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Abstract: This paper explores the potential to use the Beta to judge the risk of including properties ... average of the Betas of each sector, it is simple to calculate portfolio Betas and portfolio ...

International Real Estate Society Conference ‘99
Cosponsors: Pacific Rim Real Estate Society (PRRES)
Asian Real Estate Society (AsRES)
Kuala Lumpur, 2630 January 1999
USES FOR BETAS IN PROPERTY PORTFOLIO
CONSTRUCTION
PATRICK ROWLAND
Department of Property Studies, Curtin University of Technology,
Perth, Western Australia.
Telephone: (08) 92667723, Fax: (08) 92663026, Email: [email protected]
Keywords: Property portfolio optimisation, sector weightings, Beta.
IRES conference, 1999  Rowland Use of Betas in property portfolio construction
Abstract
Some fund managers use portfolio optimisation models to help them decide how much
to allocate to each sector of the property market (with sectors defined typically by use
and region). The models use past average periodic performance of each sector to search
for combinations of the sectors that have offered the highest rate of return for a given
amount of risk in the portfolio. The risk is measured by the weighted standard deviation
of returns of each sector and their correlation coefficients. Usually, the average
performance is based upon property indices and these models are relevant only for those
funds which hold diversified property portfolios.
This paper explores the potential to use the Beta to judge the risk of including properties
from one sector within a property portfolio. Because the Beta measures how volatile a
sector has been, compared with the market average, it is appropriate as a measure of
risk for diversified property funds. Because the Beta for the whole fund is the weighted
average of the Betas of each sector, it is simple to calculate portfolio Betas and portfolio
returns with different weightings to each property sector.
The paper compares the bases, critical assumptions and interpretations of the Markowitz
and Sharpe approaches to portfolio optimisation and their suitability for guiding
allocations to the major sectors of the property investment market. The restrictive
assumptions of both models, their applications to real estate and their legitimacy in
determining property sector weightings are considered.
The paper reports the results of tests applying both approaches to periodic returns for
Australian property sectors. The tests demonstrate that the two approaches suggest
similar sector weightings for given degrees of risk aversion, although some differences
are evident at low levels of risk. The tests show that both approaches tend to reduce
portfolio construction to choices between the two most favoured sectors (unless
constraints are placed on the sector weightings). Further analysis of past returns
indicates that Betas appear to be slightly more stable over time than standard deviations
and correlation coefficients between the sectors.
The paper concludes that, despite some theoretical objections to applying the capital
asset pricing model to portfolio decisions, the Beta is a measure that can help in
adjusting sector weightings for property portfolios.
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
Uses for Betas in property portfolio construction
Patrick Rowland, Department of Property Studies, Curtin University of
Technology, Perth, Western Australia.
Part 1: Introduction
Investors and fund managers are aware of the need for diversification and must gauge
which combinations of investments will lower risk most effectively. In building a
portfolio of incomeproducing properties, they must decide how much prominence to
give to different categories of properties, often segmented by the type of buildings, their
uses and by their locations. Modern portfolio theory offers measures of diversification
and risk which are one (but rarely the sole) input to portfolio restructuring.
Past periodic returns of groups of properties enable objective calculations of
diversification and are used on the assumption that the past covariances (or correlation
coefficients) are a guide to their likely diversity in future. The most common method is
meanvariance optimisation, which builds the covariance into a measure of portfolio
risk. This paper considers the alternative of using Betas, similarly calculated from
periodic returns from samples of properties, as a guide to the kinds of properties that
can be combined to lower portfolio risk.
In Part 2 of this paper, meanvariance optimisation of different categories of property
(or property “sectors”) is contrasted with Betas as an alternative definition of risk for a
fund. The Beta compares the volatility of each sector with an index of the performance
of the whole market. The Beta is the usual measure of risk in single index models and
its relevance in gauging the benefits of diversification and portfolio risk is explored.
Part 3 describes the mathematical relationship, first, between sector covariances and the
Betas of those sectors and, secondly, between portfolio standard deviations and
portfolio Betas. From this, it is clear why portfolio variances may indicate different
optimal combinations of sectors to those suggested by the sector Betas. Also, this
illustrates why sector covariances and portfolio variances cannot be interpreted in the
same way as portfolio Betas.
Part 4 calculates these statistics for the main nonresidential property sectors using data
from the Property Council of Australia Investment Performance Index. These are used
to test how portfolios constructed for optimal means and variances might differ from
those based upon sector Betas.
The fifth and final part of the paper draws conclusions about the viability, advantages
and disadvantages of using sector Betas to guide investors and fund managers in the
construction of property portfolios. The paper does not try to suggest that either method
of portfolio construction is wrong but shows that Betas can be of practical help to
investors and fund managers when they are deciding upon sector diversification.
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
Part 2: Constructing efficient property portfolios
The usual objective of portfolio management is either to maximise the expected return
from the portfolio for a given level of risk or to minimise risk at a target rate of return).
Typically, past returns are used as guides to future performance.1 The portfolio return is
the valueweighted average of the rates of return of each investment in the portfolio.
Risk, as seen in the volatility of the periodic returns from the portfolio, can be measured
by the standard deviation of returns. The portfolio standard deviation is the weighted
average of the standard deviations of each investment, reduced by their lack of
correlation. Portfolios are efficient if no other combinations of properties earned a
higher rate of return with no higher standard deviation.
In practice, this approach is difficult to apply to the effect on a portfolio of acquiring a
single property as historic details of the property are often not available or may be
heavily influenced by unusual events in the recent history of the property. It is more
reliable when measuring averages from groups of similar properties (Brown, 1991: 172)
but it is unclear whether these retrospective diversification gains are statistically
significant (Rubens et al., 1998: 78). Meanvariance optimisation may be helpful in
selecting the preferred property sector for further acquisitions or disposals although it is
unlikely to be conclusive ever.
Although not all funds have a clear “topdown” strategy, most operate under some
approximate guidelines for the valueweighting of different property sectors within their
portfolios (Rowland, 1997: 283). They are likely to check the past returns, volatility and
covariances of their own properties in different categories to judge what would have
been efficient property portfolios. They may refer to the returns, volatility and
covariances of a larger sample of properties, such as those in a property index and its
indices of sectors and subsectors.2
The traditional methods of diversifying real estate portfolios are by property use (such
as office, retail, industrial and leisure properties) and by location. There have been
many studies of the covariances (standardised to the correlation coefficients) of periodic
returns between properties in different uses and in different locations. The general
conclusions have been that there have been strong benefits from diversifying property
portfolios by the use of the buildings. Most studies have shown the benefits of
diversifying by region within one country have been less but still significant, even if the
regions are defined in terms of their economic base (Eichholtz et al., 1995: 45; Hartzell
et al., 1993: 8; Mueller, 1993: 65).
Many of these studies have then adopted the meanvariance framework to gauge
weightings for each property sector that would have resulted in efficient portfolios at
different levels of risk.3 The conclusions as to which sectors should be held by investors
are expressed as an efficient frontier of target returns and levels of risk. The results of
1
It is doubtful whether past property returns are truly comparable with the measures for other
investment classes, largely because property returns are based upon infrequent valuations (the
issues are summarised in Rowland, 1997: 282). As this paper concentrates solely on
comparisons amongst different property sectors, this is largely irrelevant.
2
In a US survey of pension fund managers, 37 per cent used correlation coefficients between
asset classes when determining real estate asset allocation and 24 per cent used modern portfolio
theory (Worzala and Bajtelsmit, 1997 :51).
3
Lee and Byrne (1998: 38) measure risk as the mean absolute deviation and obtain similar
results to conventional meanvariance optimisation.
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
the studies have favoured different sectors, dependent on the country, the time period
and how the sectors are defined. A dramatic difference between the favoured weightings
in the 1980s and in the 1990s can be observed, as well as a tendency to construct
portfolios with heavy or exclusive emphasis on one or two categories of property that
have performed above average.
The alternative to selecting efficient portfolios by their means and variances is to
consider the means and portfolio Betas. The Beta is a measure of risk derived from the
capital asset pricing model, which ignores those uncertainties which will be diversified
away by holding a large portfolio of investments. The Beta is the remaining or
systematic risk, expressed as a ratio of the average market volatility.
When considering sector weightings in a property portfolio, it is the systematic risk
which is of concern to those investors whose portfolios include enough properties from
each sector to cancel out most, if not all, of the “sectorspecific” risk. There would be
dangers in relying upon Betas to weight subsectors of a property fund which invested
in only one sector. For example, a property trust specialising in shopping centres is
exposed to risks that the retail sector might underperform the composite property index
from which the Beta had been calculated.
However, it is also true that investors cannot rely on sector correlations calculated from
large samples of properties if their own properties in each sector are not sufficiently
diverse to approximate the return from the sample which has been compiled into the
sector index. Recent research has noted that a property portfolio must be large and
varied to be reasonably diverse and to track an index (Brown, 1997: 133; Brown and
Matysiak, 1995: 34; Schuck and Brown, 1997: 173).
Part 3: The mathematical basis of these two portfolio models
Because these two models of portfolio risk are deceptively similar, it is helpful to
contrast their mathematical formulations. This clarifies some of the potential uses and
misuses of sector Betas. First, the interpretation of and relationships between sector
variances, covariances, correlation coefficients and Betas are described. Then, portfolio
Betas are compared with portfolio variances as measures to optimise sector weightings,
in particular when adding a property or properties of one sector to a portfolio.
The covariance of the periodic returns from two sectors measures how closely one
varies about its mean in comparison with the other. The covariance is the first building
block of portfolio theory and can be found as:
C O V ij = ρ ij σ i σ j
where C O V is the covariance between the periodic returns of sector i and sector j;
ij
ρ ij is the correlation coefficient between the periodic returns of sector i and
sector j;
σ i is the standard deviation of the periodic returns of sector i;
σ j
is the standard deviation of the periodic returns of sector j.
Although the covariance incorporates both a measure of correlation and the standard
deviation of each sector, it is not a standardised measure, making it impossible to
compare covariances between different sectors. The correlation coefficient is
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
standardised (between 1 and 1) but does not include a guide to the volatility of either of
the sectors. Using the Markovitz model, the correlation coefficients cannot be used to
judge which type of properties should be aggregated in a portfolio without knowing
how volatile each sector has been.
The Beta is a measure of both correlation and relative volatilities. The Beta is normally
formulated as:
C O V im
βi =
σ 2
m
where βi is the Beta of asset or sector i;
COVim is the covariance between the periodic returns of sector i and the
market average or index (m); and
σ 2 is the variance of the periodic returns of the market average or index.
m
As COVim = ρ im σ i σ m , the Beta can be expressed as:
σi
β i = ρ im
σm
where ρ im is the correlation coefficient between the periodic returns of sector i and
of the market average or index (m).
And it is now evident that, first, the Beta only measures that portion of the relative
volatility of the sector that can be explained by changes in the periodic returns in the
market ( ρ im ); and, secondly, Beta is a measure of the relative volatility of the sector
and the market (σ i / σ m). As such, Betas are a convenient guide to the effects on
portfolio risk of each sector, provided that the portfolio is reasonably diversified across
all aspects of the market.4
If the capital asset pricing model provides a reasonable (linear) fit of sector returns to
Betas, the relationship between sector covariances to sector Betas is as follows:
CO Vij = β i β j σ 2
m
where β j
is the Beta of asset or sector j.
This can be derived from the expectations operator (Benninga, 1997: 90; Brown, 1991:
47). If there are many sectors, this may provide a quick way of estimating the variance
and covariance matrix (provided that the Betas are reasonable predictors of return, but it
is probably unnecessary when considering covariances between a small number of
sectors). The formulation is shown here to indicate the relationship between the two
4
It follows that, if the investor or fund is specialised, the Beta should be calculated using a sub
set of specialised properties to construct the index.
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
indicators of portfolio diversification. From this equation, the correlation coefficient
between sectors i and j can be found as:5
ρ ij = ρ im ρ jm
In Part 4 below, the accuracy of calculating sector correlation coefficients in this way is
tested on Australian data.
Turning to portfolio construction, both the portfolio standard deviation and the portfolio
Beta indicate risk (to be evaluated together with the portfolio return in the search for an
efficient portfolio). The following formulae can be found in many financial and
portfolio management texts but are printed below to show the contrasts.
The portfolio standard deviation requires the calculation of a matrix of all the possible
covariances beween each sector as well as the variances of each sector, as follows.
s s
σ p = ∑ ∑ w i w k C O V ij
i = 1k = 1
where σ is standard deviation of the portfolio;
p
wi and wk are the percentages by value of each of the sectors 1 to s.
Although this is not complicated when the number of sectors is small, it is difficult for
an investor to tell at a glance how changing sector weightings will influence risk.
The Beta of a portfolio is the valueweighted average of the sector Betas and hence it is
reasonably easy to anticipate the effects of changing weightings.
s
β p = ∑ wi β i
i=1
where β p is the Beta of the portfolio;
wi is the percentage by value of each of the sectors 1 to s; and
βi is the Beta of sector i.
To illustrate, the following formulae show the effect of adding a property or properties
of sector i to an existing portfolio j. Using the Markovitz model, the standard deviation
of the new portfolio p is found as on the following page and it is far from obvious what
the effect of the change to the portfolio risk will be.
C O V ij = β i β j σ β i β j σ 2 . Substituting σi
5 2 is the same as
m ρ =
m β = ρ im
ij
σ iσ j
i
σm
σ j
and β = ρ and simplifying this gives ρ
j jm
σm ij = ρ im ρ jm
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
σ p = wi2σ i2 + (1 − wi ) 2 σ 2 + 2 ρ ij wi (1 − wi )σ iσ
j j
where σ p
is the standard deviation of the new portfolio p;
σis the standard deviation of sector i from which the additional properties
i
come;
σ j is the standard deviation of the existing portfolio j; and
wi is the percentage by value of the new portfolio that comprises the
additional properties in sector i.
The Beta of the new portfolio is found as:
β p = wi β i + (1 − wi )β j
where β p
is the Beta of the new portfolio p; and
β j is the Beta of the existing portfolio j.
The change in the portfolio Beta is wi ( β i − β j ) and the effects of adding properties
from one (or more) sector to the portfolio are evident.
Advantages of using sector Betas to gauge portfolio risk (rather than the portfolio
standard deviation) are the simplicity of calculation and the ease of anticipating the
effects of changing sector weightings. Betas may be valid when one or more of the
assumptions of meanvariance analysis are breached (Lee and Byrne, 1998: 39).
However, it must not be overlooked that portfolio Betas would understate risk for funds
which do not have a reasonable spread of investments across all sectors of the index.
Using Betas for comparison of sectors or subsectors, the index should have a similar
breadth as the fund.6
The Betas of sectors or subsectors of the property market compare the relative risks of
each sector. However, if much of the risk is specific to one sector, that sector will have
a low (or even negative) correlation with the market and little of the volatility of the
sector will show up in its Beta. In contrast, the high specific risk will increase the
portfolio standard deviation, even though the sector may have low or negative
correlations with most other sectors. This is the main reason why portfolio standard
deviations and Betas may suggest different sector weightings.
Part 4: Empirical tests of Betas for weighting property sectors
In this part of the paper, the periodic returns from the Property Council of Australia
Investment Performance Index are used to test whether sector and portfolio Betas give
meaningful guidelines for investors. It is assumed that the investor has a diversified
portfolio of properties and is seeking guidance as to which sector or sectors to expand
without taking unnecessary risk. This is the most likely occasion when portfolio models
might be used by investors or fund managers.
6
Single index models using a narrow index of one sector provide insights into subsector
weightings but but the results are not relevant to the concept of a broad “market portfolio” and
“market risk”, as envisaged by the capital asset pricing model (Van Horne, 1997: 74).
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
Table 1 presents the main characteristics of the Property Council of Australia
Investment Performance Index, as at June 1998, including the percentage by value of
the sectors and subsectors used in the tests (all the tables and graphs can be found at
the end of the paper). Table 2 displays annualised rates of return and a variety of
measures of risk, all based upon returns over each 6 month period between December
1984 and June 1998. It is evident that retail properties have considerably outperformed
the other three sectors. The retail sector showed higher annual returns, lower volatility
(as measured by both the standard deviation and the coefficient of variation) and also
the lowest correlation coefficients with other sectors.
The Beta has been calculated using the composite property index as the market average.
It follows that, because Beta is a combined measure of correlation and volatility, the
retail sector has the lowest sector Beta. With such clear dominance by one sector, it is
impractical to test whether Betas provide a suitable guide to portfolio construction. The
retail sector during this period dominated all the others and efficient portfolios would
contain retail properties only. The ranking of each sector by risk is the same by their
standard deviations and their Betas, being the reverse of the expected ranking by rates
of return. This inconsistency with modern portfolio theory (which assumes higher
returns will go to those who take more risk) undermines the confidence of investors
who might otherwise rely on past performance to guide future portfolio structure.
A further criticism of practical applications of portfolio theory is that the statistics are
often unstable over different eras. Whilst it might be anticipated that rates of return
would change with the state of the market, portfolio diversification relies upon lasting
patterns in volatility and covariance. If standard deviations and correlation coefficients
of sectors are unstable, meanvariance optimisation will suggest major portfolio
revisions regularly. This is not viable for property investments because of the
transaction costs. Any measures of performance which are less variable during different
states of the market instill more confidence in investors.
Tests of the relative stability of sector means, standard deviations, correlation
coefficients and Betas were carried out by adopting a rolling 10 year period for analysis.
Table 3 confirms that the Betas are less variable over these periods than the standard
deviations, correlation coefficients and covariances. The average coefficient of variation
of the changing Betas over time was 0.038, compared with 0.182 for the covariances.
The smaller variability may be because Betas are calculated from a composite index of
performance rather than from the relationships between individual sectors. Graphs 1 to
4 that returns, standard deviations and correlation coefficients have generally declined
in more recent ten year periods but curiously Betas have increased slightly.
A further test of the stability of these portfolio models over time is to compare the
effects of changing the portfolio weightings on the portfolio return, the portfolio
standard deviation and the portfolio Beta. Table 4 displays the results of substituting 10
per cent of a composite property portfolio with additional properties in each sector. In
each of the 10 year rolling periods, the change in return, standard deviation and Beta
might be different. The variation in those differences, as expressed as their standard
deviations is shown for each sector in Table 4. The absolute variation is shown and, on
the next row, this is expressed as a percentage of the sector average variation. The
percentage variation for the Betas (0.29%) is less than those of the standard deviations
(0.48%), again suggesting that the Beta provides a more stable portfolio measure.7
7
It is unlikely that any of these differences would be statistically significant.
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IRES conference, 1999  Rowland Use of Betas in property portfolio construction
In Part 3 above, it was shown how, if the return from each sector has a linear
relationship with its Beta, the correlation coefficient can be calculated from the sector
Betas or more simply,
ρ ij = ρ im ρ jm
The sector correlation coefficients calculated from this equation are displayed in Table
5 (with the coefficients calculated directly from the covariance of each sector in
brackets). Considerable differences are evident and it would seem that, for this data,
Betas are an unreliable way of deriving correlation coefficients for each sector. This is
not surprising given the overwhelming conclusion from tests of the capital asset pricing
model that either it is a poor predictor of returns or the market index is defined
incorrectly (Fama and French, 1992: 427; Roll, 1977: 129).
Because of the difficulties of using portfolio models with data that does not conform to
expected risk and return relationships, further analysis has been carried out on the sub
sectors of retail properties in the Property Council of Australia Investment Performance
Index. Subsector periodic returns are published for four states only but the composite
retail index does include a small number of properties from elsewhere.
The same statistics have been calculated for the subsectors as for the sectors in Table 2.
Past returns from the retail subsectors in Australia show a pattern of volatility and
average returns that is more typical. These are displayed in Table 6, together with the
matrix of correlations and covariances and the Betas of the subsectors. Betas were
calculated using the composite property index as the market average. Because the retail
sector has been considerably less volatile than the composite property index, all the
Betas are well below 1.
The standard deviations and Betas rank the subsectors differently. However, when the
subsector correlation coefficients are considered, the standard deviations are largely
consistent with the subsector Betas. One of the subsectors (Victoria) with a low Beta
has a high standard deviation, which can be explained by the low correlation
coefficients between Victoria and the other subsectors. The strong diversification
benefits of the Victorian retail subsector compensate for its low returns. Using either
meanvariance or meanBeta measures of performance, an investor looking for a low
risk retail region would select Victoria based upon its past returns.
Queensland retail properties would also be attractive based upon either their low
standard deviation or low Beta, despite their poorer diversification benefits. WA retail
properties appear suited only to less riskaverse investors. Based upon its riskadjusted
performance (using either its standard deviation or Beta), the NSW retail sector has
been the weakest subsector of the four.
The next comparisions of the statistics in this subsector involved constructing optimal
portfolios at different levels of risk using meanvariance and using meanBeta criteria.
Meanvariance optimisation (without short sales) was achieved using an Excel Solver
routine for the variance/covariance matrix, as described by Benninga (1997: 127). This
routine maximises Theta, being:
Rp − C
σp
where Rp is the portfolio average return;
Page 9
IRES conference, 1999  Rowland Use of Betas in property portfolio construction
σ p is the portfolio standard deviation; and
C is a constant, varied in successive calculations to achieve portfolios of
different levels of risk.
MeanBeta optimisation was achieved with a similar Excel Solver routine to minimise
Betas for given portfolio average returns. The shapes of the two efficient frontiers can
be compared in Graph 5. The efficient frontier found by meanvariance optimisation is a
gradual curve over a short range of returns. The frontier found by meanBeta
optimisation has two straight sections, reflecting the additive properties of sector Betas.
Nevertheless, the frontiers are not greatly different.
The portfolio weightings suggested as optimum at four different points on the two
frontiers are compared in Graph 6 (MV for the meanvariance frontier and B for the
Betafrontier). At the higher target returns (15.4 and 15.9 per cent per annum), there is
virtually no difference between the weightings, with heavy reliance on Western
Australian retail properties for risktolerant investors and more Queensland retail
properties for those who are more risk averse. At lower target returns (14.5 and 14.9 per
cent per annum), the frontier based on Betas introduces more Victorian properties than
the meanvariance frontier, which favours New South Wales properties. A Betafrontier
will never use sectors that are “inferior”, in the sense that they show a higher risk for
less return. This is because the portfolio Beta is a weighted average of the sector Betas.
A meanvariance frontier may introduce sectors that appear inferior in isolation but are
redeemed by their lack of correlation with the other sectors.
Meanvariance optimisation is often criticised because it suggests portfolios which rely
heavily or exclusively on one or two categories of property that have performed above
average. This is because the portfolio returns and standard deviations are determined
largely by the weightings in each sector, with the lack of correlation having limited
impact on the portfolio risk. These tests suggest that meanBeta optimisation has
exactly the same tendency. To overcome this shortcoming, users of portfolio models
impose constraints upon the sector weightings.
Meanvariance and Betafrontiers were compared using constraints on the retail
portfolio (NSW restricted to between 30 and 60 per cent of the value of the portfolio;
Victoria and Queensland between 20 and 40 per cent; and Western Australia between
10 and 30 per cent). The efficient frontiers with these constraints are displayed in Graph
7. The constraints lower and limit the range of returns on both frontiers but otherwise
their characteristics are similar to those with unconstrained weightings.
The portfolio weightings for the two frontiers are compared at four different levels of
return in Graph 8. At the highest target return (14.65 per cent per annum), there is
virtually no difference between the weightings, with heavy reliance on Western
Australian retail properties and the minimum for each other State. At the 14.5 per cent
per annum target return, Queensland properties replace some of the Western Australian
ones. are substituted for At lower target returns (14.0 and 14.25 per cent per annum),
the frontier based on Betas introduces more Victorian properties, whereas the mean
variance frontier increases the weighting of Queensland properties to the maximum
(with the minimum for each other State).
The Betafrontier (with and without constraints) favours Victorian retail properties at
lower levels of risk. The Victorian retail sector has a much lower correlation with the
property index than the other States (see Table 6). As noted above, this offsets the
Page 10
IRES conference, 1999  Rowland Use of Betas in property portfolio construction
effects of its high standard deviation, which is more important to the meanvariance
frontier.
These tests with Australian data suggest that the results from using the meanvariance
framework to establish property sector weightings are broadly similar to the results
based on the mean and Beta of portfolios. However, the differences are large enough to
warrant further investigation with different sets of data and some more practical trials of
how investors and fund managers would cope with different measures to help them
construct diversified portfolios. The data gives no support to the adoption of the capital
asset pricing model to determine required rates of return.
Part 5: Conclusions
Diversification within a real estate portfolio is a major consideration for most fund
managers when they are deciding what type of property or region should be the focus of
the search for further property acquisitions. In recent years, some fund managers have
used meanvariance optimisation models to help with these decisions.
There appear to be no theoretical reasons why they should not use a single index model
in place of sector correlations and portfolio standard deviations. The Beta is the best
known measure of volatility and correlation with a single index (although there may be
other formulations that are appropriate). Both variances and Betas measure related
aspects of risk but their derivations may lead to differing conclusions about appropriate
sector weightings.
Tests of Australian data confirm that broadly similar conclusions are drawn from mean
variance and Betafrontiers. Betas for sectors and subsectors are valid measures only if
the investor holds a sufficiently diversified portfolio to ignore sectorspecific risk.
However, investors can only rely on sector correlations calculated from large samples
of properties if their own properties in each sector are sufficiently diverse to
approximate the return from the sample compiled into the sector index. Recent research
has noted that a property portfolio must be large and varied to be reasonably diverse and
to track an index (Brown, 1997: 133; Brown and Matysiak, 1995: 34; Schuck and
Brown, 1997: 173).
Betas are easier to interpret and calculate and these tests suggest that they may be
slightly less variable over time than portfolio variances. Portfolio standard deviations
and portfolio Betas are superficially similar measures of risk but they do not serve the
same functions. The use of a single index model to evaluate property sectors and
weightings is worthy of further investigation.
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