well-founded estimation of the expected IR.
The ideal ratio between alpha and beta risk is the dependent of two factors:
o The height and the slope of the efficient frontier (these define the expected return per unit beta risk);
o The expected information ratio of the investor (this defines the expected return per unit of alpha risk).
In the optimal situation the expected marginal return per unit portfolio alpha risk has to equal the expected marginal return per unit beta risk. As long as this is not the case, the expected return per unit portfolio risk can be increased by exchanging beta risk for alpha risk or vice versa.
What is the optimal ratio between alpha and beta risk in the example above? It appears that under these assumptions the beta risk will fall from 7.9% to about 3%. The alpha risk then is allowed to grow to 7.4%. The expected return on the portfolio rises from 5% (0% alpha risk) to 7.4% with the total risk unchanged. The ratio alpha:beta now completely changed to more than 1:2.
At a lower assumed IR the optimal alpha risk is evidently lower. The stylised Dutch institutional portfolio, with 7.9% beta, and 1.5% alpha risk, appears to have an optimal distribution of alpha and beta risk at a collectively (implicitly) assumed IR of around 0.05. For the collective this assumption may not be so strange, but individually speaking this seems very modest.
Expected information ratio: distributed over different sources of alpha.
In general it can be stated that for an (individual) investment strategy, an IR of 0.4 is a respectable expected (gross) IR. With the costs subtracted (25 to 40% of the gross IR) this leaves a net expeted IR of 0.25 – 0.3. In reality, investors are often content if their realised IR reached 0.1.
Chart 5 shows that if an investor has access to a number of modest sources of IR (0.1%) these can add up to one strong whole, if they are (highly) independent of each other. This pleads for combining as much independent sources of alpha as possible.
The expected IR increases with the square root of the number of strategies that is combined. If an investor had access to 16 sources with an IR of 0.1 each, the expected IR rises to about 0.4%.
This is a result of the diversification effect that arises between independent sources of alpha. Richard Grinold called this relation ‘The Fundamental Law of Active Management’.
Part four: Practical matters and challenges
In this part a few points of caution will be described relating to the introduction and implementation of a shift from beta to alpha sources in portfolio management. This overview shows that a great number of skills are needed. In many cases one will have to learn step by step.
A shift to more alpha risk will often imply the use of unknown strategies, new instruments and additional external asset managers. To succeed, intensive communication with all the relevant parties such as the pension fund board and the supervisor is needed.
o Strategic research. Does the organisation posses or have access to consistent sources of alpha? What is a realistic objective for the IR?
o Adjusting the strategic investment plan. In the strategic plan explicit attention should be paid to alpha and beta. How much risk will be allocated to alpha? How much is the aimed return?
o Formulating a plan of approach. Develop a plan of how to reach the new situation starting from the current situation.
o People and knowledge. Does the organisation have the right people and the relevant knowledge? Where are the people and the knowledge located? Internal? External? What are the requirements for external managers?
o Process. How will the process of finding and combining of alfa-sources be organised? What will be done in house? What will be outsourced? To whom? What do you want from your external managers and how will you monitor them?
o Tools. Which tools are available/ should be developed for measuring, monitoring and managing the alpha and beta risks?
o Risk budgets and reports. Creating a consistent framework where all managers and sources of alpha and beta come together.
Creating an operational framework. Tactical aspects
o Identification of (independent) sources of alpha. As shown above, finding of a number of independent sources of alpha is essential to increase the expected IR. Finding sources of alpha as well as re-evaluation those sources costs much energy;
o Selection and monitoring of alpha managers. In addition to ‘classical’ asset managers, non-traditional managers will play a role. In selecting those managers operational risks play an important role;
o Separating alpha and beta risks. Above it was shown that keeping apart the alpha and beta components of external managers is important considering the fee;
o Tactical portfolio construction. Which allcation does the manager receive? Is this a constant allocation or are there market circumstances or regimes under which his or her approach has more or less chance of success?
Jaap van Dam is the manager responsible for investment consultancy at Zanders & Partners Investment Consultancy based in Bussum
(1) The Information Ratio (IR) is the added value per unit relative risk compared to the relevant benchmark (alpha/tracking error)
Summary and conclusions
o The generally accepted approach of investing in the past decades is not sufficient anymore. Although a number of the ingredients are visible, a new generally accepted approach still has to be developed.
o In the past decades alpha and beta risks were separated. Beta risks – deciding on the strategic asset mix – were the exclusive domain of asset and liability management (ALM) studies, while alpha risks, - defining the tracking error – was the domain of the investor. An important development is that alpha and beta decision making is integrated. This requires
a new way of thinking about the (strategic) organisation of investment portfolios.
o The role of alpha investments will grow compared to the role of beta investments. The current ratio of 5:1 between alpha and beta offers investors who have access to alpha (‘skill’) the opportunity to increase the absolute return of a portfolio without a proportional increase in the risk: the return per unit of risk increases.