Quantitative Methods Flashcards
A portfolio has an expected return of 12% and a standard deviation of 15%. What is the portfolio’s coefficient of variation?
A. 0.83
B. 1.25
C. 1.87
D. 2.50
B - 1.25
The coefficient of variation is calculated by dividing the standard deviation by the expected return
CofV = 15% / 12%
1.25
What is the difference between a sample and a population?
A sample is a smaller representative group taken from a larger population. Analysis of a sample can be used to make inferences about the entire population
What are common measures of dispersion?
Measures of dispersion quantify the spread or variability of data. Stand Deviation and Range are common measures
A portfolio manager has an expected return of 10% and a standard deviation of 15%. The risk-free rate is 2%. What is the portfolio’s Sharpe Ratio?
The Sharpe Ratio is calculated as:
(Portfolio Return - Risk-Free Rate) / Standard Deviation
Therefore,
(10% - 2%) / 15% = 0.53
What statistical measure is most appropriate for describing central tendency of a dataset with extreme outliers?
The median is the most appropriate because it is not influenced by extreme values. The mean is sensitive to outliers while the mode and standard deviation describe frequency and dispersion
What is not a measure of dispersion?
A. Variance
B. Standard Deviation
C. Mean
D. Range
E. Interquartile Range
C - Mean
The mean is a measure of central tendency, indicating the average value of a dataset. Dispersion measures, such as variance, standard deviation, range, and interquartile range, describe the spread or variability of data points around central tendency
A portfolio has an expected return of 12% and a standard deviation of 18%. The risk-free rate is 3%. What is the portfolio’s Sharpe Ratio?
(12% -3%) / 18%
(0.12 - 0.03) / 0.18 = 0.50
What is the future value of an investment of $10,000 if it earns an annual interest rate of 8%, compounded quarterly, for 5 years
The future value of an investment that earns an annual interest rate of 8 %, compounded quarterly, for 5 year is calculated as
FV = PV x (1 + r/n)^(n x t)
where PV is present value
r is the interest rate
n is the number of compounding periods
t is the number of years
FV - $10000 x (1 + 0.08/4)^(4 x 5) =
$14,859.47
What is t6he Present Value of a $5000 payment to be received in 8 years if the discount rate is 6%?
The present value of a future cash flow is calculated as:
PV = FV / (1 + r)^ n
where FV is future value
r is the discount rate
n is the number of years
PV = $5000 / (1 + 0.06)^8 =
$3137.06
What measure of central tendency is most affected by extreme values?
The mean is the arithmetic average of a set of values and is calculated by adding up all the values and dividing by the total number of values. It is highly sensitive to extreme values because it takes into account all the values in the dataset, including outliers. Therefore, the mean can be significantly affected by extreme values, which can distort its value
What measure of dispersion is most affected by extreme values?
The standard deviation measure the dispersion of a set of values around the mean. It takes into account all the values in the dataset, including outliers. As such, extreme values can have a significant impact on the standard deviation, causing it to increase or decrease depending on the direction of the outlier. In contrast, the range and interquartile range are less sensitive to extreme values
What graphs are best used for comparing the frequency distribution of two datasets?
A histogram is a graph that displays the frequency distribution of a set of data. It consists of a series of adjacent rectangles, where the width of each rectangle represents the interval of values and the height represents the frequency of observations within that interval. A histogram is particularly useful for comparing the frequency distribution of two or more datasets, as it allows for a visual comparison of the shape, central tendency, and dispersion of each distribution.
A stock has a 70% chance of returning to 10% and a 30% chance of returning to -5%. What is the expected return of the stock?
The expected return of the stock is calculated by multiplying each possible return by its probability and summing the results.
In this case, the expected return is: Expected return = (0.7 x 0.10) + (0.3 x -0.05) = 0.07 - 0.015 = 0.055 = 5.5%
An investor has portfolio of two stocks, Stock A and Stock B. The probability of Stock A increasing in value on any given day is 0.6, and the probability of Stock B increasing on any given day is 0.4. What is the probability that at least one of the stocks will increase in value on any given day?
To calculate the probability that at least one of the stocks will increase in value on a given day, we can use the complement rule. The probability that neither stock will increase in value is:
P(neither) = P(A does not increase) * P(B does not increase) = (1 - 0.6) * (1 - 0.4) = 0.4 * 0.6 = 0.24 Therefore, the probability that at least one of the stocks will increase in value is:
P(at least one) = 1 - P(neither) = 1 - 0.24 = 0.76
A company produces widgets with a mean weight of 10 grams and a standard deviation of 2 grams. What is the probability that a randomly selected widget will weigh between 8 and 12 grams?
C. Since the weight of widgets is normally distributed with a mean of 10 grams and a standard deviation of 2 grams, we can use the standard normal distribution to find the probability that a randomly selected widget will weigh between 8 and 12 grams. First, we need to standardize the values of 8 and 12 grams using the formula:
z = (x - mean) / standard deviation So, z for 8 grams is: z = (8 - 10) / 2 = -1 And z for 12 grams is: z = (12 - 10) / 2 = 1 Next, we use a standard normal distribution table to find the area between z = -1 and z = 1, which is 0.6827. Therefore, the probability that a randomly selected widget will weigh between 8 and 12 grams is 0.6827.
A distribution has a kurtosis of 3. this indicates that the distribution is ?
Kurtosis measures the peakedness or flatness of a distribution relative to the normal distribution. A kurtosis of 3 indicates that the distribution is more peaked than the normal distribution (which has a kurtosis of 0), and is therefore leptokurtic.
What is true about normal distribution?
It is symmetric and unimodal. The normal distribution, also known as the Gaussian distribution or the bell curve, is a continuous probability distribution that is characterized by its symmetric and unimodal shape. The curve is symmetric around its mean and has a bell-shaped appearance. It is not positively skewed, which means that its tail is not longer on the right side. The normal distribution has a kurtosis of zero, which means that it has the same level of peakedness as the standard normal distribution. It is a continuous distribution, which means that it can take on any value within a range, and is not a discrete distribution.
A stock has a 70% chance of returning to 10% and a 30% chance of returning to -5%. What is the expected return of the stock?
A portfolio has an expected return of 15% and a standard deviation of 20%. The risk-free rate is 4%. What is the portfolio’s Sharpe Ratio?
