2. 2
ACKNOWLEDGEMENTS
This thesis on Monte Carlo simulation and how it may be used within the Real Estate
industry primarily arises from a risk management perspective and its implementation in
investment markets. It was introduced to me in my postgraduate studies whilst undertaking
the unit ‘Investment Evaluation Techniques for Real Estate’. It was progressed on within
‘Corporate Property finance’. Both of these units were lectured by Mr. John Garimort.
I would like to acknowledge and thank Mr. John Garimort on his guidance and
discussions on the topic. For the reply of emails and the ‘short notice’ meetings to clarify
particular aspects in asset allocation and the initiation of simulation model building and
directing me on how to construct it.
I would like to express my gratitude to my thesis supervisor, Professor Nick Blismas
for providing direction in structuring the dissertation and taking the time to read and edit my
excessively long sentences! I’d also like to acknowledge the availability he made for myself
and all other students during a busy semester.
To RMIT University, particularly the School of Property, Construction and Project
Management, thank you for implementing a beneficial program and allowing myself and
other students to undertake research into our own interests.
Finally, to friends, family and fellow students that showed support, or listened to my
monotonous speaking on the topic, thank you.
3. 3
TABLE OF CONTENTS
ACKNOWLEDGEMENTS 2
LIST OF TABLES AND FIGURES 5
GLOSSARY OF TERMS 6
1. INTRODUCTION 8
1.1. RESEARCH PROBLEM 8
1.2. RESEARCH QUESTION 9
1.3. METHODOLOGY 9
1.4. STRUCTURE OF THE THESIS 10
2. LITERATURE REVIEW 12
3. RESEARCH DESIGN 16
3.1. INTRODUCTION 16
3.2. METHODOLOGY 16
3.2.1. DATA SOURCES 17
3.2.2. ECONOMIC PERIODS 18
3.2.3. ASSET ALLOCATION 20
3.2.4. SHARPE RATIO 20
3.2.5. MONTE CARLO SIMULATION 21
3.2.6. EFFICIENT FRONTIER 21
3.3. RESEARCH PROCEDURE 21
3.4. CONCLUSION 24
4. ANALYSIS OF DATA 25
4.1. INTRODUCTION 25
4.2. ANALYSIS OF DATA 25
4.2.1. PROPERTY RETURNS 25
4.2.2. GROWTH PERIOD 27
4.2.3. DECLINE PERIOD 30
4.2.4. STABLE PERIOD 34
4.3. SUMMARY, DISCUSSION AND MAIN FINDINGS 36
4. 4
5. CONCLUSION 39
5.1. INTRODUCTION 39
5.2. CONCLUSION ON RESEARCH QUESTIONS 39
5.3. CONCLUSION ABOUT RESEARCH PROBLEM 39
5.4. IMPLICATIONS TO PRACTICE 40
5.5. LIMITATIONS 40
5.6. FURTHER RESEARCH 41
6. BIBLIOGRAPHY 43
APPENDIX 1: 45
6. 6
GLOSSARY OF TERMS
Asset Allocation: An investment strategy that aims to balance risk and return through
adjusting an investment among different assets.
Deterministic Modeling: A statistical model where variables are determined by parameters in
the model and are based on initial conditions.
Diversification: Diversification is a risk management technique that mixes a specified amount
of asset classes within a portfolio.
Efficient Frontier: A set of optimal portfolios that offers the highest expected return for a
defined level of risk or the lowest risk for a given level of expected return.
Mean-Variance: The process of weighing risk (variance) against expected return.
Portfolio Risk: One standard deviation, or 68% of all probable outcomes, unless otherwise
stated.
Probabilistic Modeling: Statistical analysis tool that estimates, based on probability, an output
occurring. Monte Carlo simulation is a probabilistic model.
Sharpe Ratio: A measure for calculating risk-adjusted return. This ratio is commonly used in
industry practice.
Standard Deviation: A statistical measure of how far a set of data is from its mean. The more
spread apart the data, the higher the deviation.
Stochastic Modeling: A statistical model that is for the purpose of estimating the probability
of outcomes. One or more of the variables within the model are random. Also referred to as
Probabilistic Modeling.
Variability: The statistical distribution of data points from its mean value.
8. 8
1. INTRODUCTION
Asset allocation is the process of mixing asset weight within a portfolio to yield the most
favourable risk-return trade-off (Cardona 1998; Seiler, Webb & Myer 1999; Sing & Ong 2000).
This research will investigate if varying asset allocation during different economic phases (i.e.
growth, decline and stable), optimizes and enhances the performance of a portfolio, when
compared to an asset allocation that remains static.
The investigation will be undertaken by using Monte Carlo simulation as a risk
management tool to determine the most likely risk-adjusted returns of each portfolio.
Portfolio performance will be measured by a Sharpe ratio, this factors portfolio risk along with
portfolio return to enable a true indication of risk-adjusted portfolio performance.
Initial portfolio performance, prior to Monte Carlo simulation, is measured through
deterministic modeling, that contains no randomness and the output would always produce
the same risk-adjusted return as long as the initial inputs remained the same.
There are three economic periods that both Monte Carlo simulation and deterministic
modeling will be operated within. Each economic period produced asset returns and
deviations that different across the entire cycle. This produced the opportunity to enhance
portfolio performance through the selection of the appropriate portfolio that produced the
highest risk-adjusted return in each period.
1.1. RESEARCH PROBLEM
The body of knowledge within this research area is limited. Most research on Asset
Allocation has been conducted on different asset classes, such as equities and fixed interest.
Studies that have included property as an asset class, are mostly concerned with the asset as
part of a mixed-asset portfolio. Of the remaining research that does focus upon ‘within real
estate’ asset allocation, most examines the diversification of property by property-type,
geographical region or economic industries (Mueller 1993; Mueller & Ziering 1992). There
were no studies found that examine asset allocation, based on Monte Carlo simulation, in
differing economic conditions.
10. 10
portfolio performance over the differing economic conditions, i.e. will a particular portfolio
perform as efficiently in a ‘Stable’ period as it does in a ‘Growth’ period? Portfolio
performance is measured on a risk/return basis, not return-only.
Whilst this dissertation does not indicate the probability of future returns, it provides the
basis of how to model Monte Carlo simulation, for optimal asset allocation and diversification
benefits. Historic risk/return data can be substituted for forecasted returns and standard
deviations where a probabilistic outcome may be derived.
This methodology is advantageous amongst the two types of simulation models
(deterministic and probabilistic) that are often used in investment strategy to forecast the
risk-return of a prospective investment. The variables of a probabilistic model, unlike a
deterministic model that uses fixed single-point input variables, the variables are represented
by probability distributions (Byrne 1996). A comparison between the returns of the two
models is made in the data analysis.
1.4. STRUCTURE OF THE THESIS
A probabilistic model is beneficial as the ex-returns an asset provides cannot be forecasted
with certainty, however using the past returns in different phases of economic conditions,
along with the variability, i.e. standard deviation, the model can produce a range of ‘most
likely’ figures for the decision maker to then interpret and act upon (Byrne 1996). It also
enables the decision maker to use an efficient frontier to determine which assets produce the
most efficient returns for a specified level of risk.
The following chapters of this dissertation focuses on reviewing relevant literature, model
methodology, data analysis and conclusion of the model findings. Chapter 2 reviews literature
that have relevance to this dissertation. This included aspects of asset allocation,
diversification, Modern Portfolio Theory and Monte Carlo Simulation. Chapter 3 focuses upon
the research design, including important aspects such as the Sharpe ratio and the procedure
of Monte Carlo simulation modelling.
Chapter 4 analyses the output data from the Monte Carlo simulation after the Monte Carlo
simulation in Chapter 3 was undertaken. It will compare returns and results between time
12. 12
2. LITERATURE REVIEW
Literature on stochastic computer simulation of asset allocation is limited within real
estate. There is a plethora of research that focuses upon asset allocation and portfolio
optimization, though the mass of this research is focused upon the more liquid assets in capital
markets, i.e. stocks and government bonds (Amenc et al. 2011; Cardona 1998; Faff, Gallagher
& Wu 2005). However, Harry Markowitz’s Modern Portfolio Theory (MPT) was one strategy
that reappeared in almost every piece of literature (Detemple, Garcia & Rindisbacher 2003;
Fisher & Liang 2000; Seiler, Webb & Myer 1999; Sing & Ong 2000; Viezer 1999, 2000).
In 1952, Markowitz was the first to discuss the concept of diversification through the
formal development of the MPT (Seiler, Webb & Myer 1999). However research has
demonstrated that the mean-variance concept, which is based on the process of weighting
variance (risk) against returns in a normal and independent distribution, is limited when asset
returns are skewed and form an abnormal distribution (Sing & Ong 2000). Therefore, the
mean-variance concept and MPT may not be the best concept for measuring and determining
optimal asset allocation within real estate, or at least on its own. Information asymmetries,
high transaction costs, illiquidity, uniqueness of asset characteristics, private property rights,
tax, land use legislation are some of the reasons why capital market theories, such as MPT, do
not adequately perform within real estate markets (Coleman & Mansour 2005; Souza 2014).
From the literature that has been reviewed, most agree that diversification and asset
allocation have evolved as important tools to mitigate risk in real estate portfolios (Coleman
& Mansour 2005) and are intimately related to risk management (Amenc et al. 2011).
Optimizing portfolio performance for an individual’s level of risk tolerance (Cardona 1998) is
as important an aspect of portfolio management as pursuing superior returns (often
correlated with higher risk).
Tactical and Strategic Allocation are other strategies that can be used to structure a
diversified portfolio (Cardona 1998). Typically, strategic allocation is what the populace
consider when they hear the broad term ‘asset allocation’. Target allocations are established
for different asset classes, in this instance, office, retail and industrial, and these holdings are
periodically rebalanced to the original targets as the investment returns skew the position
14. 14
Take the same input values for a DCF, Monte Carlo simulation would create random
varieties on each input (often within a standard deviation) and produce thousands of
outcomes for each output (Thomopoulos 2013). A mean-average of these outcomes make it
a more efficient decision making tool and reduces risk as it factors the uncertain variability
and complexities of the real world.
Monte Carlo Simulation is readily used and researched amongst industries outside of Real
Estate, from harbor protection (Males & Melby 2011) to the Manhattan Project in the 1940s,
where it was the prominent tool in the development of the hydrogen bomb (Thomopoulos
2013). The model has been used in a wide range of applications since the Manhattan Project,
where it gained its validity. It was deemed that as long as the probability distributions and
parameters values selected were authentic, the model is powerful enough to assist in decision
making as crucial as constructing a hydrogen bomb, such as the Manhattan Project
(Thomopoulos 2013). Since this project, there has been no obvious or compelling evidence to
suggest Monte Carlo simulation is ineffective as a decision making/risk management tool.
The model is now extensively used in all industries and government decisions
(Thomopoulos 2013). In reference to harbor protection, Males and Melby state;
“Monte Carlo simulation modeling that incorporates engineering and economic
impacts is a worthwhile method for handling the complexities involved in real world
problems” (2011, p 1).
Although the Manhattan Project and harbor protection differ substantially from financial
markets and real estate investment, using risk management tools from other industries offer
risk management principles that may be adjusted and implemented to suit the demands of
the situation.
The basic principle of Monte Carlo simulation is that is a methodology for analysing
problems where there are uncertainties (Males & Melby 2011). It is useful in representing real
world situations where there are many uncertain variables but the parameter or behavior
values are known (Males & Melby 2011), e.g. the future expected return is unknown &
effected by many uncertain variables, although the parameters of historic returns and
variability through standard deviation are extremely useful in determining the output.
17. 17
Secondly, by presenting the process in a case study format, it communicates to the
readers how to interpret the input and output data of the model. The probabilistic model, or
any model, is only as accurate as the inputs determined by the user and the interpretation of
the outputs received of those inputs. Monte Carlo Simulation is no exception, the model only
provides probabilistic outputs, as nothing in reality can be forecasted with certainty, therefore
understanding and interrupting the variables associated with the model is a critical
component to running an effective simulation. Many investors are suspicious that the model
operates like a black box, in which data is fed and results appear, possibly with the chance for
unscrupulous manipulation by others (Rowland 2010).
Once a reader understands and is capable of interpreting the data, they are then able to
implement the model in their own practice. Due to the complexity of Monte Carlo Simulation
and the mathematical equations behind it, a case study provides the best approach of
transferring the knowledge into practice. Many papers focus on the complex mathematical
equations behind the model, however in reality, the user does not need extensive
understanding of the equations behind the model; they need to know how to it, its limitations
and how to interpret what it produces.
The following sections contain material that will allow for understanding the components
of the model, enabling a greater interpretation of the research procedure and outcomes in
Chapter 4: Analysis of Data.
3.2.1.DATA SOURCES
The data sources used within this research modeling are from reliable sources. Property
returns are obtained from MSCI: IPD Australia Quarterly Digest, September 2015. MSCI Data
holds real estate asset information on hundreds of institutional investors, whilst also
producing indexes for both privately held real estate portfolios and publicly listed
organisations (MSCI 2016). It provides quarterly data returns for each primary sector (Retail,
Office, Industrial) over a period from December 1985 to September 2015. Property returns
(Rolling Annual Returns) for each sector have been utilised from June 2005 to March 2014
(Table 3.1). These correspond with the economic periods used in modeling.
18. 18
Government Bond rates, were obtained from the Reserve Bank of Australia ‘Capital
Market Yield: Government Bond tables’. The bond rate is used as the risk free rate, a rate of
return that carries no risk and the investment return is certain. The bond rate is used in the
Sharpe ratio formula.
3.2.2.ECONOMIC PERIODS
The Monte Carlo Simulation was operated in three distinct economic periods. Each period
represents differing economic conditions where property returns significantly changed in line
with the Market Cycle (Figure 3.1). These periods were;
• Growth: June 2005 – March 2008
• Decline: June 2008 – March 2011
• Stable: June 11 – March 2014
These economic periods also coincide with the Global Financial Crisis (GFC), which
drastically affected the investment market. The periods can also be perceived as Pre-GFC
(Growth), GFC (Decline) and Post-GFC (Stable).
The simulation will determine, by probabilistic means, the portfolios that are likely to
produce the highest mean return and Sharpe ratios (risk/reward) in each economic period.
The procedure of the modeling will be explained in section 3.4. Research Procedure.
21. 21
‘𝜎𝑝?
or Standard Deviation is the variation around the mean. In a normal distribution, +/-
1 standard deviation from the mean returns accounts for 68% (34% above the mean and 34%
below the mean) of all probable outcomes, +/-2 standard deviations accounts for 95% of all
probable outcomes and +/-3 standard deviation accounts for 99.7%. In calculating and
analysing the Sharpe ratio, +/-1 standard deviation is used. In undertaking the Monte Carlo
simulation, +/-2 standard deviations were used.
3.2.5.MONTE CARLO SIMULATION
The Monte Carlo simulation makes use of random numbers to produce a probabilistic
outcome (Byrne 1996). The random numbers are pseudorandom, where the numbers
generated derive from predetermined parameters. The inputs are selected +/-2-standard
deviations of the average weighted return of the portfolio, representing 95% of all probable
outcomes. The Monte Carlo simulation will enable the decision maker to determine which
portfolio and its corresponding asset allocation weighting, may enhance portfolio
performance. It will also produce data that provide a range of efficient portfolios that may be
plotted along an efficient frontier.
3.2.6.EFFICIENT FRONTIER
The efficient frontier plots the set of portfolios that return the greatest yield per unit of
risk (Peterson 2012) based on a calculated weighted combination of portfolio assets (Higgins
& Fang 2012). The X-Axis contains the portfolio risk; the Y-Axis comprises the portfolio return.
All portfolios that are along the efficient frontier are considered to be the most efficient
returning portfolios relative to the specific risk level (Best 2014). Portfolios located within
(below) the frontier are deemed inefficient, as for the same level of risk they contain, a greater
return can be achieved through a portfolio along the frontier. The portfolio that offers the
lowest possible risk level for a rate of expected return is called the Minimum Variance
Portfolio.
3.3. RESEARCH PROCEDURE
Summarising the particular aspects of the probabilistic modelling in section 3.2 enables a
comprehensive understanding of how the simulation was undertaken. The following steps are
22. 22
how Monte Carlo simulation was utilized to determine if altering asset allocation during
differing economic conditions, enhances portfolio performance.
Step 1.
Property data was extracted from MSCI: IPD Australia Digest. Mean returns, Variance
and Standard Deviation were all calculated for each asset class (retail, office, industrial) in
each economic period (growth, decline, stable).
Step 2.
Asset Allocations weighting for each portfolio were determined. In total, there were 87
portfolios. Where portfolios contained only 2 asset classes, an asset variance of 5% was
applied, for example;
• ‘Portfolio A’ allocated 100% Retail/0% Office/0% industrial
• ‘Portfolio B’ allocated 95% Retail/5% Office/0% Industrial
• ‘Portfolio C’ allocated 90% Retail/10% Office/0% Industrial
Where portfolios contained all 3 asset classes, an asset variance of 10% was applied, for
example;
• ‘Portfolio XA’ allocated 90% Retail/5% Office/5% industrial
• ‘Portfolio XB’ allocated 80% Retail/10% Office/10% Industrial
• ‘Portfolio XC’ allocated 70% Retail/15% Office/15% Industrial
For asset allocation of all 87 portfolios, refer to Appendix 1.
Step 3.
For each portfolio, the weighted mean-return, weighted risk (standard deviation) and
Sharpe ratio were calculated. The weighted mean-return was achieved by multiplying each
asset weighting by asset return in the respective period. As such, the weighted-mean return
for a given portfolio is the sum of all asset weighted returns. The figures were repeated for
each economic period.
23. 23
Step 4.
Once asset allocation and risk/return data had been computed based on historic data,
the Monte Carlo simulation model was developed. In order to achieve the simulation, a
‘Pseudorandom Number Generator’ produced a return for each asset that was between +/-2
standard deviations of the mean asset return, within that economic period. This was then
weighted with the corresponding asset weighting for the particular portfolio to produce the
‘Simulation Variables’.
Step 5.
The Monte Carlo simulation, using the predetermined ‘simulation variables’, operates
1000 iterations through a ‘What-If Analysis’, a manipulation of input variables in order to ask
what the effect will be on the output (Forgionne & Russell 2008). The input variables are
constrained within the parameters of standard deviation. The number of iterations that can
be run in a simulation are user specified and can be as little as 1 or 2 or as many as 1,000,000.
The results of the simulation are recorded as ‘Simulation Output’, which from the 1000
iterations, acquires the mean average return, median return, minimum return, maximum
return, standard deviation and the Sharpe ratio. Again, as every economic period has different
returns, its repeated for the respective period.
Step 6.
Once the simulation has been processed and recorded for each portfolio in each
economic period, the portfolios are ranked accordingly to mean return (return only) and
Sharpe ratio (return relative to risk). This allows the decision maker to quickly analyse which
portfolio has the greatest return and which portfolio has the greatest return per unit of risk in
each period. However, it does not allow the decision maker to deem which portfolio is
probable to achieve the greatest return relative to investor risk tolerance, an efficient frontier
is used for this purpose.
Step 7.
Once all results have been graphed and a ranking/comparison has been completed, it is
easy to determine if altering asset allocation in different economic periods tested by Monte
Carlo simulation is effective in enhancing portfolio performance. For example, the decision
maker can realise that ‘Portfolio A’ has the highest Sharpe ratio in the growth period, but
changing allocation composition, as the market declines, to ‘Portfolio XC’ will enhance the
24. 24
portfolio return with minimal risk. Additionally, the results of Monte Carlo simulation can give
the decision maker an advantage in minimizing the quantity of portfolios to investigate
through interpreting the data appropriately.
3.4. CONCLUSION
Once the simulation model was created and the user was equipped with the
understanding and process of application, the alteration of the model to suit many particular
purposes is simplistic. The model can determine the optimal portfolio asset allocations in each
economic cycle, or which portfolios to further analyse without the need to comprehensively
analyse each option. The models accuracy is subject to ensuring the data used within the
simulation is reliable. With falsified or flawed data, the model will produce an unreliable
output that decisions should not be based upon.
The model answered the research question, as found in the following chapter, that
altering asset allocation, based on Monte Carlo simulation, in differing economic periods,
enhanced portfolio performance through delivering the portfolios and their asset allocation
weights that contain the highest risk-adjusted returns. If the user wishes to use the model for
forecasted returns, step 1 need be forecasted return data, rather than historic data and the
same steps may be followed.
26. 26
Property Returns
Period All Property Retail Office Industrial Bonds
Growth (June ’05 – Mar ’08) 17.65% 16.83% 18.73% 15.98% 5.83%
Decline (June ’09 – Mar’ 11) 2.83% 3.78% 1.94% 1.22% 4.81%
Stable (June ’11 – Mar ’14) 9.72% 9.35% 9.73% 9.98% 3.10%
In the ‘Growth’ period, from June ‘05 to March ‘08, total property assets returned 17.65%,
reaching a peak return of 19.80% in March 2007. The ‘Office’ sector was preeminent with a 3-
year annualized return of 18.73%, reaching 23.20% at its highest in September 2007. Retail
followed, with a 3-year annualized return of 16.83% and Industrial returning 15.98% over the
same period.
Once the market entered into declining status from June ’08 to March ‘11, the retail sector
surpassed office sector considerably with a 3.78% return, comparative to office returning
1.94%. The retail sector outperformed the real estate market, which returned a total 2.83%.
However, mean returns do not depict the period appropriately. At the trough of the cycle,
assets were losing money, with the industrial sector experiencing the poorest performance,
returning as low as -8.9% in June ‘09. In such volatile conditions, returns alone are poor
indicators for portfolio decision making and factoring risk through standard deviations are as
important as the return, if not more important.
In June ’11, the property market stabilized with each asset sector providing similar returns
(See Table 3.1). Importantly in this period, volatility (risk) was at its lowest over the three
various periods, meaning that the returns over the entire 3-year period were stable with
minimum variance between annual returns.
It is apparent within Figure 4.1 that the market took a downwards shift, experiencing the
most difficult period between June ’08 - March ’11. From there, the market stabilized with
little increase or decrease in total returns and comparative returns between asset classes. The
variance within the asset class through the differing economic periods is the primary interest
in asset allocation. As can be seen in Figure 4.1, one asset class did not drastically outperform
the others throughout the entire market cycle e.g. office returns significantly outperformed
retail and the market in the Growth phase, however experienced underperformance to both
Table 4.1: Mean property returns by sector, in each economic period
28. 28
Growth - Total Return (%), 3 year Annualised
Retail Office Industrial Bonds
Expected Return 16.83% 18.73% 15.98% 5.83%
Variance 4.30% 16.05% 1.74% 0.27%
Standard Deviation 2.07% 4.01% 1.32% 0.52%
Sharpe Ratio 5.300 3.218 7.694 N/A
Given that Office has superior returns, being overweight in the Office sector through an
asset allocation of R:0%/O:100%/I:0% during a growth period would deem to offer the
greatest return. Conversely this is not optimal and does not conform with the logic of
diversification, nor does it produce a high ranking Sharpe ratio.
Table 4.3 below displays the Top 6 portfolios, ranked by Sharpe ratio. In deterministic
modeling, these are the top 6 portfolios that produce the highest Sharpe ratio. As they are
deterministic, they do not process a range of possible outcomes within the variance of the
portfolio. These rankings can be compared to the rankings of portfolios after Monte Carlo
simulation, found in Table 4.4.
Top 6 Portfolios, by Sharpe Ratio
Portfolio
Asset Allocation Portfolio
Risk
Portfolio
Return
Sharpe
Ratio
Sharpe
Rank
Retail Office Industrial
BA 0% 0% 100% 1.32% 15.98% 7.694 1
BB 5% 0% 95% 1.36% 16.02% 7.511 2
BC 10% 0% 90% 1.39% 16.06% 7.338 3
BD 15% 0% 85% 1.43% 16.11% 7.174 4
AT 0% 5% 95% 1.45% 16.12% 7.077 5
BE 20% 0% 80% 1.47% 16.15% 7.018 6
Table 4.2: Output data of property returns in ‘Growth’ Period
Table 4.3: Deterministic model Ranking, in ‘Growth’ period, by Sharpe ratio
30. 30
decision. If an investor wishes to increase their risk tolerance to pursue higher returns, the
portfolios located along efficient frontier are the most efficient portfolios, per unit of risk at a
given return. Figure 4.2 below demonstrates the efficient frontier of all portfolios within the
‘Growth’ period. If the investor was ‘risk seeking’, portfolio ‘T’ is probable to return, on
average, 18.87% with 1 standard deviation in the range of 14.47% - 23.27%.
These results indicate that Monte Carlo simulation was effective in enhancing
portfolio performance by optimizing asset allocation that provided higher risk-adjusted return
& Sharpe ratios whilst also providing efficient portfolios along the frontier in Figure 4.2 that
offered higher returns per unit of risk.
4.2.3.DECLINE PERIOD
In analysing the ‘Decline’ period in similar form to the ‘Growth’ period, Retail proved
to be the best performing sector, outperforming all asset classes and the total property
market. However, unlike office in the ‘Growth’ period, it also exhibited the highest Sharpe
ratio, meaning on average, it produced the highest returns, with the lowest risk.
T
P
L
ZI
XE
ZE
ZC
BG
BC
14.00%
15.00%
16.00%
17.00%
18.00%
19.00%
20.00%
0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00%
Return
Risk
Figure 4.2: Efficient Frontier of Portfolios in ‘Growth’ period.
31. 31
Decline - Total Return (%), 3 year Annualised
Retail Office Industrial Bonds
Expected Return 3.78% 1.94% 1.22% 4.81%
Variance 26.37% 51.72% 46.22% 0.86%
Standard Deviation 5.14% 7.19% 6.80% 0.93%
Sharpe Ratio -0.201 -0.399 -0.527 N/A
Given the situation of highest return and lowest risk, being heavily weighted in this
asset class is likely to conform to superior portfolio performance. Table 4.6, below depicts the
top 6 portfolios in the ‘decline’ period prior to probabilistic modeling. All being heavily
weighted in ‘Retail’
Using Deterministic modeling, Portfolio Risk of all 6 portfolios may be skewed in a
market downturn. Regardless, as the Sharpe ratios are <1, the probabilistic outcome for every
portfolio, is not satisfactory. However, in an unstable market, it may be more appropriate to
examine Sharpe ratios relative to market conditions and not as absolute figures.
Monte Carlo simulation produced (refer Table 4.7), after 1000 iterations, a risk
associated with portfolio ‘B’ that was less than estimated in the deterministic model. This
indicated that the portfolio risk associated with portfolio ‘B’ is likely to be less than assumed
through deterministic modeling, which provides no randomness in its estimation. As a result,
portfolio ‘B’ offers a higher risk-adjusted return/Sharpe ratio after Monte Carlo simulation.
Top 6 Portfolios, by Sharpe Ratio
Portfolio
Asset Allocation Portfolio
Risk
Portfolio
Return
Sharpe
Ratio
Sharpe
Rank
Retail Office Industrial
A 100% 0% 0% 5.14% 3.78% -0.201 1
B 95% 5% 0% 5.24% 3.69% -0.214 2
BT 95% 0% 5% 5.22% 3.65% -0.222 3
C 90% 10% 0% 5.34% 3.59% -0.228 4
XA 90% 5% 5% 5.32% 3.56% -0.235 5
D 85% 15% 0% 5.44% 3.50% -0.240 6
Table 4.5: Output data of property returns in ‘Decline’ Period
Table 4.6: Deterministic Portfolio Ranking, in ‘Decline’ period, by Sharpe ratio
33. 33
This is where Monte Carlo simulation may substantially enhance portfolio performance.
Often, when the investing sentiment is negative, as in a market downturn, diversification is
often used as an important tool to mitigate risk in a real estate portfolio (Coleman & Mansour
2005). Monte Carlo simulation, as presented here, shows that diversification offers little
advantage of risk reduction when there is systematic or market risk (Viezer 2000). It also
provides realistic measure of risk associated with portfolio selection, where as previously
mentioned, can be positively or negatively skewed by deterministic modeling.
The efficient frontier, as shown below in Figure 4.3, indicates that portfolio ‘B’ is the most
efficient portfolio for the specified unit of risk. If an investor is risk averse, the minimum
variance portfolio is portfolio ‘XE’ (R:50%/O:25%/I:25%), providing a more diversified portfolio
that tolerates less variance in overall risk, although whilst providing lower absolute risk, has
more risk per unit of return compared to portfolio ‘B’.
Similarly, to the previous ‘Growth’ period, Monte Carlo simulation provides the
opportunity to enhance portfolio performance by selecting the portfolio (portfolio ‘B’) that
offers the highest risk-adjusted return. The asset allocation, both pre and post Monte Carlo
simulation is heavily weighted within the Retail sector, emphasizing that overweighting in
Retail is the optimal asset class to enhance portfolio performance.
B
BS
DE
XC
XE
XG
YH
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%
Return
Risk
Figure 4.3: Efficient Frontier of Portfolios in ‘Decline’ period.
34. 34
4.2.4.STABLE PERIOD
All asset classes in the ‘Stable’ period produced comparable risk/return outputs, without
one asset class significantly outperforming another. Each asset class produced very high
Sharpe ratios that yield excellent investments. These values are a result of by low government
bond rates and high risk premiums in a low risk market. Portfolio selection in this period is
likely to contain a positive return, regardless of decision. For the purpose of enhancing
portfolio performance, Monte Carlo simulation was used to determine which asset allocation
weighting will provide superior Sharpe ratio.
Stable - Total Return (%), 3 year Annualised
Retail Office Industrial Bonds
Expected Return 9.35% 9.73% 9.98% 3.10%
Variance 0.31% 0.27% 0.37% 0.43%
Standard Deviation 0.56% 0.52% 0.61% 0.65%
Sharpe Ratio 11.226 12.816 11.343 N/A
After examining the output data for total return in Table 4.9, the top 6 performing
portfolios, by deterministic modeling, are heavily weighted in the industrial sector. These
portfolios in Table 4.10, as within the previous periods, are mean average from a range of data
inputs, and not the most probable average found through Monte Carlo simulation.
Top 6 Portfolios, by Sharpe Ratio
Portfolio
Asset Allocation Portfolio
Risk
Portfolio
Return
Sharpe
Ratio
Sharpe
Rank
Retail Office Industrial
AA 0% 100% 0% 0.52% 9.73% 12.816 1
T 5% 95% 0% 0.52% 9.71% 12.731 2
AB 0% 95% 5% 0.52% 9.74% 12.731 3
AC 0% 90% 10% 0.53% 9.75% 12.646 4
S 10% 90% 0% 0.52% 9.69% 12.646 5
YA 5% 90% 5% 0.52% 9.72% 12.646 6
Table 4.9: Output data of property returns in ‘Stable’ Period
Table 4.10: Deterministic Portfolio Ranking, in ‘Stable’ period, by Sharpe Ratio
35. 35
As all asset sectors have very similar mean-returns and Sharpe ratios, Monte Carlo
simulation was able to weight asset allocation evenly across all sectors to determine the
maximum return for the minimum risk. The results, like the former periods, produced
portfolios that were opposed to the deterministic model. 3-asset class portfolios
outperformed all 2-asset class, reflecting true diversification theory. This is different than
other economic periods, where one asset class has offered a significant outperformance and
top performing portfolios comprised of 2-asset classes.
The top performing portfolio after Monte Carlo simulation, by Sharpe ratio, is portfolio
‘YF’. Portfolio ‘YF’ returns 0.21% less than Portfolio ‘AA’ in the deterministic model, though
portfolio ‘YF’ carries 33.71% less portfolio risk. The top performing Sharpe ratio portfolios
after 1000 iterations of probabilistic modeling are below in Table 4.11.
The efficient frontier below (Figure 4.4) indicates that if a higher return is sought, portfolio
‘AQ’ is the most efficient portfolio to do so. It is probable that it will return 9.98%, though it
carries a higher unit of risk for return than the minimum-variance portfolio (portfolio ‘ZH’). As
portfolio ‘XD’ is below the minimum variance portfolio on the efficient frontier, thus for less
portfolio risk, a higher return can be achieved in portfolio ‘ZH’. This is what is known as an
inefficient portfolio.
Top 6 Portfolios, by Sharpe Ratio
Portfolio
Asset Allocation Portfolio
Risk
Portfolio
Return
Sharpe
Ratio
Sharpe
Rank
Retail Office Industrial
YF 30% 40% 30% 0.37% 9.71% 17.740 1
ZG 35% 35% 30% 0.37% 9.67% 17.722 2
ZH 40% 40% 20% 0.37% 9.62% 17.716 3
XG 30% 35% 35% 0.37% 9.72% 17.711 4
YE 25% 50% 25% 0.38% 9.71% 17.585 5
XF 40% 30% 30% 0.38% 9.66% 17.412 6
Table 4.11: Monte Carlo simulation ranking, in ‘Stable’ period, by Sharpe ratio
36. 36
AQ
AL
XI
XG
ZH
XD
9.30%
9.40%
9.50%
9.60%
9.70%
9.80%
9.90%
10.00%
10.10%
0.00% 0.10% 0.20% 0.30% 0.40% 0.50% 0.60%
Return
Risk
4.3. SUMMARY, DISCUSSION AND MAIN FINDINGS
Using Monte Carlo simulation enabled us to verify that altering asset allocation, during
differing economic conditions, enhancing portfolio performance. Monte Carlo simulation
used 1000 iterations of possible outcomes to determine the most probable outputs (portfolio
return, portfolio risk & Sharpe ratio) of each portfolio. The use of a pseudorandom process
generates a more compelling model.
The findings within the research are extensive. The portfolios that offered the highest
absolute mean-return (often with higher risk), were inefficient on return per unit of risk. That
is, for the increased risk associated with the investment, the return offered in compensation
was inefficient. The absolute mean-returns on a deterministic model were frequently similar
to the returns from probabilistic modeling, meaning that the Monte Carlo simulation is
somewhat accurate in forecasting the most probable return and can provide confidence in
decision making. However, Monte Carlo was also able to determine asset allocations that
were most likely to produce higher Sharpe ratios.
Figure 4.4: Efficient Frontier of Portfolios in ‘Stable’ period.
37. 37
Diversification among 3-asset classes had inefficient Sharpe ratios in two out of three
economic periods. Results in the ‘Growth’ and ‘Decline’ period indicate being overweight in
an outperforming asset sector often produces a greater return with less risk than diversifying
across all 3 asset classes. It is only in the ‘Stable’ period where portfolio risk in all 3 asset
classes had similar (and low) risk, that a 3-asset class portfolio enhanced portfolio
performance. This is an important finding for tactical asset allocation.
Undoubtedly, altering asset allocation does enhance portfolio performance, however the
discussion point taken from this research is, can these optimal asset allocations that enhance
portfolio performance, be obtained through simplistic/deterministic modeling? These results
indicate that Monte Carlo provides more realistic outputs.
The table above (Table 4.12) shows that the Sharpe ratios associated with the most
probable outcome in probabilistic modeling (Monte Carlo simulation) outperforms the results
from deterministic modeling in every economic condition, thus making asset allocation
decisions based on probabilistic modeling likely to significantly enhance portfolio
performance.
An important consideration in diversification strategies is that “whilst theoretically
diversification is cost free, in reality this certainly isn't the case. There are costs associated
with optimally diversifying a portfolio including hard costs of developing, implementing and
monitoring diversification schemes, along with opportunity costs resulting from changing
Deterministic vs Probabilistic Comparison
Model Portfolio
Asset Allocation Portfolio
Return
Portfolio
Risk
Sharpe
Ratio
Retail Office Industrial
Growth Period
Deterministic BA 0% 0% 100% 15.98% 1.32% 7.694
Probabilistic ZC 15% 15% 70% 16.57% 1.31% 8.172
Decline Period
Deterministic A 100% 0% 0% 3.78% 5.14% -0.201
Probabilistic B 95% 5% 0% 3.73% 5.73% -0.189
Stable Period
Deterministic AA 0% 100% 0% 9.73% 0.52% 12.816
Probabilistic YF 30% 40% 30% 9.71% 0.37% 17.740
Table 4.12: Comparison of best performing portfolios in Deterministic & Probabilistic models
38. 38
market conditions and reduced flexibility of capital deployment” (Fisher & Liang 2000).
Therefore, the costs associated with buying, selling and leasing real estate must be measured.
39. 39
5. CONCLUSION
5.1. INTRODUCTION
The objective of this thesis study was to gain an understanding on the applicability and
implementation of Monte Carlo simulation in real estate investment, specifically, whether it
can enhance portfolio performance through altering asset allocation. Through the literature
review, a broad understanding of Monte Carlo simulation was attained and its
(non)implementation within the real estate industry. Tactical asset allocation was considered
to be applicable to Monte Carlo simulation to direct diversification strategies.
5.2. CONCLUSION ON RESEARCH QUESTIONS
This research concludes that portfolio performance can be enhanced by altering asset
allocation, during different economic conditions, based on Monte Carlo simulation. The
hypothesis was considered valid as Monte Carlo simulation repeatedly produced portfolios
that had greater Sharpe ratios and outperformed deterministic, or single-value modeling. This
meant that portfolios ranked the highest after probabilistic modeling, are likely to provide a
greater return per unit of risk, or have less risk per unit of return than the highest ranked
portfolios after deterministic modeling.
Producing portfolios with greater Sharpe ratios signifies that certain asset allocations
mixes can enhance portfolio performance. Changing the portfolio position in each economic
period through the tactical adjustment of asset allocation weighting, rather than remaining
static in one portfolio over the entire economic cycle, will significantly enhance risk-adjusted
returns.
5.3. CONCLUSION ABOUT RESEARCH PROBLEM
The case study argues that using probabilistic modeling gives a better representation of
actual, or most probable return. The principle of ‘law of large numbers’ states that as the
sample size grows or the frequency of events increases, the mean-average will represent the
41. 41
periods was inefficient for the timeframe allocated to complete this study. Inexperience with
Monte Carlo simulation prior to this study resulted in significant time learning and developing
the model and limited time extracting information from the model. If more time was allocated
to extracting the information, a more comprehensive analysis may have been conducted.
Allocation Variance may also limit the possibility to further enhance portfolio
performance. In this study, all 2-asset portfolios had a variance of 5% (Refer Appendix 1, Table
7.1), i.e. Portfolio ‘A’ allocated R:100%/O:0%/I:0%, Portfolio ‘B’ allocated R:95%/O:5%/I:0%
etc. 3-Asset portfolios had a variance of 10%. If variance was reduced, would asset allocation
produce even further enhancement and would the portfolio rankings change?
5.6. FURTHER RESEARCH
Related to the limitations of the study, further research may be conducted with the
application of Monte Carlo simulation with forecasted data. Compiling appropriate and
reliable data would take considerable time, however if one has access, it would be interesting
to operate the model and record the actual returns to determine how accurate Monte Carlo
simulation was in forecasting the most probable risk and return.
Research may be conducted in the size of asset variance within allocation weightings. If
asset variance was reduced, i.e. R:97.5%/O:1.25%/I:1.25%, would those portfolios with
smaller variance offer superior Sharpe ratios and further enhance portfolio performance?
What is the optimal asset variance?
Research on the applicability of Monte Carlo simulation can also be focused on geographic
location of the asset rather than Asset class, i.e. Office: Sydney CBD vs Office: Melbourne CBD.
The amount of portfolio iterations may be increased or decreased to determine if running
more iterations improves the accuracy of output data.
Finally, a theoretical case study using monetary values would be interesting to determine
the final financial positions using the different models (deterministic vs probabilistic) and
different asset allocation in the differing economic conditions. Would the outcome of the
former study add to the conclusion of this study? This may be determined by an increase or
43. 43
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