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

T

t

tr rTE1

)( 1

1

)(1

2)(

2

T

ErT

t

r

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1

)(1

2)(

T

ErS

T

t

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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