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