Question

In a normal economy, Dracula’s stock is expected to give 15.7% return. During an economic recession the stock would give -11.6 % return. Dracula thinks normal economy will prevail with 80% probability and 20% probability of a recession. What is Dracula’s stocks returns’ variance?

Answer #1

Variance is a measure of how spread out a data set is.

To calculate variance, start by calculating the mean, or average, of your sample. Then, subtract the mean from each data point, and square the differences. Next, add up all of the squared differences. Finally, divide the sum by n , where n equals the total number of data points in your sample.

Scenario | Return | Probability | Multiple |

Normal | X | 0.8 | 0.8X |

Recession | -11.6 | 0.2 | -2.32 |

Total | 0.8X-2.32 |

We know the expected return to be 15.7% i.e 0.8X -2.32 = 15.7

i.e X = 22.525%

Scenario | Return | Probability | Multiple | Square of Difference from Mean |

Normal | 22.525 | 0.8 | 18.02 | 5.3824 |

Recession | -11.6 | 0.2 | -2.32 | 5.3824 |

Total | 15.7 | 10.7648 |

Variance = Square of difference from Mean / Number of samples

= 10.7648/2= **5.3824**

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