Question

You invest in a stock over a 5-year period. The returns in each of the 5 years are: 10%, 1%, -12%, 4%, and 20%. For all questions, answer should be given in terms of %, and rounded to one decimal place.

1) What is the 5-year Holding Period Return (HPR) of your stock investment? (in %, 1 decimal place)

2) What is the compound annual growth rate of the investment over the 5-year period? (in %, 1 decimal place)

Answer #1

1)

Holding Period Return = [(1 + R1)(1 +R2)(1 + R3)(1 + R4)(1 + R5)] - 1

Holding Period Return = [(1 + 0.1)(1 +0.01)(1 - 0.12)(1 + 0.04)(1 + 0.2)] - 1

Holding Period Return = [1.1 * 1.01 * 0.88 * 1.04 * 1.2] - 1

Holding Period Return = [1.220145] - 1

**Holding Period Return = 0.220 or 22.0%**

2)

compound annual growth rate = [(1 + R1)(1 +R2)(1 + R3)(1 + R4)(1
+ R5)]^{1/n} - 1

compound annual growth rate = [(1 + 0.1)(1 +0.01)(1 - 0.12)(1 +
0.04)(1 + 0.2)]^{1/5} - 1

compound annual growth rate = [1.1 * 1.01 * 0.88 * 1.04 *
1.2]^{1/5} - 1

compound annual growth rate = [1.220145]^{1/5} - 1

compound annual growth rate = 1.0406 - 1

**compound annual growth rate = 0.041 or 4.1%**

Assume these are the stock market
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Year
Stock Market Return
T-Bill Return
Year 1
?
33.03
5.00
Year 2
32.60
1.30
Year 3
13.66
.31
Year 4
4.88
.08
Year 5
20.66
.10
a.
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1
0.340
33.20%
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2
0.420
8.40%
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0.24
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Year
Treasury Bills
Inflation
1
10.45%
12.55%
2
11.36
16.00
3
9.06
10.29
4
8.34
7.97
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8.88
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11.23
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14.11
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15.97
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