# Optimal Structure of Real Estate Portfolio Using EVA: A Stochastic Markowitz Model Using Data from Greek Real Estate Market

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

- Select the maximum return for a given level of risk;
- The least risk to a given level of return.

- Τhe probability function of the returns can be estimated by investors;
- The basic principle is to maximize the utility function of investor;
- Investors tend to avoid risk in pursuit of profit;
- Financial markets are smooth;
- The existence of transaction cost and taxes is absent.

## 3. Data

- Residential;
- Office;
- Retail.

- Athens;
- Thessaloniki;
- Rest of Greece.

^{®}is a variant of residual income marketed by Stern Stewart & Co., a New York consulting firm, with the purpose of promoting value–maximizing behaviour in corporate managers, as described by Stewart (2009):

## 4. Methodology

#### The Theoretical Point of View of Our Model

- Apartment;
- Offices;
- Retail.

- Apartment;
- Offices;
- Retail.

## 5. Estimations-Empirical Analysis

#### 5.1. Estimations

#### 5.2. Portfolio Optimization Results

## 6. Discussions and Conclusions

#### 6.1. Discussions and Key Findings

#### 6.2. Theoretical Implication-Practical Implication

#### 6.3. Restrictions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | We use the median of stock exchange listed companies on Greek Real Estate Market by ICAP database. |

2 | Cost of Capital (nyu.edu) accessed on 25 August 2022. |

3 | (bankofgreece.gr) accessed on 25 August 2022. |

4 | See note 1 above. |

5 | The corporate tax rate reduced from 24% to 22% in 2021 year. |

6 | RE/MAX 2021 (remax.gr) accessed on 25 August 2022. |

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Trend Calculation | Residential Price | Residential Rental | Office Price | Office Rental | Retail Price | Retail Rental |
---|---|---|---|---|---|---|

Constant | 0.084352 ** (0.016981) | 0.024585 ** (0.003304) | 0.099045 ** (0.026144) | 0.056284 ** (0.014164) | 0.137812 ** (0.025751) | 0.074128 ** (0.0293267) |

Dummy (Crisis) | −0.05005 ** (0.016458) | −0.021662 ** (0.003582) | −0.05338 ** (0.020369) | −0.02444 ** (0.00965) | −0.05128 ** (0.017526) | −0.079506 ** (0.0269355) |

t | −0.01737 ** (0.003061) | −0.000589 ** (0.000199) | −0.03121 ** (0.009109) | −0.02191 ** (0.004864) | −0.04314 ** (0.008759) | −0.030405 ** (0.0089870) |

${\mathrm{t}}^{2}$ | 0.000633 ** (0.000107) | - | 0.002342 ** (0.000594) | 0.00149 ** (0.000353) | 0.003123 ** (0.000601) | 0.002498 ** (0.0005930) |

${\mathrm{t}}^{3}$ | - | - | −4.6 × 10^{−5} **(1.12 × 10 ^{−5}) | −2.7 × 10^{−5} **(7.15 × 10 ^{−6}) | −6.1 × 10^{−5} **(1.17 × 10 ^{−5}) | −5.148 × 10^{−5} **(1.22826 × 10 ^{−5}) |

Method | Multiple Regression | Multiple Regression | Multiple Regression | Multiple Regression | Multiple Regression | Multiple Regression |

Observations | 30 | 30 | 30 | 30 | 30 | 30 |

R-squared | 0.8682 | 0.7134 | 0.8249 | 0.8223 | 0.8539 | 0.7084 |

R-squared Adjusted | 0.8530 | 0.6922 | 0.7969 | 0.7938 | 0.8305 | 0.6618 |

F-Statistic | 57.10521 | 33.60277 | 29.44065 | 28.91856 | 36.5238 | 15.18509411 |

**Source:**Authors’ Calculations. Note: ** indicates significant at 0.05 level.

Real Estate Return | 1 | 2 | 3 |

Expected Return | 5.46% | 7.72% | 10.19% |

Standard Deviation | 4.94% | 3.01% | 5.45% |

V-C | 1 | 2 | 3 |

1 | 0.2436% | 0.0965% | 0.2161% |

2 | 0.0965% | 0.0905% | 0.1509% |

3 | 0.2161% | 0.1509% | 0.2972% |

**Source:**Authors’ Calculations.

Lilliefors Test Results | WR1 | WR2 | WR3 |
---|---|---|---|

Sample Size | 30 | 30 | 30 |

Sample Mean | 0.05464 | 0.07720 | 0.10189 |

Sample Std Dev | 0.04935 | 0.03009 | 0.05451 |

Test Statistic | 0.1550 | 0.1080 | 0.1364 |

CVal (15% Sig. Level) | 0.1378 | 0.1378 | 0.1378 |

CVal (10% Sig. Level) | 0.1457 | 0.1457 | 0.1457 |

CVal (5% Sig. Level) | 0.1592 | 0.1592 | 0.1592 |

CVal (2.5% Sig. Level) | 0.1699 | 0.1699 | 0.1699 |

CVal (1% Sig. Level) | 0.2326 | 0.2326 | 0.2326 |

**Source:**Authors’ Calculations. Note: Bold color indicate is not significant at the respective significant level.

Constraining Value | Valid Trials | Best Value | Trial | Goal Cell Statistics | Adjustable Cells | Hard Constraints | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

(for Constraining Value) | Mean | Std. Dev. | Min. | Max. | B5 | C5 | D5 | RiskMean(B10) | E5 = 1 | |||

6.00% | 0 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |

5.50% | 69 | 4.89% | 265 | 5.51% | 4.89% | −9.85% | 23.50% | 0.0% | 10.6% | 89.4% | 5.51% | 1 |

5.00% | 182 | 3.88% | 373 | 5.00% | 3.88% | −7.09% | 19.72% | 0.0% | 31.1% | 68.9% | 5.00% | 1 |

4.50% | 299 | 3.07% | 760 | 4.50% | 3.07% | −5.51% | 15.98% | 0.0% | 51.4% | 48.6% | 4.50% | 1 |

4.00% | 447 | 2.62% | 436 | 4.00% | 2.62% | −5.14% | 12.48% | 3.3% | 65.2% | 31.5% | 4.00% | 1 |

3.50% | 595 | 2.35% | 752 | 3.54% | 2.35% | −5.02% | 11.78% | 18.0% | 55.7% | 26.3% | 3.54% | 1 |

3.00% | 681 | 2.29% | 800 | 3.25% | 2.29% | −5.50% | 11.14% | 22.7% | 58.7% | 18.7% | 3.25% | 1 |

2.50% | 728 | 2.29% | 800 | 3.25% | 2.29% | −5.50% | 11.14% | 22.7% | 58.7% | 18.7% | 3.25% | 1 |

**Source:**Authors’ Calculations.

Constraining Value | Valid Trials | Best Value | Trial | Goal Cell Statistics | Adjustable Cells | Hard Constraints | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

(for Constraining Value) | Mean | Std. Dev. | Min. | Max. | B5 | C5 | D5 | RiskStdDev(B10) | E5 =1 | |||

2.00% | 0 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |

2.50% | 48 | 3.80% | 471 | 3.80% | 2.48% | −5.94% | 11.20% | 7.7% | 65.1% | 27.2% | 2.48% | 1 |

3.00% | 292 | 4.45% | 448 | 4.45% | 3.00% | −6.98% | 13.44% | 0.0% | 53.4% | 46.6% | 3.00% | 1 |

3.50% | 400 | 4.79% | 511 | 4.79% | 3.50% | −7.56% | 15.12% | 0.0% | 39.5% | 60.5% | 3.50% | 1 |

4.00% | 532 | 5.06% | 766 | 5.06% | 3.98% | −8.55% | 16.90% | 0.0% | 28.6% | 71.4% | 3.98% | 1 |

4.50% | 632 | 5.32% | 50 | 5.32% | 4.50% | −9.69% | 19.26% | 0.0% | 18.0% | 82.0% | 4.50% | 1 |

5.00% | 788 | 5.56% | 706 | 5.56% | 5.00% | −10.73% | 21.54% | 0.0% | 8.4% | 91.6% | 5.00% | 1 |

5.50% | 1000 | 5.77% | 4 | 5.77% | 5.45% | −11.63% | 23.53% | 0.0% | 0.0% | 100.0% | 5.45% | 1 |

6.00% | 1000 | 5.77% | 4 | 5.77% | 5.45% | −11.63% | 23.53% | 0.0% | 0.0% | 100.0% | 5.45% | 1 |

6.50% | 1000 | 5.77% | 4 | 5.77% | 5.45% | −11.63% | 23.53% | 0.0% | 0.0% | 100.0% | 5.45% | 1 |

**Source:**Authors’ Calculations.

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## Share and Cite

**MDPI and ACS Style**

Petropoulos, T.; Liapis, K.; Thalassinos, E.
Optimal Structure of Real Estate Portfolio Using EVA: A Stochastic Markowitz Model Using Data from Greek Real Estate Market. *Risks* **2023**, *11*, 43.
https://doi.org/10.3390/risks11020043

**AMA Style**

Petropoulos T, Liapis K, Thalassinos E.
Optimal Structure of Real Estate Portfolio Using EVA: A Stochastic Markowitz Model Using Data from Greek Real Estate Market. *Risks*. 2023; 11(2):43.
https://doi.org/10.3390/risks11020043

**Chicago/Turabian Style**

Petropoulos, Theofanis, Konstantinos Liapis, and Eleftherios Thalassinos.
2023. "Optimal Structure of Real Estate Portfolio Using EVA: A Stochastic Markowitz Model Using Data from Greek Real Estate Market" *Risks* 11, no. 2: 43.
https://doi.org/10.3390/risks11020043