Statistics

Question 1

Coefficient of Variation

CV

Answer 1

Formula: CV = standard deviation/mean.

• aka: relative standard deviation

Question 2

Skewness
Limitations
Positive & Negative

Answer 2

For distributions that are non normal, the standard mean variance analysis is limited, which means standard deviation is simply less meaningful.
With a positive skew, we have fewer, but more extreme outcomes to the right of the mean. Those outcomes pull the distribution and mean to the right. For a positive skew, the standard deviation may be overestimating the risk.
With a negative skew, we have fewer, but more extreme outcomes to the left of the mean. Those outcomes pull the distribution and mean to the left. SD may underestimate risk.

Question 3

Standard Deviation %s

Answer 3

+/- 1 SD: 68.26%
+/- 2 SD: 95.44%
+/- 3 SD: 99.74%

Question 4

Semi-variance

Answer 4

• Semi-variance is the average of the squared deviations of all values less than the average or mean.

Question 5

Kurtosis

Answer 5

• if kurtosis is positive (leptokurtic) a chart will show more extreme outcomes, creating a tendency for the observations around the mean to seem great (relative to those between the mean and tails) and appearing to have a higher peak
• if kurtosis is low (platykurtic) a chart will show thinner tails (i.e., fewer extreme outliers) with a tendency for a distribution that appears to have a flatter top (less peakedness) because those observations that would otherwise be concentrated around the mean are elsewhere in the distribution;
  –
  higher kurtosis suggests greater risk than reflected in the normal distribution relied upon in the traditional mean variance framework.

Question 6

Which theory depends on a normal distribution

Answer 6

Normal distribution is considered foundational in the development of Modern Portfolio Theory.

Question 7

Disadvantages of Monte Carlo simulations

Answer 7

Generates a normal distribution where the most likely scenario is found in the middle of the events this is not always realistic and can create overconfidence which may lead to developing overly aggressive, risky portfolios; these models are not built to allow for a wide range of inputs: factors, expectations, etc.; model assumes efficient markets

Question 8

Is Multi-period Forecasting useful?

How about seasonality?

Answer 8

Benefits to multi period forecasting may include improved accuracy, consistency, and smoothing of volatility. Adjusting past performance or forecasts for demonstrated or expected impact of factors such as seasonality may be beneficial when analyzing data including specific company and industry stock returns and volatility.