QUESTION: 589

An investor faces the following investment scenarios:

Scenario Probability Return
Bull market 60% 30%
Neutral market 30% 7%
Market crash 10% -25%

The variance of the investor's rate of return is ________.

17.6%%
4.17%%
307.4%%
6.17%%

Answer(s): C

Explanation:

The expected return equals 0.6 * 30% + 0.3 * 7% + 0.1*(-25%) = 17.6%. To calculate the variance, an easy way is to first calculate the second moment, which is the expected value of the square of the return. Thus, the second moment equals 0.6*[(30%)^2] + 0.3*[(7%)^2)] + 0.1*[(-25%)^2] = 617.2%%.
The variance of a random variable equals the second moment minus the square of the mean. In this case, the variance equals 617.2%% - 17.6%^2 = 307.4%%

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QUESTION: 590

According to Chebyshev's Theorem, what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

Cannot compute because it depends on the shape of the distribution
56%
95%
67%
None of these answers

Answer(s): D

Explanation:

Chebyshev's theorem applies regardless of the shape of the distribution. The minimum proportion that lie within k standard deviations of the mean is at least 1-[1/(k^2)]. In this case k = 1.75. k^2 = 3.0625. So we get 67%.

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QUESTION: 591

Which of the following is/are true?

The mean of a sample represents its average value.
II. The median can only be calculated if the sample contains an odd number of values.
III. The mode is not affected by extreme outliers in the data.
IV. For samples with an even number of data points, the mode is preferable to the median as a measure of central tendency.
III only
IV only
II only
I only
I & II
I, III & IV
II & III
I & III

Answer(s): H

Explanation:

Note that the mode is not affected by outliers unless an extreme value occurs frequently. In such a case, it is likely that the observed data contain large errors and hence, it must be reexamined. The median of a set with odd number of observations equals the "middle" observation. If the number of observations is even, the median is the mean of the two middle observations. Thus, II is false.
Finally, there is no reason for a rule like (IV) to hold.

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QUESTION: 592

Consider the following three investments with annual compounding:

Present value years interest rate
1.$22,500 56% per year
2.$10,000 75% per year
3.$15,000 38% per year

The future values of the 3 investments, at the ends of their investment periods, are:

$26,454, $12,067, $17,181
$23,850, $10,500, $16,200
$30,110, $14,071, $18,896
$16,813, $7,107, $11,907

Answer(s): C

Explanation:

Future value = Present value*(1+r)^N for annual compounding. Therefore, Present value years rate Future value
1.22,500 56% 22,500*(1.06)^5 = 30,110
2.10,000 75% 10,000*(1.05)^7 = 14,071
3.15,000 38% 15,000*(1.08)^3 = 18,896
Note that the future value must always be greater than the present value.

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