Question

• Explain the four moments with respect to investing and specifically, to risk-return.  How does this link to normality assumptions?  What information does each contain?

Answer 1

There are 4 moments with respect to investing namely, 1. Mean, 2. Variance, 3. Skewness and 4. Kurtosis.

1. Mean : This gives you the average value of the returns over a period of time by taking a weighted average value of the returns over the interval. Here, weights can be probabilities assigned for the respetive returns. So, basically Mean alue of return gives you an expected average rate of return over a period of time.

2. Variance: This gives you the spread of the returns from mean value of returns. This basically gives us an idea of deviations of random vairable (returns) from mean value.

3. Skewness: Skewness gives us an idea of ow the values of random vairable (reurns) are spread around mean returns, whether values are positively skewed (most of the values falling on right hand side of mean returns), negatively skewed (most of the values falling on left hand side of returns) or zero skewness (prefect normal distribution with values lying evenly around mean value of return).

4. Kurtosis: Kurtosis gives us an idea of how fat are the tails of distributions from the mean value, explaining us how frequent extreme deviations or outliers are from the mean value.

following are 3 categories of Kurtosis

) A value of zero (Mesokurtic) implies the tails die down similar to normal distributions

b) A negative value (Platykurtic) implies thinner tails and flatter tops (for symmetric distributions) or more extreme deviations from the mean (e.g. Uniform distribution)

c) A positive value (Leptokurtic) implies heavier tails and peakier tops giving us extreme values