Question

Q1) A stock earned annual returns of 5%, 10%, -7%, and 16% for the last four years.

a) What is the arithmetic average return for the stock over the last four years?

b) What is the standard deviation of the returns over the last four years?

c) What is the geometric average return for the stock over the last four years?

d) What is the holding period return for the stock over the last four years?

e) What would have been the holding period return for the stock if it had earned the arithmetic average return every year for the last four years?

f) What would have been the holding period return for the stock if it had earned the geometric average return every year for the last four years?

g) Compare your answers for the holding period returns in parts (e) and (f) with the actual holding period return in part (d) and comment on which average (arithmetic or geometric) is the better indicator of longer-term returns.

Answer #1

Year |
Stock's
Return |

1 | 5% |

2 | 10% |

3 | -7% |

4 | 16% |

**a) Arithematic Average** = (5 + 10 - 7 +16) / 4
**= 6%**

**b) Standard Deviation**

**c) Geometric Averga:**

Geometric mean cannot be calculated for negative return, as it will be impossible to calculate it's under-root.

**d) Holding Period Return**

HPR = [(1+5%)*(1+10%)*(1-7%)*(1+16%)] =
**24.6%**

AHPR = (1+0.246)^(1/4) - 1 = **5.65%**

**NOTE:** Please ask max 4 subparts in a
question.

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___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
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Year Return
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2016
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2017
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2018
0.15 (or 15%)
2019
0.25 (or 25%)
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