Size, Liquidity and Concentration in the South African Equity Market and its effect on the Business of Investment Management

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Size, Liquidity and Concentration in the South African Equity Market and
its effect on the Business of Investment Management


Heidi Raubenheimer

University of Stellenbosch Business School

University of Stellenbosch Business School

P O Box 610, Bellville
7535, South Africa


Telephone: +27 83

708 1457

Email: heidiraub@telkomsa.net


Supervisor, Prof Eon Smit

evdms@usb.sun.ac.za


19
th

EDAMBA Summer Academy


Soreze, France


July 2010



Abstr
act

South Africa’s Equity market provides a large (in terms of volume) but concentrated
investment environment.
South African

pension funds are restricted from diversifying
globally and are thus faced with a restricted set of
concentrated
investment oppo
rtunities.
They are also typically restricted to long
-
only investment.
This
thesis aims to

describe and
quantif
y

the
implications of these conditions on equity portfolio construction, fund objectives
and mandates as well as ex
-
post performance monitori
ng.


Key words
: Portfolio construction, Fundamental Law of Active Management, Transfer
Coefficient, short
-
extension, Concentration, Optimisation, Active Risk, Cross
-
sectional
Variation



Introduction

The Johannesburg Stock Exchange (JSE), over 120 y
ears old
1
, is by far the largest of only 18
African stock markets
2

and ranks 18
th

in capitalisation among the world’s stock exchanges at
790 billion US Dollars
3
. Although South Africa’s equity exchange is one of the largest
among emerging markets, the JS
E represents a highly concentrated equity offering. The
FTSE/JSE All Share Index (J203) is an index of approximately165 companies’ shares and
represents 99% of the total market capitalisation of all tradeable
4

ordinary shares in South
African companies l
isted on the main board of the JSE
5
.
Figure
1

illustrates the
concentration
6

of the JSE by depicting the contribution of various shares and groups of shares
to the total value of the index.


Figure
1
: The Distribution of (Market Capitalisation) Weights on the FTSE/JSE All Share Index

BIL, 13.9%
AGL, 7.6%
SOL, 6.7%
SAB, 6.5%
MTN, 6.4%
Next 5 shares, 17%
Next 10 shares, 15%
Next 20 shares, 13%
Remaining 125 shares,
14%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% of Total Market Capitalisation Represented by the J203 Index




1

Founded in 1887

2

JSE Equity market profile
, 1
st

September 2009 [online]
http://www.jse.co.za/equity_market.jsp?sindex=31

3

Calculated
by the World Federation of Exchanges as at end of August 2009.

4

Only “free
-
float” shares are included in this index.

5

Ground Rules for the Management of the FTSE/JSE Africa Index Series
, July 2009,

version 1.8.

6

As at end of February 2009


It is well documented that the concentration of an index or benchmark can materially
constrain investment decisions and the portfolio construction proc
esses, particularly when
each investment is constrained to be held long. Furthermore, South African investors, who
are restricted by exchange controls from unconstrained global diversification, have little
reprieve from their concentrated investment uni
verse. Currently the pension fund regulations
in South Africa allow for a maximum foreign investment (across all asset classes) of 20%. It
is not uncommon for countries to restrict their pension funds’ investments to domestic
markets in this way. The

Russian Federation has recently doubled their pension funds’
foreign investment allowance from 10% to 20% from 2010 onwards; Brazil and Mexico both
allow a maximum of 20% in foreign investment; Switzerland’s pension funds and Korea’s
defined contribution
funds allow a maximum of 30% foreign investment and Columbia allows
40%
7
. For this reason, a study of the implications of equity market concentration on fund
management opportunities is particularly important in domains where geographical
diversification

is restricted and domestic markets are concentrated.


Literature Review


(Grinold, 1994) responded to criticisms of portfolio optimisation procedures as “alpha
eaters
8
”: that good excess return forecasts are distorted by portfolio optimisation procedu
res
and the resulting portfolios consequently generate less of the profit (“alpha”) which they
ought to. In developing the “Fundamental Law of Active Management”, (Grinold, 1994)
shows that, if forecasts are treated as a product of residual volatility (w
hich is assumed to be
independent across shares) times skill (as measured by the information coefficient) times a
standardised score, the resulting optimised portfolios will not exhibit the same bias toward
low residual shares. (Grinold, 1994) does not m
ention the alpha “eating” effect of constraints
on portfolios (and optimisers) but offers practical advice on how to turn a stock tip, a buy/sell
list or a series of multiple forecasts into an alpha that “won’t get eaten”.





7

Survey of In
vestment Regulation of Pension Funds
,
October 2009,
Organisation for Economic Co
-
Operation
and Development [online]
http://www.oecd.org/dataoecd/30/6/43939773.pdf


8

In other words, consumers/was
ters of potential excess return.

(Clarke, De Silva and Thorley
, 2002) and (Clarke, De Silva and Sapra, 2008) continued this
work by developing the “Generalised Fundamental Law of Active Management” and
introducing the concept of a transfer coefficient. The authors illustrate the loss of excess
risk
-
adjusted perfor
mance that can result from portfolio constraints, particularly the long
-
only
constraint. They use the transfer coefficient to quantify the extent of this loss. A transfer
coefficient of one implies that there is no “friction” between the manager’s inve
stment view
or forecast returns and the construction of the investment portfolio. A transfer coefficient
less than one implies a loss of information between the manager’s investment view and the
construction of the investment portfolio based on this view
. The authors have pioneered the
use of short
-
extension products which allow for modest short positions and have been shown


Research Problem(s) and Aim(s)


All the research questions set out below follow from the concentration of the South African
equi
ty market and South African pension funds’ constrained investment in this market. The
findings of this study will be easily replicable in countries with similar domestically
-
constrained investment requirements.

Research Question 1: Improving efficiency i
n net long investments with short extension

a)

How great is the loss of efficiency resulting from long only investing in South Africa’s
concentrated equity market?

b)

To what extent does short extension improve on this efficiency and what would the
optimal level

of leverage be?

Research Question 2: Determining the relative value of the “big 5” stocks to the remaining investment
universe.

a)

How large should the allowable short positions be in a prudent South African Equity
Investment mandate?

b)

To what extent do the

investment views on large stocks determine the position taken
in the remaining investment universe?

c)

Can stock selection skill in smaller stocks add significant value to a long
-
only
portfolio in South Africa? By implication, should pension fund managers
be paying
for company research beyond the biggest stocks in the investment universe.

Methodology


Fundamental Law


The starting point of the analysis is to recognise the Fundamental Law of Active Management
(refer Grinold (1994)) which describes the perfor
mance generation process in an active
(benchmark
-
relative) framework (refer
Equation
1
). The Fundamental Law asserts that
active, risk
-
adjusted performance is a function of forecasting skill and the breadth of this skill
(i.e. t
he number of forecasts made and exercised). This original formulation applies under
the assumption that there are no constraints on the weights of the portfolio.


Equation
1
: The Fundamental Law of Active Management



N
IC
R
E
IR
a
a












Where


IR is the information ratio or the expected excess
-
of
-
benchmark performance,


a
R
E
,
divided by the portfolio’s expected active risk,
a

,

IC is the information coefficient, a measure of manager s
kill using the correlation
between their forecasted returns and the subsequent (realised) returns

N is the breadth or number of active bets taken


The success of the fund manager can be measured by their information ratio. However, their
success may be u
ndermined by constraints binding their implementation of their investment
view. Under what Clarke et al (2002) refer to as the Generalised Law of Active
Management, the effect of the constraints imposed on the weights of a portfolio are quantified
in the

form of the transfer coefficient (TC) and incorporated into the components of
information ratio.


Equation
2
: The Generalised Law of Active Management

1
TC
0
and
TC
N
IC
IR







Where

TC is the transfer coefficient, a measure of
implementation efficiency using the
correlation between the active weights in the portfolio and the forecasted, risk
-
adjusted active returns.


The Fundamental Law (
Equation
1
) assumes no constraints on the weights in a portfolio (
i.e.
Equation
1

and
Equation
2

are identical when the TC is equal to 1).


Optimisation


The portfolio optimisation problem in a benchmark relative framework is to maximise the
forecasted active return of
the portfolio,

p
, while achieving a particular active risk target and
ensuring that the portfolio is self
-
funding.


Equation
3
: Portfolio Optimisation













0
2
1
w
w
w
w
a
a
a
a
a
a
to
subject
R
E
Maximise

α

Where


a
w
is an n x 1 vector of active

bets i.e. portfolio weights in excess of the benchmark’s
weights which must add to zero in order for the portfolio to be self
-
financing,

α

is an n x 1 vector of forecasted active returns i.e. forecasted returns in excess of
benchmark,

Σ

is an n x n covariance matrix of returns in excess of the benchmark and,

1

is an n x 1 vector of ones.


There is a unique solution to the unconstrained
9

optimisation in
Equation
3

which is a
function of the target active risk:


Equation
4
: Unconstrained optimal active weights




9

Although there is clearly a self
-
financing constraint imposed on this optimisation problem, it is generally
referred to as an “unconstrained” optimisation on account of there being no constraints placed on individual
weig
hts in the portfolio.

α
Σ
α
α
Σ
1
1
A
a





w

where

A


is the target active risk of the portfolio.

Equation
4

shows that the

size and sign of the active weight of any particular stock is directly
related to the size and sign of the forecasted active return. The target active risk magnifies the
extent of this bet or active weight and the residual risk has the opposite effect.

Thus a
positive forecast would lead a rational, unconstrained investor to a positive active position in
that same stock and the greater the aggression (i.e. the lower the risk
-
aversion) of this same
investor, the greater the active positions in their port
folio. The extent of this active position
is reduced by the uncertainty of the forecast i.e. the residual risk. This Equation also
indicates that the cross
-
sectional (across stocks) correlation between active positions and risk
adjusted active return f
orecasts will be one under this unconstrained condition i.e. TC = 1.

Analysis envisaged to address the research questions


In order to address the research questions, we begin by simulating random normal investment
views on the stock universe. These view
s form the input of the optimisation procedure and,
for a continuum of target active risk levels and a continuum of allowable total maximum short
positions, the resulting portfolios will be analysed. In particular:

a)

These portfolios will be compared to th
eir corresponding unconstrained optimised
portfolios to calculate the loss of efficiency (TC <1) as a consequence of the
constrained allowable short positions and the improvement in efficiency as a result of
the short extension.

b)

The simulated investment vi
ews will then be split between those which have a positive
investment view on the largest stocks and those which have a negative investment
view on the largest stocks. The comparison of the holdings of these two groups of
portfolios will highlight the in
vestment implications for the rest of the investment
universe of the investment view of large stocks.

c)

Finally, the “skill” of the investment views (IC) will be allowed to vary between the
largest stocks and the remaining. This will allow for us to observ
e whether an
increasing IC in smaller stocks adds significant value to the resulting portfolio
performance. By implication, it will allow us to place a value on the benefit of
employing analysts/research to cover smaller stocks in a long
-
only South Afric
an
investment house.

Conclusions thus far…


Active fund managers can only express their views in an environment where their conviction
and level of risk taking is commensurate with their constraints. The higher the allowable
active bet sizes, the less co
mpetitive a long
-
only fund manager can be alongside hedge funds
and similarly constrained long
-
short managers. This competitive disadvantage is exacerbated
by a concentrated benchmark/investment environment such as the JSE indices where only a
few of the

shares comprise most of the total investment weight.


The more constrained the investment environment, both with regard to mandated constraints
and the concentration of South Africa’s equity market, the less consistently asset managers
are able to imp
lement their views and the less symmetry there is in their range of potential
responses to forecasted excess return. Short sale restrictions, in particular, are intended to
avoid incurring a liability on the portfolio’s behalf. However, the impact of s
hort sale
restrictions combined with mandated constraints on active weights in a concentrated market
serve, not to limit risk levels, but to artificially concentrate the level of active investment
activity in a handful of listed companies.


The disadvan
tage to active management within more aggressive active weight allowances,
speaks to the success of low active risk, enhanced
-
index type strategies in the South African
market. In a long
-
only, concentrated environment, low risk active strategies provide
investors with the best “bang for their buck” because long
-
only fund managers have the
opportunity to act more fully on their active views across the full cross
-
section of available
equities at these low active weight limits. By contrast, to compel or en
courage long
-
only
managers into a more aggressive active space in a concentrated investment environment is,
ironically, only to constrain them further in their abilities to express their best active view.



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