* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Costs to Investors of Boycotting Fossil Fuels
Survey
Document related concepts
Private equity wikipedia , lookup
Pensions crisis wikipedia , lookup
Land banking wikipedia , lookup
Business valuation wikipedia , lookup
Public finance wikipedia , lookup
Greeks (finance) wikipedia , lookup
Securitization wikipedia , lookup
Private equity secondary market wikipedia , lookup
Systemic risk wikipedia , lookup
International asset recovery wikipedia , lookup
Stock trader wikipedia , lookup
Rate of return wikipedia , lookup
Investment fund wikipedia , lookup
Financial economics wikipedia , lookup
Beta (finance) wikipedia , lookup
Modified Dietz method wikipedia , lookup
Investment management wikipedia , lookup
Transcript
Costs to Investors of Boycotting Fossil Fuels July 2015 -1- Europe Economics is registered in England No. 3477100. Registered offices at Chancery House, 53-64 Chancery Lane, London WC2A 1QU. Whilst every effort has been made to ensure the accuracy of the information/material contained in this report, Europe Economics assumes no responsibility for and gives no guarantees, undertakings or warranties concerning the accuracy, completeness or up to date nature of the information/analysis provided in the report and does not accept any liability whatsoever arising from any errors or omissions. © Europe Economics. All rights reserved. Except for the quotation of short passages for the purpose of criticism or review, no part may be used or reproduced without permission. Contents Executive Summary................................................................................................................................................................. 1 1 Introduction.................................................................................................................................................................... 2 1.1 The divestment strategy to be analysed .......................................................................................................... 2 1.2 How to measure the portfolio costs of avoiding ownership of fossil fuel stocks ................................. 3 1.3 Later sections ........................................................................................................................................................ 5 2 How Restricting Portfolio Choice Damages Investor Diversification .............................................................. 6 2.1 What diversification is and the key intuition regarding how excluding certain investments has a potential diversification cost............................................................................................................................................ 6 2.2 How the cost of restricting diversification can be measured .................................................................... 7 2.3 How we have measured the diversification cost of excluding fossil fuel stocks ................................... 8 3 Results............................................................................................................................................................................ 10 3.1 Raw returns and correlation between returns............................................................................................ 10 3.2 Measuring the cost of restricted diversification .......................................................................................... 11 Appendix ................................................................................................................................................................................. 14 Executive Summary Executive Summary • • • • • • • • • • As a follow-up to similar projects analysing the potential impacts of fossil-fuel divestment in an American financial context, The Independent Petroleum Association of America’s international committee asked Europe Economics to estimate how much investors in the UK would stand to lose by such a boycott. Past studies have considered the losses from restricting portfolio investments in various ways, such as by excluding adult entertainment, alcohol, gambling, nuclear power, tobacco and weapons, or by investing only in funds deemed “socially responsible”. Some papers have found there to be little to no impact of such restrictions upon returns under certain conditions. But where impacts are found, then in normal times they lie within a fairly broad range of roughly 25-200 basis points loss from restricting portfolio choice, depending upon the excluded stocks. The typical methodology in past studies measures portfolio out- or under-performance as a degree of deviation from standard asset pricing models. Our approach in this paper, by contrast, works entirely within the orthodox portfolio theory. Orthodox theory thus teaches us that the most important loss to a non-specialist investor from excluding classes of security from a portfolio (e.g. excluding fossil fuel stocks) will be the lost ability to diversify risks. “Diversification” is a familiar concept from homely proverbs such as “don’t put all your eggs in one basket” or “what you gain on the swings, you lose on the roundabouts”. In finance, an investor diversifies by purchasing portfolios (groups of assets) where higher-return scenarios for some of the assets are likely to be correlated with (i.e. occur, fairly often, at the same time as) lower-return scenarios for other assets, so that losses tend to be cancelled out by gains elsewhere and the overall risk of the portfolio is reduced. An investor excluding certain stocks that would otherwise be important for diversification might end up with more risk but with no increase in expected return end up with less return but no reduction in risk end up with more return but also with more additional risk than would have been necessary to secure that extra return if those excluded stocks had been used instead The standard way to understand and measure the risk-return trade-off from portfolios was developed during the 1950s by Harry Markowitz. This considers the returns and variance (risk) of returns and estimates a frontier of “efficient portfolios” for any given available assets. We use Bloomberg data on the 10 “industrial sectors” from the UK FTSE All-Share and data from fossilfreeindexes.com to construct four key assets — a “services sector” asset, an “ICT sector” asset, a “fossil fuels” asset (consisting of those assets in the FTSE All Share Index that fossilfreeindexes.com indicates should be divested), and an “other” asset. We have data back to 2002 and use this data to construct the frontiers of efficient portfolios for the four assets comprising the whole market and the three assets that exclude fossil fuel assets that fossilfreeindexes.com says should be divested. We consider how much higher returns an investor in the whole UK stock exchange (e.g. via a FTSE AllShare tracker fund) would have made versus an investor excluding fossil fuel assets or, alternative, how much additional risk an investor excluding fossil fuel assets would near to bear to make the same return. We find that, investors following the recommendation of the fossil fuel divestment campaign to exclude fossil fuels would, from 2002 to mid-2015, have sacrificed the equivalent of an annual return of 0.68 percentage points (68 bps) or, if they did not want to accept lower returns, would have had to take more than 20 per cent extra risk on their investments. -1- Introduction 1 Introduction This document has been commissioned from Europe Economics by the international committee of the Independent Petroleum Association of America, which includes a number of U.S.-based companies with significant operations in the UK and other foreign jurisdictions. As a follow-up to similar projects analysing the potential impacts of fossil-fuel divestment in an American financial context, IPAA’s international committee asked Europe Economics to estimate how much investors in the UK would stand to lose by such a boycott. 1.1 The divestment strategy to be analysed The website gofossilfree.org, in its /UK subsection, defines “fossil fuel divestment” as follows: What is fossil fuel divestment? Divestment is the opposite of investment. While investment means buying stocks, bonds or other investments in order to generate financial returns, divestment means getting rid of particular stocks, bonds or investment funds that are unethical or morally dubious. Fossil fuel divestment means to avoid direct ownership of, or commingled funds that include, public equities and corporate bonds of fossil fuel companies. There are 200 publicly-traded companies that hold the vast majority of listed coal, oil and gas reserves. The Fossil Free campaign is therefore asking organisations to: • immediately freeze any new investment in the top 200 publicly-traded fossil fuel companies • divest from direct ownership and any commingled funds that include fossil fuel public equities and corporate bonds within 5 years 1.1.1 Costs of fossil fuel disinvestment to be considered here There are many potential costs and benefits of a fossil fuel disinvestment strategy that fall beyond our scope here. For example, we shall not consider to what extent, if a fossil fuel disinvestment strategy were pursued extensively, that might result in the stranding of many fossil fuel-related assets, neither shall we consider the potential spillover impacts of damaging the financial viability of fossil-fuel-related companies to their ability to invest in or develop new energy technologies. Our focus here is purely on the direct impacts upon investors themselves of pursuing this strategy. Amongst investor impacts, we can distinguish broadly between a. transitional costs — i.e. the cost of executing a disinvestment strategy such as the transactions costs involved in rebalancing an investment portfolio by selling fossil fuel stocks and buying other stocks; -2- Introduction b. ongoing risk-return costs — i.e. the cost in terms of lower returns and/or higher risks from having a portfolio limited only to non-fossil fuel stocks. Our main focus in this report will be on the latter category — the ongoing costs to investors of not investing in fossil fuel stocks. 1.2 How to measure the portfolio costs of avoiding ownership of fossil fuel stocks The standard method deployed for investigating this question involves comparing “ethical” fund returns versus all fund returns or “ethical” fund returns versus returns on the funds excluded by these “ethical” funds (either via indices or constructed sets). In the following table we summarise the findings of a number of past studies including that form of analysis. Note that in this literature it is common to refer to excluded stocks, somewhat jocularly, as “sinful” and to the funds regarded as ethical by the restricted investment strategy as “Socially Responsible Investments” (SRI). We find this terminology much less relevant in the context of fossil fuel disinvestment than it could be argued to be in the case of excluding, say, gambling or tobacco or adult entertainment stocks, and so do not use it elsewhere in this document, but we maintain it for this table. We use the term “restricted portfolio” to refer to the portfolio of investments that are permitted by whatever restrictions on stock choice are involved. Table 1.1: Past studies of the portfolio costs of restricting stock choice Study Non-invested stocks Method Years covered Renneboog, ter Horst, Zhang (2007) SRI funds vs conventional funds 1991-2003 Climent and Soriano (2010) Green funds vs conventional funds Excess return, Jensen’s alpha, Four-factor Carhart model Excess return, Jensen’s alpha, Four-factor Carhart model Lobe and Walkshäusl (2011) 6 “sinful” industries (adult entertainment, alcohol, gambling, nuclear power, tobacco, weapons) and combinations of them ESG, green, social, religion portfolio vs conventional portfolio Excess return, Sharpe ratio, Jensen’s alpha, Four-factor Carhart model 1995 – 2007 Excess return, Four-factor Carhart model; 2004-2014 Mattsson and Sandstrom (2014) -3- 1987-2009 Annual loss (+) or gain (-) from use of restricted portfolio +180bps for UK; +90bps for US Raw: • Green: +422bps • SRI: +548bps Risk-adjusted: • Green: +422bps Division by periods: • “Learning period” +544bps • “Mature period” Neither gains nor losses Raw: 41bps gain from portfolio focused on “sinful” industries* Risk-adjusted: Neither gains nor losses Raw: +7bps Risk-adjusted: Neither gains nor losses Introduction Study Non-invested stocks Method Years covered Utz and Wimmer (2014) SRI funds vs conventional funds; Excess return, Sharpe ratio, Jensen’s alpha, M-squared; 2002-2010 Ethical ratings Jensen’s alpha, Three-factor FamaFrench model, Four-factor Carhart model Nofsinger and Varma (2014) SRI funds vs conventional funds 2000-2011 and 2 crises (dotcom 20002; global financial 2007-9) Trinks and Scholtens (2015) 14 “sinful” industries and combinations of them Four-factor Carhart model 1991-2012 Fischel (2015) Portfolio without energy stocks vs market portfolio Maximise riskadjusted portfolio return 1965-2014 Annual loss (+) or gain (-) from use of restricted portfolio Raw: +5bps Risk-adjusted (CAPM): -7bps Raw: +4bps Risk-adjusted: General result: ambiguous (sign depends upon riskadjustment technique) Division by subperiods: • Non-crisis: +67 to +95 bps • Crisis: -161 to -170 bps (i.e. SRI funds do better than unrestricted funds in crisis periods) Risk-adjusted: • +25bps • 91bps gain from portfolio focused only on “sinful” industries* Raw: -70 bps (but std. deviation also smaller by 50 bps) Notes: * This is not the return on an unrestricted portfolio but is, instead, the return on a portfolio that contains only “sinful” stocks. Many of these past studies have recognised that raw returns or raw relative returns are not by themselves a complete indicator of impact. One could imagine that excluding some set of stocks from an investment portfolio might mean no change in the average return but instead a material rise in the riskiness of the portfolio. Consequently, a number of past studies have risk-adjusted returns via some model such as the Capital Asset Pricing Model (CAPM). The standard way this is done is by estimating a deviation of different portfolios from the predictions of the risk model (e.g. of CAPM). If the deviation of a portfolio from the model’s prediction is positive, then that is interpreted as a risk-adjusted gain. If the deviation is negative that is interpreted as a risk-adjusted loss. It should be noted that this literature is far from unambiguous regarding the implications of excluding stocks. Some papers have found there to be little to no impact on returns under certain conditions. But where impacts are found, then in normal times they lie within a fairly broad range of roughly 25-200 basis points loss from restricting portfolio choice, depending upon the excluded stocks. There is also some tentative indication that the losses (or indeed whether there are losses) may depend upon the time period. Restricted portfolios might outperform unrestricted portfolios during periods of financial turbulence or it might be that, over time, investors learn how best to invest in restricted portfolios, eventually limiting their losses. -4- Introduction 1.2.1 How our model in this paper differs from this previous literature As noted above, this previous literature measures portfolio out- or under-performance as a degree of deviation from standard asset pricing models. Our approach in this paper, by contrast, works entirely within the orthodox portfolio theory. Standard models for risk-adjustment (e.g. the Capital Asset Pricing Model, CAPM) are based upon the hypothesis that the investors concerned are able to diversify away all risks to the maximum extent feasible. The bearing of any net diversifiable risk, across a portfolio, is then a choice — e.g. reflecting the fact that the investor has engaged in some specialist analysis of the sector or company concerned and believes that that analysis has revealed that expected returns for that company are higher than the market price anticipates. Theory thus teaches us that the most important loss to a non-specialist investor from excluding classes of security from a portfolio (e.g. excluding fossil fuel stocks) will be the lost ability to diversify risks (i.e. a deterioration of the risk-return trade-off available to investors), not lost returns within a common risk-diversification portfolio (i.e. a shift along the risk-return trade-off available to unrestricted investors). Our main analysis in later sections of this report therefore concerns how much better the risk-return trade-off is for standard broad portfolios, such as the FTSE All-share index, than if one excludes fossil fuel stocks. This lost diversification has a price. We measure this below and express it as a percentage return equivalent. 1.3 Later sections Later sections of this report are as follows: • In Section 2 we set out the theory of how restricting portfolio choice would be expected to have a diversification cost for investors. • In Section 3 we explain how we have measured that diversification cost in this study. • In Section 4 we present our results. • Finally, there is a mathematical Appendix setting out key technical points about our model. -5- How Restricting Portfolio Choice Damages Investor Diversification 2 How Restricting Portfolio Choice Damages Investor Diversification 2.1 What diversification is and the key intuition regarding how excluding certain investments has a potential diversification cost “Diversification” is a familiar concept from homely proverbs such as “don’t put all your eggs in one basket” or “what you gain on the swings, you lose on the roundabouts”. In finance, an investor diversifies by purchasing portfolios (groups of assets) where higher-return scenarios for some of the assets are likely to be correlated with (i.e. occur, fairly often, at the same time as) lower-return scenarios for other assets, so that losses tend to be cancelled out by gains elsewhere and the overall risk of the portfolio is reduced. Of course, an investor could choose not to invest in certain stocks, even if they could be used to offset risks elsewhere. The consequence would be that the portfolio would be riskier — i.e. there would be a higher chance that the overall returns would be negative or the potential extent of losses could be greater. An investor might perfectly reasonably choose to do this if, by not offsetting risks in this way, then as well as the greater chance of a bad outcome there was also a greater chance of good outcomes. In particular, it might be reasonable to do this if, after taking account of the increased risks of both bad and good outcomes, the “average” or “expected” overall return of the portfolio was higher. Then the investor would be accepting more risk in order to secure a higher expected return. This can be described as “choosing a different risk-return trade-off”. Another kind of different risk-return trade-off might arise if, by excluding certain stocks, although the expected return fell, so did the riskiness of the portfolio. But now consider the following three possible consequences of choosing not to invest in certain stocks: • • • ending up with more risk but with no increase in expected return ending up with less return but no reduction in risk ending up with more return but also with more additional risk than would have been necessary to secure that extra return if those excluded stocks had been used instead In each of these cases, the choice to exclude those stocks from investment has not simply meant either the securing of a higher return at higher risk or lower return at lower risk — as it were, “shifting along” an existing risk-return trade-off. Instead, it has meant that the risk-return trade-off itself has worsened (there has been a “shifting of” the risk-return trade-off). Excluding certain investments from a portfolio could result in such a worsening of the risk-return trade-off (which we refer to as “damaging investor diversification”) if, for example, the excluded stocks provided positive returns in a particular sort of situation when other investments might instead fall in value. To make this point easier to grasp let us make it more concrete by considering a specific example: scenarios for oil prices. Sometimes oil prices go up and down as world demand rises and falls — in which case high oil prices are a symptom of generally higher returns. But on other occasions, oil prices rise because of shocks or threats to supply — e.g. conflict in some oil-producing country or region. It is well-established that when oil prices rise, costs to many firms rise. Significant supply-shock-driven or supply-threat-driven rises in oil prices are even sometimes said to be associated with non-trivial falls in GDP for some energyuse-intensive non-oil-producing economies. -6- How Restricting Portfolio Choice Damages Investor Diversification But when oil prices rise because of supply shocks, oil producers whose business is located mainly outside the affected regions may make higher profits. So in scenarios of high oil prices driven by supply shocks, oil company stocks may be rising in value precisely when other stocks are falling. That means a diversified portfolio that includes oil stocks will, under such a scenario, tend to do less badly than would a portfolio that excluded oil stocks. Now it might be that there could be other investments that, as it happened, tended also to do well precisely when oil prices were high. If an investor that chose not to invest in oil stocks instead chose to invest in these other assets that did well under such a scenario, the cost (in terms of higher losses in a scenario of high oil prices) would be reduced. But oil is such a significant asset that it is plausible that there is no other asset or combination of assets that allows investors to come close to duplicating the same risk diversification impact that investing in oil stocks would have. 2.2 How the cost of restricting diversification can be measured The standard way to understand and measure the risk-return trade-off from portfolios was developed during the 1950s by Harry Markowitz.1 Markowitz’ portfolio allocation theory and the potential implications of restricting portfolio choice can be explained with the aid of the following diagram. In Figure 2.1 we see in the purple line a set of possible expected returns and volatilities (risks). Each point on the purple line is associated with a different set of portfolio “weights” (different proportions of the total assets in the portfolio being invested in different of the assets in that portfolio). Expected Return Figure 2.1: Stylised representation of diversification loss from portfolio restriction Volatility (Risk) Unrestricted portfolio 1 Restricted portfolio See, for example, Markowitz, H. (1952) “Portfolio selection”, Journal of Finance, 7(1), pp77-91 -7- How Restricting Portfolio Choice Damages Investor Diversification The point furthest to the left (the point with the lowest volatility) is called the “minimum variance portfolio” (“variance” is a measure of volatility or risk; “standard deviation” is the square root of variance). All the points on the purple line below the minimum variance point are “inefficient” in the sense that they involve taking on a level of risk that could be borne at a higher expected return (by picking, instead, the point with the same volatility but higher expected return that is above the minimum variance point). All of the “efficient” portfolio choices thus lie above and to the right of the minimum variance point (this set of points is termed the “efficient portfolio frontier”). The pink line represents a restricted portfolio where the restriction means the available risk-return tradeoff is worse. That is to say, for the efficient portfolio choices on the pink line (again, above and to the right of the minimum variance point that is leftmost on the pink line), every possible return can only be achieved at a higher risk (every efficient point on the pink line is to the right of the efficient point with the same return on the purple line). This smooth, symmetric diagram represents one rather simple case for the reduction in the risk-return trade-off. It should be noted that there are other, less symmetric possibilities, also. For example, it might be that the assets excluded in the restricted portfolio are all higher-return, higher-risk assets. That might mean that the returns and risks of the restricted portfolio (the equivalent of the pink line above) converged to the unrestricted portfolio, perhaps even meeting it at the minimum-variance portfolio — so that it was only amongst the efficient portfolios that the risk-return trade-off declines. (This may seem like an unnecessary curlicue. We mention it only because this will, in fact, be the sort of case we encounter in the empirical analysis below.) Thus, in this way, if one can identify the potential expected returns and volatility in returns of assets available from an unrestricted and a restricted portfolio, it should be possible to measure the diversification loss from the restriction. 2.3 How we have measured the diversification cost of excluding fossil fuel stocks It is standard in financial analysis to regard the stocks available on a major stock market, such as the London Stock Exchange, as constituting sufficient stocks for full diversification — that is to say, to the extent that risks can be diversified away (and of course not all risk can be diversified away), that can be done using shares available in a stock market (we don’t, for example, also need gold or real estate to achieve full diversification). We use the stocks in the FTSE All Share Index as our representation of an unrestricted portfolio. According to the FT industrial classification the FTSE All Share is made up of the following ten sectors: • • • • • • • • • • Consumers’ goods Consumers’ services Financials Healthcare Telecom Technology Industrials Oil Basic materials Utilities -8- How Restricting Portfolio Choice Damages Investor Diversification We used the market capitalisation and returns data of each of the above sectors to construct the returns data for the following broad sectors:2 • • • • Services — which includes Consumers’ good, Consumers’ services, Financials, and Healthcare sectors. ICT sector — which includes Telecom, and Technology sectors. Fossil Fuels sector — we define this below. Other sectors — this includes Industrial, Oil, Basic materials, and Utilities sectors, net of the Fossil Fuels sector. We defined the “fossil fuels sector” drawing on the list of publicly listed companies compiled by fossilfreeindexes.com.3 The list consists of 100 coal companies and 100 publicly listed oil and gas companies. From these we have selected those that are traded regularly on the London Stock Exchange. This led us to a sample of 21 companies that are listed on the London Stock Exchange. Those 21 companies are the “fossil fuels sector” for our purposes here. We treat stocks in each of these four broad sectors as an “asset” for the purposes of our analysis here. So we have four “assets”. For each of the companies in the fossil fuels sector “asset” we obtained daily returns and market capitalisation data from Bloomberg from the period 01/01/2002 – 30-04-2015. This is the entire dataset available, constructed in this way. It includes a number of interesting ups and downs in the market, including the turbulent stock markets of 2002/3 and 2008/9, as well as much more rapid growth periods. It also includes periods in which oil prices rose rapidly and periods in which they fell rapidly. Based on this data the Fossil Fuels Sector’s daily returns were constructed as weighted average of the daily returns of the 21 constituent companies, i.e.: = where ∑ is the market capitalisation of company on day . Returns of the Services sector and ICT sector “assets” were constructed as weighted averages of the returns of the returns of the constituent sub-sectors of the FT-SE provided by Bloomberg (with weights proportional to share of the market capitalisation of each constituent sector within the broader sector). In order to calculate the returns for the Other Sector “asset”, we first calculated the aggregate returns of the Industrials, Oil, Basic materials, and Utilities sectors (which we refer to as ); the “Other Sector” returns were then defined as residuals returns using the following formula: = ∗ − + 2 ∗ Returns of the broad sectors were constructed as weighted averages of the returns of the 10 constituent sectors (with weights proportional to share of the market capitalisation of each constituent sector within the broader sector). We note the following two minor data anomalies: • The sum of the market capitalisation of the ten FT industrial classes making up the FTSE All Share is not always identical to the total market capitalisation of the FTSE All Share. As a result of this, the weighted average of the returns of the constituents of the FTSE All Share differ from the returns of the FTSE All Share. In order to reconcile the data we have therefore adjusted of the returns of the FTSE All Share constituents by attributing to each of them the residual error in returns (i.e. the difference between the returns of the FTSE All Share and the weighted average of the returns of the constituents of the FTSE All Share). • Data is not available for the constituents of our four classes for all FTSE trading days (e.g. Bloomberg has occasional data glitches for some constituents on some particular day). We restrict our analysis to those days for which data is available for all the constituents that we use. This affects only a handful of days over the thirteen years we consider. 3 Available at http://fossilfreeindexes.com/research/the-carbon-underground/ -9- Results 3 Results 3.1 Raw returns and correlation between returns In the following table we give the average returns for our four “assets” and compare them with the total returns for the FTSE All Share as a whole and for the restricted portfolio made up of the FTSE All Share excluding the “Fossil fuels” sector. Table 3.1: Returns, standard deviation and betas (January 2002-April 2015) Arithmetic Average Daily Returns (%) Standard Deviation (“risk”) Beta Services 0.030 1.19 0.94 ICT 0.036 1.54 0.96 Fossil fuels 0.047 1.73 1.23 Other 0.021 1.24 0.71 FTSE All Share 0.035 1.22 1.00 FTSE All Share net of fossil fuels 0.029 1.15 0.91 Sector / “Asset” The daily returns figures are calculated as the arithmetic average of the returns each day. In other words, we take the percentage returns for each of the 252 trading days each year, add them all up and divide by 252.4 We can see that, in general, higher average daily returns are associated with higher standard deviations of returns (i.e. higher risk). So, for example, ICT has a higher average return than Services (0.036 per cent versus 0.03 per cent) but that comes at the price of a higher standard deviation (1.54 versus 1.19). However, that is not universally so. The Services sector asset has both a higher average daily return and a lower standard deviation than the Other sector asset. It might appear that this would mean that a smart investor would never put anything into the Other sector asset — after all, monies invested in the Services sector, instead, produce a higher expected return at lower risk. And if investors were forced to choose to invest in only one of these assets, then indeed no investor would choose to invest in Other instead of Services. But in a diversified portfolio in which investors can use weighted combinations of assets, that is not correct, and it useful to understand why. The reason is that although the Other asset has greater variance in returns than the Services sector asset, the variation in returns for those two sectors are not perfectly correlated. So sometimes when the Services sector has a very poor return, the Other sector has a fairly average return or perhaps even an above-average return. We can use the data on returns to identify the extent to which returns on the 4 The equivalent annual figures would be produced by taking the annual percentage returns for each year from 2002 to 2014 and dividing by 13. It should be emphasized that because these are arithmetic averages, the daily averages should not be expected to compound up to produce the annual average (in other words, it is not the case that the annual average is equal (or even approximately equal) to (1 + (daily average))252 – 1). - 10 - Results different assets co-vary, which means that it can be useful to include some weight in the portfolio for the Other asset even though it is, on average and considered in isolation, higher risk and lower return than the Services asset. The final column is termed “beta”. This is a measure of the extent to which variations in returns on our various assets are correlated with variations in the returns of the market as a whole. When the beta is 1, returns are perfectly correlated with those of the market as a whole. (We see in the table that the beta of the FSTE All Share is 1 — the FTSA All Share is perfectly correlated with itself.) When the beta is greater than 1, then variation in returns on an asset are an amplified version of variations in returns on the market as a whole (i.e. if the market goes up or down by X per cent, that asset will tend to go up or down by more than X per cent). When the beta is less than 1, variation in returns on an asset are a dampened version of variations in returns on the market as a whole (i.e. if the market goes up or down by X per cent, that asset will tend to go up or down by less than X per cent). It is of interest to note that the Other sector asset has a beta that is notably lower than the beta of the Services sector (0.71 versus 0.94). This demonstrates that although the standard deviation of the Other sector is higher than that of the Services sector, the variation in its returns is less well correlated with or a dampened version of the variation in returns of the services sector, which means there is an advantage in investing in it as part of an overall diversified portfolio. Another thing we can use the beta for is to consider how correlated returns are between the unrestricted portfolio (the full FTSE All Share portfolio) and a portfolio that excludes Fossil Fuels. We can see that the restricted portfolio has a beta notably lower than 1 (specifically, 0.91). That means that by excluding Fossil Fuels, an investor would not, by purchasing all other assets, be participating in the same balance of risk and return that is available through the overall FTSE. Since the FTSE All Share is, ex hypothesi, fully diversified, an asset that is less than perfectly correlated with the FTSE All Share is not fully diversified. 3.2 Measuring the cost of restricted diversification We have calculated the efficient portfolio frontiers for two separate portfolios: • • A fully diversified portfolio consisting of the four broad sectors: Services, ICT, Fossil Fuels, and Other Sectors. Any portfolio defined in this way makes use of all the assets composing the FTSE All Share. A portfolio consisting of Services, ICT, Fossil Fuels, and Other Sectors, and which therefore excludes all the fossil fuel assets that the fossil fuel disinvestment campaign seeks to exclude. The efficient frontiers for these two portfolios are reported in the chart below. - 11 - Results Figure 3.1: Efficient Portfolio Frontier Analysis 0.0500 0.0450 Actual stock market Daily Returns 0.0400 0.0350 0.0300 0.0250 0.0200 0.0150 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 Standard Deviation (Volatility, Risk) FTSE All Share (Unresrticted Portfolio) FTSE All Share Excluding Fossil Fuels (Restricted Portfolio) The purple line here is, once again, the set of different risks and returns that could be obtained by investing different proportions in the (four) different available assets (called, in the finance jargon “applying different portfolio weights”). Each dot is associated with a different set of portfolio weights. The portfolio weights and returns we have analysed arise from a model of possibilities, even in the case of the unrestricted portfolio. We can get a sense of how close to or far from reality our model is by considering how close to our ideal efficient portfolio frontier is to the actual stock market as a whole. We do with the large purple dot, which as can be seen is very close indeed to our idealised efficient frontier — close enough in fact that the difference is much more likely to arise from slight measurement differences between the time periods in our model and the fact that real investors can rebalance their portfolios by making new investments every day or even every second. The pink line is, once again, the available risks and returns from different portfolio choices in the restricted portfolio that excludes fossil fuels. We can see that, as we have defined and constructed our portfolios, the portfolio restriction has an impact on all but only efficient portfolio choices — the available inefficient portfolio choices below the minimum variance portfolio are the same for the restricted and unrestricted portfolios. This is a slight difference from the simpler stylised case presented earlier, but in respect of the efficient portfolio choices (which are in any event the only ones that rational investors would choose amongst) the message is exactly as in our stylised case. The restriction to investment choice created by excluding fossil fuels means that amongst the efficient portfolio choices the available risk-return trade-off is worse — to obtain any level of return available in the unrestricted portfolio, an investor in the restricted portfolio that excludes fossil fuels would have to take greater risks. We can quantify the cost that this has to investors by considering how much lower the returns would be to an investor that took the same risk as was taken by an investor in the unrestricted market as a whole. We can see in the diagram that the large purple dot comes with a standard deviation of 1.22. In our model, - 12 - Results on the efficient portfolio frontier (on the purple line) a standard deviation of 1.22 secures average daily returns of 0.034 per cent. Vertically below that (i.e. at the same standard deviation but on the pink line), we can see that the return for the restricted portfolio that excludes fossil fuels is 0.032 per cent per day. This daily average difference compounds over a year to equate to a reduction in annual returns of 0.68 per cent (68 bps). Another way to consider the cost is to consider how much extra risk an investor in the restricted portfolio would have had to take in order to secure the same return. We can see that the market portfolio (again, the large purple dot) has daily returns of 0.0352 per cent. On the efficient frontier in our model for the unrestricted portfolio, 0.0352 per cent daily returns are associated with a standard deviation of 1.24 for the portfolio as a whole. To secure that same return from the portfolio that excludes fossil fuels, investors would have had to bear a standard deviation of 1.51. In other words, they would have had to have taken more than 20 per cent more risk in order to secure the same return. So to spell the point out, investors following the recommendation of the fossil fuel divestment campaign to exclude fossil fuels would, from 2002 to mid-2015, have sacrificed the equivalent of an annual return of 0.68 percentage points (68 bps) or, if they did not want to accept lower returns, would have had to take more than 20 per cent extra risk on their investments. - 13 - Appendix Appendix This section sets out the mathematical derivation of the efficient portfolio frontier using Markowitz’s optimal portfolio allocation methodology. Let there be a set of investable risky assets, where each asset is indicated by = 1, … , . The expected return and variance of each asset are indicated respectively by $ and % . The expected return of a portfolio composed of the assets is simply the weighted average of the assets within the portfolio, i.e.: $ & & = ' $ = where ' is the weight of asset within the portfolio, and the variance of the portfolio is: ( ' ') % ) ) where % is the variance of asset , i.e. % = (* asset +, i.e. % ) = ,-* . , ) / = ,-* . ) , /. = % , and % ) is the covariance between asset and We assume here that ' ≥ 0 for any , and ∑ ' = 1. The positivity constraint on the assets’ weights implies that the portfolio considered is a long-only portfolio (i.e. we do not account for the possibility of short-selling any asset). The goal of Markowitz’s optimal portfolio allocation problem consists in finding portfolio weights that minimise the overall portfolio variance, whilst guaranteeing that the portfolio’s return equal a target return ∗ . Formally this implies solving the following constraint minimisation problem: min . .: ∗ 8 9 ∑< ;=> :; :> ?@ … :< ?@ ( & The efficient portfolio frontier can be determined by solving the above minimisation problem iteratively for a number of different target return levels, and by then plotting each target return against the variance of the corresponding optimal portfolio. - 14 -