Investment risk analysis. The risk of a portfolio of financial assets is sometimes called investment risk. In general, investment risk is typically measured by computing the variance or standard deviation of the probability distribution that describes the decision maker’s potential outcomes (gains or losses). The greater the variation in potential outcomes, the greater the uncertainty faced by the decision maker; the smaller the variation in potential outcomes, the more predictable the decision maker’s gains or losses. The two discrete probability distributions given in the next table were developed from historical data. They describe the potential total physical damage losses next year to the fleets of delivery trucks of two different firms.

Firm A |
Firm B |
||

Loss Next Year |
Probability |
Loss Next Year |
Probability |

$ 0 |
.01 |
$ 0 |
.00 |

500 |
.01 |
200 |
.01 |

1,000 |
.01 |
700 |
.02 |

1,500 |
0.02 |
1,200 |
0.02 |

2,000 |
.35 |
1,700 |
.15 |

2,500 |
.30 |
2,200 |
.30 |

3,000 |
.25 |
2,700 |
.30 |

3,500 |
.02 |
3,200 |
.15 |

4,000 |
.01 |
3,700 |
.02 |

4,500 |
.01 |
4,200 |
.02 |

5,000 |
.01 |
4,700 |
.01 |

a. Verify that both firms have the same expected total physical damage loss.

b. Compute the standard deviation of each probability distribution and determine which firm faces the greater risk of physical damage to its fleet next year.

Step 1 of 3:

Here the experiment under consideration is study of investment risk.

The data regarding the total physical damages losses next year for the fleets of the delivery trucks for the two firms is given.

This data is developed from the historical data.

Firm A |
Firm B |
||

Loss next year |
Probability |
Loss next year |
Probability |

$0 |
0.01 |
$0 |
0 |

500 |
0.01 |
200 |
0.01 |

1,000 |
0.01 |
700 |
0.02 |

1,500 |
0.02 |
1,200 |
0.02 |

2,000 |
0.35 |
1,700 |
0.15 |

2,500 |
0.3 |
2,200 |
0.30 |

3,000 |
0.25 |
2,700 |
0.30 |

3,500 |
0.02 |
3,200 |
0.15 |

4,000 |
0.01 |
3,700 |
0.02 |

4,500 |
0.01 |
4,200, |
0.02 |

5,000 |
0.01 |
4,700 |
0.01 |

Using this data we need to find the required values.

Step 2 of 3:

(a)

Here we need to find the expected total physical damage loss for the two firms and we have to check whether both the firms have same expected loss.

For the firm A, the expected loss is given by

E(X)=xp(x)

=0(0.01)+500(0.01)+1000(0.01)+1500(0.02)+2000(0.35)+2500(0.3)+

3000(0.25)+3500(0.02)+4000(0.01)+4500(0.01)+5000(0.01)

=0+5+10+30+700+750+750+70+40+45+50

=2450

For the firm B,

E(X)=xp(x)

=0(0.00)+200(0.01)+700(0.02)+1200(0.02)+1700(0.15)+2200(0.30)+

2700(0.30)+3200(0.15)+3700(0.02)+4200(0.02)+4700(0.01)

=0+2+14+24+255+660+810+480+74+84+47

=2450

Thus, the two firms have the same expected physical damage loss.