burning0spear

Which measure of central tendency can be used for both numerical and categorical variables?

A) Mean.

B) Median.

C) Mode.

---

The mode is the only choice that makes sense since you cannot take an average or median of categorical data such as bond ratings (AAA, AA, A, etc.) but the mode is simply the most frequently occurring number or category.

burning0spear

For the last four years, the returns for XYZ Corporation’s stock have been 10.4%, 8.1%, 3.2%, and 15.0%. The equivalent compound annual rate is:

A) 9.2%.

B) 9.1%.

C) 8.9%.

---

(1.104 × 1.081 × 1.032 × 1.15)0.25 − 1 = 9.1%

burning0spear

What is the compound annual growth rate for stock A which has annual returns of 5.60%, 22.67%, and -5.23%?

A) 7.08%.

B) 6.00%.

C) 8.72%.

---

Compound annual growth rate is the geometric mean. (1.056 × 1.2267 × 0.9477)1/3 – 1 = 7.08%

burning0spear

Find the mean, median, and mode, respectively, of the following data:

3, 3, 5, 8, 9, 13, 17

A) 8; 8.28; 3.

B) 8.28; 8; 3.

C) 3; 8.28; 8.

---

Mean = (3 + 3 + 5 + 8 + 9 + 13 + 17) / 7 = 8.28; Median = middle of distribution = 8 (middle number); Mode = most frequent = 3.

burning0spear

An investor has a $15,000 portfolio consisting of $10,000 in stock A with an expected return of 20% and $5,000 in stock B with an expected return of 10%. What is the investor’s expected return on the portfolio?

A) 12.2%.

B) 7.9%.

C) 16.7%.

---

Find the weighted mean where the weights equal the proportion of $15,000. [(10,000 / 15,000) × 0.20] + [(5,000 / 15,000 × 0.10] = 16.7%.

burning0spear

An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. If last year’s return on cash was 2.0%, the return on bonds was 9.5%, and the return on stock was 25%, what was the return on the investor’s portfolio?

A) 36.50%.

B) 18.05%.

C) 22.30%.

---

Find the weighted mean of the returns. (0.10 × 0.02) + (0.30 × 0.095) + (0.60 × 0.25) = 18.05%

burning0spear

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

A) Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.

B) A normal distribution has excess kurtosis of three.

C) The mean and variance completely define a normal distribution.

---

Even though normal curves have different sizes, they all have identical shape characteristics. The kurtosis for all normal distributions is three; an excess kurtosis of three would indicate a leptokurtic distribution. Both remaining choices are true.

burning0spear

An investor has the following assets:

• $5,000 in bonds with an expected return of 8%.
• $10,000 in equities with an expected return of 12%.
• $5,000 in real estate with an expected return of 10%.

What is the portfolio's expected return?

A) 10.00%.

B) 11.00%.

C) 10.50%.

---

Expected return is the weighted average of the individual expected values. The expected return is: [(5,000) × (10.00) + (5,000) × (8.00) + (10,000) × (12.00)] / 20,000 = 10.50%.

burning0spear

A portfolio is equally invested in Stock A, with an expected return of 6%, and Stock B, with an expected return of 10%, and a risk-free asset with a return of 5%. The expected return on the portfolio is:

A) 7.0%.

B) 8.0%.

C) 7.4%.

---

(0.333)(0.06) + (0.333)(0.10) + 0.333(0.05) = 0.07

burning0spear

Which of the following statements about the arithmetic mean is least accurate?

A) The arithmetic mean of a frequency distribution is equal to the sum of the class frequency times the midpoint of the frequency class all divided by the number of observations.

B) If the distribution is skewed to the left then the mean will be greater than the median.

C) The arithmetic mean is the only measure of central tendency where the sum of the deviations of each observation from the mean is always zero.

---

If the distribution is skewed to the left, then the mean will be less than the median.