JustasS

Tracking error for a portfolio is best described as the:

A) sample mean minus population mean.

B) portfolio return minus a benchmark return.

C) standard deviation of differences between an index return and portfolio return.

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Tracking error is the difference between the total return on a portfolio and the total return on the benchmark used to measure the portfolio’s performance. The difference between a sample statistic and a population parameter is sampling error. The standard deviation of the difference between a portfolio return and an index (or any chosen benchmark return) is more often referred to as tracking risk.

JustasS

A portfolio begins the year with a value of $100,000 and ends the year with a value of $95,000. The manager’s performance is measured against an index that declined by 7% on a total return basis during the year. The tracking error of this portfolio is closest to:

A) −2%.

B) −5%.

C) 2%.

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Tracking error is the portfolio total return minus the benchmark total return. The portfolio return is ($95,000 − $100,000) / $100,000 = −5%. Tracking error = −5% − (−7%) = +2%.

JustasS

A discount brokerage firm states that the time between a customer order for a trade and the execution of the order is uniformly distributed between three minutes and fifteen minutes. If a customer orders a trade at 11:54 A.M., what is the probability that the order is executed after noon?

A) 0.750.

B) 0.500.

C) 0.250.

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The limits of the uniform distribution are three and 15. Since the problem concerns time, it is continuous. Noon is six minutes after 11:54 A.M. The probability the order is executed after noon is (15 − 6) / (15 − 3) = 0.75.

JustasS

The probability density function of a continuous uniform distribution is best described by a:

A) line segment with a curvilinear slope.

B) line segment with a 45-degree slope.

C) horizontal line segment.

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By definition, for a continuous uniform distribution, the probability density function is a horizontal line segment over a range of values such that the area under the segment (total probability of an outcome in the range) equals one.

JustasS

Consider a random variable X that follows a continuous uniform distribution: 7 ≤ X ≤ 20. Which of the following statements is least accurate?

A) F(21) = 0.00.

B) F(12 ≤ X ≤ 16) = 0.307.

C) F(10) = 0.23.

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F(21) = 1.00 The probability density function for a continuous uniform distribution is calculated as follows: F(X) = (X – a) / (b – a), where a and b are the upper and lower endpoints, respectively. (If the given X is greater than the upper limit, the probability is 1.0.) Shortcut: If you know the properties of this function, you do not need to do any calculations to check the other choices.
The other choices are true.

• F(10) = (10 – 7) / (20 – 7) = 3 / 13 = 0.23
• F(12 ≤ X ≤ 16) = F(16) – F(12) = [(16 – 7) / (20 – 7)] − [(12 – 7) / (20 – 7)] = 0.692 − 0.385 = 0.307

JustasS

A random variable follows a continuous uniform distribution over 27 to 89. What is the probability of an outcome between 34 and 38?

A) 0.0645.

B) 0.0546.

C) 0.0719.

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P(34 ≤ X ≤ 38) = (38 − 34) / (89 − 27) = 0.0645

JustasS

If X has a normal distribution with μ = 100 and σ = 5, then there is approximately a 90% probability that:

A) P(93.4 < X < 106.7).

B) P(90.2 < X < 109.8).

C) P(91.8 < X < 108.3).

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100 +/- 1.65 (5) = 91.75 to 108.25 or P ( P(91.75 < X < 108.25).

JustasS

Which of the following statements about a normal distribution is least accurate?

A) Approximately 34% of the observations fall within plus or minus one standard deviation of the mean.

B) The distribution is completely described by its mean and variance.

C) Kurtosis is equal to 3.

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Approximately 68% of the observations fall within one standard deviation of the mean. Approximately 34% of the observations fall within the mean plus one standard deviation (or the mean minus one standard deviation).

JustasS

A normal distribution is completely described by its:

A) mean, mode, and skewness.

B) median and mode.

C) variance and mean.

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By definition, a normal distribution is completely described by its mean and variance.

JustasS

In a normal distribution, the:

A) mean is less than the mode.

B) mean is greater than the median.

C) median equals the mode.

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In a normal distribution, the mean, median, and mode are all equal.