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Answers to Questions and Problems
Using Excel:
FV = 10 * (1.045)^5 = $12.46
7.17
The future value for a continuously compounded rate is given by
equation (7.15). The rate (r) is the continuously compounded rate,
which is 9 percent or .09. The time T in the formula is 2.50. The fu-
ture value is $12.52.
FV = 10 x e rT
= 10 x e 0.09x2.5 = $12.52
Using Excel function for ex:
FV = exp(9% * 2.5) = $12.52
7.18
The arithmetic average is 1.73 percent (monthly). The geometric aver-
age is 1.64 percent. Note that a dollar invested during that year
would have grown to $1.216. If the arithmetic average is com-
pounded for a year, the future value is $1.228. However, if the geo-
metric average is compounded for a year, the future value matches the
actual experience.
|
Rate |
1 + Return |
Cumulative |
|
2.25% |
1.02 |
1.022500000 |
|
-1.75% |
0.98 |
1.004606250 |
|
8.15% |
1.08 |
1.086481659 |
|
-4.40% |
0.96 |
1.038676466 |
|
-3.30% |
0.9 |
1.004400143 |
|
3.55% |
1.04 |
1.040056348 |
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9.15% |
1.09 |
1.135221504 |
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1.85% |
1.02 |
1.156223102 |
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3.65% |
1.04 |
1.198425245 |
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2.25% |
1.02 |
1.225389813 |
|
-3.60% |
0.96 |
1.181275780 |
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2.95% |
1.03 |
1.216123415 |
Arithmetic average |
1.73% |
|
1.228417070 |
Geometric average |
1.64% |
|
1.216123415 |
Standard deviation |
15.09% |
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HEDGE FUND COURSE
ccc_mccrary_answers_225-274.qxd 10/6/04 1:47 PM Page 250
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