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PORTFOLIO OPTIMISATION. AGENDA Introduction Theoretical contribution Perceived role of Real estate in the Mixed-asset Portfolio Methodology Results Sensitivity.

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Presentation on theme: "PORTFOLIO OPTIMISATION. AGENDA Introduction Theoretical contribution Perceived role of Real estate in the Mixed-asset Portfolio Methodology Results Sensitivity."— Presentation transcript:

1 PORTFOLIO OPTIMISATION

2 AGENDA Introduction Theoretical contribution Perceived role of Real estate in the Mixed-asset Portfolio Methodology Results Sensitivity Conclusion and Advice

3 INTRODUCTION OBJECTIVE :  Portfolio Optimization  Consider proportion of Property Investments Client:  UK Pension Fund  Institutional Investor  Invest only in UK assets  Risk minimization !!!

4 THEORETICAL CONTRIBUTION Geltner, 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

5 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

6 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

7 Markowitz Portfolio Theory (MPT)

8 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”

9 PERCEIVED ROLE OF REAL ESTATE IN MIXED-ASSET PORTFOLIO Represents alternative asset class Opportunity for further fund diversification Why ? Not highly correlated with other asset classes  Hence high Diversification benefit

10 METHODOLODY Determine “Sharp Maximising Portfolio Calculate Asset Statistics Determine Asset Universe - Optimal Portfolio weights -Expected Return -Variance -Standard deviation -Bonds -Stocks - Real Estate

11 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 Equation (1) – Expected ReturnEquation (2) - Variance Equation (3) – Standard DeviationEquation (4) - Correlation

12 METHODOLOGY Determine sharp maximising Portfolio … Ratio that measure return premium per unit of Risk Given by formula below Where: r p : Portfolio return r f : Risk free rate S p : Portfolio sigma ( standard deviation)

13 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.

14 METHODOLOGY Maximise: Where Total portfolio weights sum up to 1 : Solved Using Excel Solver No short selling Constraints were imposed.

15 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 StocksBondsRetailOfficeIndustrialResidential Expected Returns0.090.020.100.080.10 0.15 Variance 0.02 0.01 Standard deviation 0.14 0.070.100.120.10

16 RESULTS Correlation Matrix:  Real estate shows very low, some negative, correlations with asset classes  Good Diversification benefits Matrix StocksBondsRetailOfficeIndustrialResidentialOther Stocks10.250.270.330.180.370.05 Bonds 1.000.17-0.060.02-0.07-0.12 Retail 1.000.860.870.670.77 Office 1.000.890.810.79 Industrial 1.000.610.80 Residential 1.000.58 Other 1.00

17 RESULTS Optimal asset allocations: Asset ClassWeights 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%

18 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]VolatilityStocksBondsRetailOfficeIndustrialResidentialOther 5.00%5.28%2%60%0% 7%30% 8.00%5.51%0%46%0% 37%17% 11.00%6.79%0%30%0% 66%5%

19 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


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