Question

Risk in future financial returns can be measured in terms of dispersion about some

expected return. Answer the following in this regard ...

a)

How do we calculate expected return?

b)

How do we measure dispersion?

c)

How might the distribution vary from normal?

d)

W

hat are the risk implications of a skewed distribution?

e)

What are the risk implications of a distribution with fat tails?

Answer 1

(a): Expected return is computed by multiplying potential outcomes by the chances or probability of these outcomes occurring. The total of all the values are then added to get the expected return. Its formula is: Expected Return = SUM (Returni x Probabilityi)

(b): Dispersion is the range of potential outcomes of investments based on historical volatility or returns. We measure dispersion using metrics like range, variance, and standard deviation. In finance dispersion means the range of possible returns on an investment. Dispersion in finance is used to measure the risk inherent in a particular security. In finance we use metrics of alpha and beta. Alpha measures risk-adjusted returns while beta measures returns relative to a benchmark index.

(c ): A distribution may vary from normal if it is skewed. For a distribution that varies from normal distribution the mean, median and mode are not all equal. When a distribution varies from normal distribution then there will not be a symmetrical bell shaped curve.

(d): A skewed distributions give rise to a risk that is referred to skewness risk. Mean and median are different. As such when computing ‘value at risk’ in finance the presence of skewness risk leads to technical implications. If skewness risk is ignored then the value of risk calculations will not be proper and will be flawed.

(e): The risk implications of a distribution with fat tails are that a probability is present that an investment can move beyond three standard deviations. The distribution of returns in this case will be not normal and there will always be a probability (it can be small) that an investment will move more than three standard deviations from the mean.