Quants Flashcards
How do you calculate the median and first quartile of a data set?
Median is the 1/2*(n+1)th value
First quartile is 1/4*(n+1)th
How do you calculate variance and standard deviation?
Variance is the sum of the squared differences between the data points and the mean divided by the degrees of freedom
Standard deviation is the square root of the variance
How do you calculate the coefficient of variation, and what does it measure when considering returns of an investment?
Standard deviation / Mean
It measures the amount of risk you take per unit of return
What is the main feature of a normally distributed dataset?
The mean, median and mode are all equal to each other
What is meant by a positively skewed distribution?
The mean is in the right tail of the distribution, and is greater than the median, which is greater than the mode. Distributions like this indicate the presence of extreme outliers above the mean.
Mean > Median > Mode
What is the difference between kurtosis and excess kurtosis?
A normal distribution has a kurtosis of 3. Kurtosis above or below this is called excess kurtosis. It is possible to have negative excess kurtosis.
Out of platykurtic and leptokurtic distributions, which indicates the presence of more extreme datapoints?
Leptokurtic distribution (also sometimes called fat-tailed distribution)
How do you calculate the variance and the standard deviation of expected returns using the BAII?
Enter the expected returns into the data function and weight them by the probability of them occurring (frequency/ y), then go to the 1-V stat function and scroll to the population standard deviation. Square it for variance.
What is the central limit theorem?
The central limit theorem states that the distribution of sample means of a population will be approximately normal, with the population mean as it’s mean. This is true regardless of the distribution of the population.
(Note that this is only true for sufficiently large samples - minimum 30)
How do you calculate the standard error of a sample?
Standard error is the standard deviation divided by the square root of the sample size.
SE = SD / √n
I believe that the mean of a population is greater than 10. When testing this, what would my null hypothesis be?
The null hypothesis must ALWAYS have an equals sign in it, so in this case we would set the assumption that the mean is greater than 10 as the alternate hypothesis, and that it is equal to or less than 10 as the null hypothesis.
Ho: Mean ≤ 10
Ha: Mean > 10
If you want to test if the variances of two populations are equal, what test would you use?
f-test
What is the decision rule?
If the test stat is great than the critical stat, reject the null hypothesis
If you want to test if the variance of a single population is equal to the sample variance, what test would you use?
Chi-squared test
What is a type-1 error?
Rejecting the null when it is true
What is a type-2 error?
Failing to reject (accepting) the null when it is false
What are the critical test statistics for a one-tailed test at a 10%, 5%, and 1% significance level?
(approximately)
10% - 1.3
5% - 1.6
1% - 2.3
What are the critical test statistics for a two-tailed test at a 10%, 5%, and 1% significance level?
(approximately)
10% - 1.6
5% - 2.0
1% - 2.6
What is the ‘power’ of a test?
The probability of not making a type-2 error (1 - β)
Would you reject a null hypothesis if the test statistic was equal to the critical statistic?
No. You only reject the null if the test stat exceeds the critical stat.
