## Risk diversification example portfolio of projects

As an investor you have a portfolio with real estate objects with estimated characteristics as shown in Table 2.3.

You first add the portfolio characteristics to the MCS software or alternatively open the sample project [O e_mcs-3].

You can check the portfolio's characteristics by clicking either the 'Input' or 'PortFolio Input' tab. This will show output as shown in Figure 2.5.

You can then click the 'Perform Portfolio Simulation' button to calculate the probability distribution of the expected return (profit) for the portfolio.

The output (Fig. 2.6) shows that the portfolio has a mean profit of 41% with a standard deviation of 0.6%. The probability P that the profit will exceed a threshold R, given by formula (4.1) (page 48) of Open Design, a Collaborative Approach to Architecture, is represented in the S-shaped graph. Note that the mean of 41% corrresponds with a 50% probability that the profit will exceed that value.

Adding a new project to the portfolio should result in a higher standard deviation and a higher profit. We choose a profit threshold having a 90% (cumulative) probability, in this case a profit of 42%.

A new project is offered with the characteristics as shown in Table 2.4.

After adding this project to the existing portfolio, the probability distribution of the expected return (profit) for the portfolio can be calculated again (alternatively, open the sample project [O e_mcs-4]).

### The output is shown in Figure 2.7.

Adding the new project to the portfolio indeed results in a higher standard deviation and a higher profit. The standard deviation has risen from 0.6 to 0.8. The profit threshold having a 90% probability, has risen from 42% to 58%.

The portfolio could mainly consist of projects that are near the end of their

Table 2.4 Characteristics new real estate project

Project |
Estimate |
New |

low |
8 | |

Investment |
best |
10 |

high |
15 | |

low |
3% | |

Interest |
best |
5% |

high |
6% | |

low |
1.0 | |

Revenues |
best |
1.3 |

high |
2.0 | |

low |
1.8 | |

Rest value |
best |
2.0 |

high |
2.1 | |

Life time |
50 |

life time. It is then likely that the portfolio, as a whole, has passed it's pay-back period. This implies that the profit, as an internal rate of return, is impossible to calculate. The program then calculates the net present value of the portfolio. This also implies that choosing between a moderate return, low risk project and a high return, high risk project becomes irrelevant. In effect one is adding projects to a (virtually) new portfolio.

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