Modern Portfolio Theory

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1 66 Trusts & Trustees, Vol. 15, No. 2, April 2009 Modern Portfolio Theory Ian Shipway* Abstract All investors, be they private individuals, trustees or professionals are faced with an extraordinary range of options when it comes to building and maintaining a portfolio. At the point in time when the portfolio is created decisions have to be made as to what assets to include and in what proportion. This article provides the reader with an understanding of the foundations underpinning Modern Portfolio Theory that provides a framework within which to make sensible asset allocation decisions. Introduction All investors, be they private individuals, trustees or professionals are faced with an extraordinary range of options when it comes to building and maintaining a portfolio. At the point in time when the portfolio is created decisions have to be made as to what assets to include and in what proportion known as asset allocation. When running the portfolio decisions have to be made about when to make any adjustments as a consequence of a changing economic environment or requirements, decisions that are often complicated by consideration of taxes and costs. The purpose of this article is to provide the reader with an understanding of work that has been done on asset allocation over the past 50 years that provides a framework within which to make sensible decisions. This body of work is known as Modern Portfolio Theory. My intention is to provide a basic understanding so that the reader feels comfortable with their investment advisers when Modern Portfolio Theory techniques are being employed, and is able to question the rationale for any alternative methodology when it is not. First establish what you want to achieve As with all activities in life, when building a portfolio it is important first of all to know what it is that you are trying to achieve. In investment terms, it is not sufficient to simply say that you want to achieve the best returns possible. It is impossible to separate the pursuit of the best returns from the consequential exposure to risk that you will face along the way. For example, the national lottery might provide the best possible return available in the United Kingdom right now; for a stake of 1 you might earn many millions. However the risk, and it is a very high risk, is that you will suffer a 100 per cent loss on your investment of 1. It is impossible to separate the pursuit of the best returns from the consequential exposure to risk that you will face along the way Looking at the same question the other way round it is not a sensible starting point to set an investment objective of taking no risk and accepting the investment returns consequent upon that decision. If you place your 1 under the bed and come back some time later you will find that your 1 is still 1. You will have achieved the objective of taking no investment risk, but your money will not have grown in value at all. If you need to achieve a positive return in order to meet the objectives of your investment *Ian Shipway, Managing Director, Bluefin Wealth Management, Park House, Heathcote Road, Camberley, Surrey, GU15 2EU. Tel: þ ; ian.shipway@bluefingroup.co.uk ß The Author (2009). Published by Oxford University Press. All rights reserved. doi: /tandt/ttn129

2 Trusts & Trustees, Vol. 15, No. 2, April 2009 Articles 67 strategy, to provide an income for a beneficiary for example or even just to maintain its value against inflation, then placing your money under the bed has made it certain that you will not meet your objective. You have effectively countered one risk, but in doing so you have opened yourself to another. It can be seen that in formulating an objective for the portfolio we cannot rely solely on a one dimensional view, either of return or of risk. We need to frame our objective in the collective terms of the return which we seek and the amount of risk we are prepared to take in pursuit of that return. This is a necessary first step in the creation of an investment policy. Without this information any investment strategy will be run in a vacuum. You might inadvertently be running much higher risks than you would be comfortable with, or conversely you might be expecting a return that has very little chance of being delivered. The consequence is that the investor will have no idea of whether the strategy has any chance of being successful in the pursuit of the objectives. So, having carried out an initial planning exercise, an investor might then ask how a portfolio might be constructed to meet the requirements for return while remaining within the desired tolerance to risk. A framework for portfolio construction It was when considering this question that Harry Markowitz in 1952 published an article in the Journal of Finance that laid the foundations for what is now known as Modern Portfolio Theory. At its simplest, this can be interpreted as a mathematical interpretation of the old adage don t put all your eggs in one basket. At the time that Markowitz was doing his research, the prevailing influence on portfolio management was some work done in the 1930s on security valuation. That work provided a foundation upon which individual securities could be valued by looking at the fundamentals of the underlying business. Therefore a share was purchased only when its intrinsic value was more than the price demanded by the market, or sold when the market was offering to buy it at more than its intrinsic value. Markowitz considered that if the only thing an investor were interested in was the value of the portfolio, then in order to maximize that value one need only invest in a single security the one that provided the greatest return. However, this is not the way investors did, or should, act. The reality is that investors spread their money between a number of holdings because they are interested in risk as well as return. If something goes wrong with one holding all is not lost as you still have investments in a number of other holdings. It is the same intuition that makes lottery players buy more than one ticket with many tickets there is more chance of your numbers coming up so the risk is spread. This insight led to the development of a mathematical framework for mixing investments within a portfolio to calculate the expected returns for any given level of risk. The basic theory requires an understanding of three factors; the expected return and risk of each component of the portfolio and the way each behaves in relation to the other. The simplest of the three factors to understand is the expected return. This is the annual return that we expect to receive from holding an investment over time. So for example let us assume that we held an investment that we expected would provide us with an annualized return of 5 per cent when held over the long term. What this means is that in future years when we look at the value of our investment we expect it to have risen by the equivalent of 5 per cent of its previous year s value. However, although this provides us with the average return when looked at over multiple years, it does not give us any idea of how much that growth rate varied on a year by year basis. Our second measure, that of risk, provides us with this information and gives us an idea of how much our assumption for return might deviate in any one year. We know from looking at past history that investments rarely provide steady returns year by year. What actually happens is that they go up and down in value, and

3 68 Articles Trusts & Trustees, Vol. 15, No. 2, April 2009 although, using the example above, the expected long-term return might be 5 per cent, in any one year the return might be much higher or lower. We therefore need some measure that provides us with this information and the one that Markovitz selected is a statistical measure called the standard deviation. It is important to understand that standard deviation is a statistical measure that describes the range above or below the average that is likely to be experienced in two out of three years. In the other year the deviation from the mean is likely to exceed the standard. So, if our standard deviation was say 8 per cent, what that would tell us is that in two years out of three we should expect our investment to provide returns of between 3 per cent (5 8 per cent) and 13 per cent (5 þ 8 per cent). Investments with a high standard deviation are described as having a high volatility because their behaviour is volatile, while those with a low standard deviation are described as having low volatility. All things being equal, it is better to hold investments with a lower volatility. To illustrate this let us assume that we invest 100 into two investments, one rises and falls in value by 50 per cent each year while the other neither increases nor decreases. The first investment after one year goes up 50 per cent and is worth 150, but in year two falls in value to 75 and so on. After four years, this investment will be worth about 56 while the other will still be worth 100. Both have an average annual return of zero, but the more volatile investment has fallen in value. So far we have concluded that we need to build our portfolio from a number of different investments and that all things being equal it is better for the portfolio to have a lower volatility. The question is how do we select our individual component parts and what proportions do we hold in each one. The answer lies with the third factor, correlation, which measures how similar the ups and downs in value of any two investments are to each other. For example if two investments both rose and fell in value at exactly the same time then they would have an exact correlation to each other, whereas if one rose in value at the same time as another fell in value then they would be negatively correlated. When constructing a portfolio it is better to include a variety of different assets that go up and down in value at different times to each other. To appreciate this let us assume that you have the opportunity to invest in two businesses, one that sells deckchairs and another that sells umbrellas. If you decide to put all of your investment into the deckchair business you will do well when the sun is shining but not so well when it is raining. This is illustrated by the blue line A in chart 1 where the value of your investment is rising when the sun shines, but falls when it rains. If the deckchair business was your only investment you would suffer a lot of ups and downs in the value of your portfolio, although you should expect a positive return over the long term. Conversely if you only purchased shares in the umbrella manufacturer, illustrated by red line B, you would suffer a fall in the value of your investment during sunny periods and a rise during rainy periods. Owning either investment on its own would give you sleepless nights. A B Now consider what would happen if you put half of your money into the deckchair company and the other half into the umbrella company. Your overall return would be the same as when investing all of your money into one or the other. However, the value of the combined portfolio will not suffer the ups and downs of the individual holdings as taken together the ups and downs cancel each other out, as illustrated by the value of black line C, and you are left with just the aggregate value. C

4 Trusts & Trustees, Vol. 15, No. 2, April 2009 Articles 69 By combining investments that do not go up and down in value at the same time as each other you have reduced your risk without reducing your return. This is often referred to as the only free lunch in the investment world. In the real world no two investments that exactly mirror each other s movements exist but the principle of mixing investments that do not move exactly like each other remains sound. So Modern Portfolio Theory was founded on the observation that investors did not hold just one investment but created a portfolio made up of a number of individual investments. The theory created a mathematical framework that allowed the portfolio manager to mix these individual investments and to have some idea of the risk and return that might be expected from the combination. Modern portfolio theory was founded on the observation that investors did not hold just one investment but created a portfolio made up of a number of individual investments that provide the best return for any given level of risk. This technique is still in wide use today. To understand how it works let us start by assuming that we have only two investments available to select from; UK shares and cash. Our portfolio can be made up entirely of shares, entirely of cash or of a combination of the two. These two portfolios are represented by points A and B on chart 2, with point A being all cash and point B being all shares. Looking backwards we know that over the past 50 years shares in the United Kingdom, as represented by the all share index, have provided a return of the order of 12 per cent a year, while cash has provided a lower return of the order of 8 per cent a year. However, in achieving the higher returns shares have suffered an annual standard deviation of just over 19 per cent, while cash has been much more stable and has a standard deviation on an annual basis of less than 1 per cent. What we can see from the chart therefore is that although portfolio B has a higher return than portfolio A, the risk has been much higher. The theory also made two key assumptions: Investors are rational and want to achieve a return commensurate with risk. All investors are risk averse. This does not mean that investors do not want to take any risk, but means that given two assets that offer the same expected return, investors will prefer the less risky one. Conversely, an investor will take on increased risk only if compensated by higher expected returns. This was all very well, but what investors next wanted to know was what combinations of investments provided the best return for any given level of risk. Further work by the mathematicians and the advent of computers provided an answer. A process, known as optimization, was the solution. In this process a computer can be used to calculate the risk and return characteristics of a very large number of combinations of different investments to find those What this tells us as investors is that, based upon past history, if we want a higher return then we must accept a higher risk. If we return to the chart you will see that other points have been plotted for portfolios that contain other combinations of cash and shares, with each portfolio from A to B having an increased

5 70 Articles Trusts & Trustees, Vol. 15, No. 2, April 2009 equity content. What is immediately obvious is that the line joining all of these points is not a straight line but is curved. This is due to the third factor that we discussed above, correlation, and is a consequence of the fact that our cash and shares do not go up and down in value at the same time or extent as each other. The portfolios on chart 2 are made up of just two asset classes. On chart 3 we have introduced a third asset class, small company shares, and the red line plots the risk and return for portfolios made up of all three. It can be seen that the effect is to tilt the line upwards, or in other words we have increased our expected returns without increasing our risk. What this illustrates is that by adding a number of different asset classes together we can create combinations that increase returns without necessarily increasing risk. With the help of a computer, we can look at many combinations of investments to give us the optimum combination for risk and return. If we plot these portfolios on a graph similar to chart 3, we will find that they would all fall along a line that bent inwards towards the top left corner similar to the red line on chart 3. This line represents the best possible combination from a range of assets and is referred to as the Efficient Frontier. This ability to optimize a portfolio based upon the risk and return characteristics of its underlying components is a compelling proposition. There are many websites where investors can gain access to an optimizer and can create their own efficient portfolios. Indeed one might ask if there is a need for professional investment advice if the most efficient portfolio can be created by a computer. As compelling as it may seem, there are drawbacks and it is important to understand the limitations of the methodology. Going back to the beginning, you will recall that three inputs are required: return, risk and correlation. If these were all steady or fixed numbers we would have no problem. The reality is that they are not fixed but vary over time. For example the annual returns from equity markets have been very different in the past 12 months to what they were five years ago and the range between highs and lows have also varied to a significant degree. Therefore, if we run our optimizer based on the set of statistics from five years ago we will get a markedly different answer to that if we used today s figures. These differences are not small and will usually result in a significantly different optimum portfolio depending upon which set of figures is used. To some degree this can be countered by using very long-term assumptions, but in the short term our actual experience may vary considerably from the long-term averages. A further complication is that correlations between different assets changes over time. Although we may select the assets for our portfolio based on their low correlation to each other, it is not helpful if those correlations break down. This most frequently happens at the moment we least want it, such as when all world markets fall at the same time due to events such as the recent credit crunch. So, although we can produce graphs that look very compelling and that highlight where an investor should be invested, the reality is that the efficient frontier does not exist in real life because the risk, return and correlations are constantly changing. A more appropriate way of looking at the issue is that there is a broad area where portfolio characteristics are better, towards the top left corner of a risk return chart, where returns are higher and

6 Trusts & Trustees, Vol. 15, No. 2, April 2009 Articles 71 risks lower. We will never have the absolute answer to what is the optimum portfolio, but we can get an idea of what is and what is not in the right ballpark. So far I have referred to historic characteristics of risk, return and correlation in order to calculate our efficient frontier. This need not be the case and we could use figures that we believe are reasonable on a forward looking basis. So we might determine that although cash has provided returns of around 8 per cent a year over the past 50 years, returns going forward will be lower. Another problem with Modern Portfolio Theory is the way in which it deals with risk. The risk measure that is used is the deviation of returns from an expected midpoint. A low risk investment under this definition is one that has a low dispersion of returns, while a risky investment has a high dispersion of returns. Going back to the examples of UK shares and cash used above, our expected annual return from a portfolio consisting entirely of shares is approximately between 7 per cent and 31 per cent, a range of 38 per cent. However, the range of long-term returns from cash is expected to be between 6 per cent and 8 per cent, a very much smaller range of 2 per cent. On this basis, the cash is defined as having a lower risk, because it has a lower dispersion or volatility. It is reasonable, however, to question whether a measure of deviation of returns around an expected mean is an appropriate measure of risk for an investor. The reality is that most clients are not really bothered about the upside risks, it is the downside risks that they are concerned about. It is rare for an investor to complain when an upside risk is being experienced, but when suffering a downside risk they will want to know why. To put this into perspective consider once again our UK share portfolio, which has an expected return of around 12 per cent and deviation of around 19 per cent. If we were to find another investment that had a higher expected annual return of say 20 per cent but the same standard deviation then it would be considered just as risky as our share portfolio. This is clearly counter intuitive and is a further reason why the theoretical benefits of Modern Portfolio Theory are not accurately reflected in the real world. The reality is that most clients are not really bothered about the upside risks, it is the downside risks that they are concerned about In practical terms, it is also important to understand other risks that face the investor. These will include inflation risk, deflation risk, default risk, stock-specific risk and market risk amongst others. To a greater or lesser extent these risks can be mitigated within the portfolio by including investments that individually counter these specific risks, whilst still having the return, volatility and correlation characteristics to be of use in getting us somewhere near the efficient frontier. The greatest risk faced by an investor, however, is the risk of not meeting the clients-stated objectives. So, to return to where we started, the first and most important question for investors is what they are trying to achieve with the portfolio. This will provide an indication of the returns that will be needed to achieve the objective. The next issue is to identify the risks that the investor will face along the way, which will include short-term ups and downs in the portfolio value as well as a host of other risks. Building blocks can be selected that have certain characteristics to counter some of the risks identified. For example, cash is very resilient to short-term ups and downs in value whilst commercial property is an effective hedge against inflation. Individual shares can lose all of their value, while collective funds containing a diversified portfolio of shares cannot. Once we have decided on the list of building blocks that we might want to use, we can employ Modern Portfolio Theory to get an idea of what a sensible portfolio might look like. This should not be viewed as the perfect solution, but forms a sound foundation on which to base a decision. The alternatives, based usually upon individual opinion or consensus views, also have significant weaknesses and rarely offer a superior basis on which to run a long-term portfolio strategy.