Question

Suppose the average return on Asset A is 6.8 percent and the standard deviation is 8 percent, and the average return and standard deviation on Asset B are 3.9 percent and 3.3 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.

a. What is the probability that in any given year, the return on Asset A will be greater than 10 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b. What is the probability that in any given year, the return on Asset B will be greater than 10 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

c-1. In a particular year, the return on Asset A was −4.35 percent. How likely is it that such a low return will recur at some point in the future? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c-2. Asset B had a return of 10.6 percent in this same year. How likely is it that such a high return will recur at some point in the future? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer #1

The formula for Normal Distribution function in excel is NORMDIST(value of reference,mean, Standard deviation, True)

By definition, the result that a NORMDIST function gives indicates the less than referene value probability. Hence for identifying the value of more than 10% in Asset A, we have to reduce the value arrived using NORMDIST function by 1. i.e 1-NORMDIST.

Value of Reference | Mean | SD | NORMDIST Result | Greater than value | Final result | |

Question 1 Asset A | > 10% | 6.80% | 8% | 0.66 | =1-0.66 | 0.34 |

Question 1 Asset A | <0% | 6.80% | 8% | 0.20 | 0.20 | |

Question 2 Asset B | > 10% | 3.90% | 3% | 0.97 | =1-0.97 | 0.03 |

Question 2 Asset B | <0% | 3.90% | 3% | 0.12 | 0.12 |

In a continuous distribution, probability of any particular single value from a continuous distribution is always zero. Hence the probability of getting a return of -4.35% from Asset A or 10.6% from Asset B is Zero. Answer to Question C-1 and C-2 is Zero.

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