Quantitative Methods II

Question 1

Descriptive vs. inferential

Answer 1

1. Descriptive: summarize large datasets

2. Inferential: forecasts/estimates of population based on statistical characteristics of a sample.

Question 2

Measurement scales (NOIR)

Answer 2

1. Nominal - no order
2. Ordinal - categorized
3. Interval - equal distance, no zero
4. Ratio - equal w/ true zero

Question 3

Median & Mode

Answer 3

1. Median - midpoint when arranged from lowest to highest.

2. Mode - occurs most often

Question 4

Geometric mean

Answer 4

Think compounded/annualized returns, same concept

Question 5

Harmonic mean

Answer 5

N / [sum(1/xi)]

Question 6

Volatility and means?

Answer 6

harmonic < geometric < arithmetic

Question 7

Percentile formula

Answer 7

(N+1) * (percentile / 100)

Question 8

Mean absolute deviation (MAD)

Answer 8

Sum[abs(X - Xbar)] / n

Question 9

Variance

Answer 9

Sum[(X - Xbar)^2] / n

Note: use n - 1 for sample

Question 10

Standard deviation

Answer 10

square root of variance

Question 11

Chebyshev’s inequality

Answer 11

% of observations within k standard deviations of the mean is at least: 1 - 1/k^2

E.g. +-2stdev = 1 - 1/2^2 = 0.75

Question 12

Coefficient of variation (CV)

Answer 12

CV = standard deviation of x / average value of x

Measures relative dispersion

Question 13

Sharpe ratio

Answer 13

(portfolio return - risk free return) / standard dev. of portfolio

Question 14

Positive skew

Answer 14

Outliers in the upper region or right tail

Mode < median < mean

Question 15

Negative skew

Answer 15

Outliers int he lower tail

Mean < median < mode

Question 16

Skew formula

Answer 16

(1/n) * [Sum((X-Xbar)^3) / stdev^3]

Positive = positive skew, etc

> 0.5 is significant

Question 17

Excess kurtosis

Answer 17

Normal distribution = 3

Positive (>3) = leptokurtic i.e. more peaked

> 1 is rather large

Question 18

Kurtosis formula

Answer 18

(1/n) * [Sum((X-Xbar)^4) / stdev^4]