Download Costs to Investors of Boycotting Fossil Fuels

Costs to Investors of
Boycotting Fossil Fuels
July 2015
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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
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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.
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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;
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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)
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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.
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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.
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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.
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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
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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
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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/
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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).
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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.
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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,
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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.
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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.
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