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1

What is correlation

Correlation measures how returns move in relation to each other. It is between +1 (returns always move together) and -1 (returns always move in opposite way)

2

Skewness

Skewness for a normal distribution is zero, and any symmetric data
should have a skewness near zero
• Negative values for the skewness indicate data that are skewed left
• Positive values for the skewness indicate data that are skewed right

3

Positive and negative Kurtosis

- Positive excess kurtosis indicates a "peaked" distribution
- Negative excess kurtosis indicates a "flat" distribution

4

Leptocurtic Distribution

Leptocurtic Distribution - K > 3
A distribution with wide tails and a tall narrow peak is called leptokurtic
Compared with a normal distribution, a larger fraction of the returns are at the
extremes rather than slightly above or below the mean of the distribution

5

Platykurtic Distribution

Platykurtic Distribution - K

6

Which returns are better Leptocurtic or Platykurtic

Leptocurtic

7

Why Leptocurtic Returns?

- Low probability of extreme outcomes
- Regulatory process (e.g. managed exchange rate) dampens moderately
deviant returns, forcing them closer to the mean than they would have been
otherwise

8

Simple diversification

- Invest an equal amount in each of N assets
• Portfolio weight 1/N
- Select the assets randomly
- The portfolio is well-diversified if N is reasonably large and fully
diversified if N → ∞

9

More advanced diversification

- Pick assets and determine optimal weights using the variance
covariance structure of the returns
• Exploits the trade-off between risk and return by using a
maximizing criterion – e.g. expected utility maximization

10

Why Portfolio variance equals
the average covariance

- Gauges the systematic risk
that affects all assets
- Unique risk (individual variances)
diversified away

11

Diversification

Strategy designed to reduce risk by spreading
the portfolio across many investments.

12

Unique Risk

Risk factors affecting only that firm
- Also called “diversifiable risk”

13

Market Risk

Economy-wide sources of risk that affect the
overall stock market
- Also called “systematic risk”
- Reason why stocks have a tendency to move together – common factor affecting all stocks

14

What does correlation measure

Correlation measures how returns move in relation to each other