PORTFOLIO OPTIMISATION
AGENDA
IntroductionTheoretical contributionPerceived role of Real estate in the Mixed-
asset PortfolioMethodologyResultsSensitivityConclusion and Advice
INTRODUCTION
OBJECTIVE : Portfolio Optimization Consider proportion of Property Investments
Client: UK Pension Fund Institutional Investor Invest only in UK assets Risk minimization !!!
THEORETICAL CONTRIBUTIONGeltner, Miller, Clayton and Eiccholtz (2006): Chapter 21
• Markowitz Portfolio Theory (MPT): – Framework for strategic asset allocation of investor’s capital
across asset classes– Widely used in practice– In particular by institutional investors– Also called Modern Portfolio Theory
Markowitz Portfolio Theory (MPT) • Basic Assumptions:
– Investors want to maximize return and minimize risk in their wealth portofolios (1)
hold portfolio on the efficient frontier– There exists a riskless asset (2)– Common Expectations (3)
• Two-fund theorem: (1) + (2)“all investors will prefer combinations of the riskless asset and a single specific risky asset portfolio”
• Two-fund theorem + Common Expectations Everyone will hold the same portfolio of risky assets,
i.e. the market portfolio
Markowitz Portfolio Theory (MPT) • Selection of risky asset portfolio
– Maximize the slope of the straight line connecting the portfolio’s risk & return with the risk and return of the riskless asset
– I.e. Maximize the Sharpe ratio
• Sharpe Ratio– Represents the price of risk – Risk premium per unit of risk
Markowitz Portfolio Theory (MPT)
Markowitz Portfolio Theory (MPT)
• Basic Assumptions: – Investors want to maximize return and minimize risk in their
wealth portofolios (1)
hold portfolio on the efficient frontier– There exists a riskless asset (2)
• Two-fund theorem: (1) + (2)
“all investors will prefer combinations of the riskless asset and a single specific risky asset portfolio”
PERCEIVED ROLE OF REAL ESTATE IN MIXED-ASSET PORTFOLIO
Represents alternative asset classOpportunity for further fund diversificationWhy ?Not highly correlated with other asset classes
Hence high Diversification benefit
METHODOLODY
Determine “Sharp Maximising
Portfolio
Calculate Asset Statistics
Determine Asset Universe
- Optimal Portfolio weights
- Expected Return- Variance
- Standard deviation
-Bonds- Stocks
- Real Estate
METHODOLOGY
Identify Asset Universe for inclusion in Portfolio Stocks, Bonds & Real Estate
Determination of individual Asset statistics Expected Return Variance Standard Deviation Determine Asset Correlation coefficients
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t
tr rTE1
)( 1
1
)(1
2)(
2
T
ErT
t
r
S
1
)(1
2)(
T
ErS
T
t
rt
Equation (1) – Expected Return Equation (2) - Variance
Equation (3) – Standard Deviation Equation (4) - Correlation
ji
j
SSCOVC i
ij
METHODOLOGY
Determine sharp maximising Portfolio …Ratio that measure return premium per unit of
RiskGiven by formula below
p
fp
S
rrP
Where:
rp: Portfolio return
rf : Risk free rate
Sp: Portfolio sigma ( standard deviation)
METHODOLOGY
Maximisation of Sharp Ratio Maximizes Return ( Vertical Axis) At the Lowest possible portfolio Risk (horizontal Axis)
Creates portfolio that lies at point P Results in Portfolio with best return premium per unit of Risk
assumed.
METHODOLOGY
Maximise:
Where Total portfolio weights sum up to 1 :
Solved Using Excel SolverNo short selling Constraints were imposed.
p
fp
S
rrp
NiWi
N
i
iw
,.......1,0,,
1
1
Summary statistics: Residential Property has the highest expected return The Government bonds have the lowest expected return & lowest
standard deviation Stocks have the highest Variance and standard deviation
Stocks Bonds Retail Office Industrial Residential
Expected Returns 0.09 0.02 0.10 0.08 0.10 0.15
Variance 0.02 0.01 0.01 0.01 0.01 0.01
Standard deviation 0.14 0.07 0.10 0.12 0.10 0.10
RESULTS
Correlation Matrix: Real estate shows very low, some negative, correlations
with asset classes Good Diversification benefits
Matrix Stocks Bonds Retail Office Industrial Residential Other
Stocks 1 0.25 0.27 0.33 0.18 0.37 0.05
Bonds 1.00 0.17 -0.06 0.02 -0.07 -0.12
Retail 1.00 0.86 0.87 0.67 0.77
Office 1.00 0.89 0.81 0.79
Industrial 1.00 0.61 0.80
Residential 1.00 0.58
Other 1.00
RESULTS
Optimal asset allocations:Asset Class Weights
Stocks 15.3%
Bonds 8.2%
Real Estate - Retail 4.5%
Real Estate - Office 0.0%
Real Estate - Industrial 42.6%
Real Estate - Residential 29.4%
Real Estate - Other 0.0%
Mean Return 9.2%
Standard Deviation 7.9%
Sharp Ratio 61.7%
SENSITIVITY
Adjustments made to asset expected returns – The re-run solver We believe that the returns of residential assets are too high, So we made an adjustment (supposing that the returns will fall 6%) and the
government bond will rise 2%. then we ran the solver again, and the weights of the optimal portfolio changed (residential has much less weight then before)
E[r] Volatility Stocks Bonds Retail Office Industrial Residential Other
5.00% 5.28% 2% 60% 0% 0% 0% 7% 30%
8.00% 5.51% 0% 46% 0% 0% 0% 37% 17%
11.00% 6.79% 0% 30% 0% 0% 0% 66% 5%
CONCLUSION AND ADVICE
Current weight of Real estate in pension Portfolio : 16%
Proposed weight of Real estate : 76.5% Therefore client should increase his
investment in Real estate as per the Sharp maximising Portfolio