week 2

Question 1

problem with standard deviation

Answer 1

does not distinguish between upside and downside risk

investors are concerned about downside risk.

Question 2

although standard deviation does not distinguish between upside and downside risk, why is it still a reasonable measure of risk?

Answer 2

as long as probability distribution is more or less symmetric about the mean, variance/standard deviation is a reasonable measure of risk

If returns are normally distributed, expected return and standard deviation perfectly describe the range of possible outcomes.

Question 3

The process of investment management/portfolio selectoin is dramatically simplified if asset returns are normally distributed

why?

Answer 3

The distribution is completely described by its mean and standard deviation;

The risk of the investment is fully described by the standard deviation of its returns;

Portfolios comprising stocks with normally distributed returns will also have normally distributed returns, meaning the preceding comments will apply equally to such portfolios; and,

The Sharpe ratio is a complete measure of portfolio performance and thus a tool for investment comparisons.

Question 4

If the return distribution is positively skewed and negatively skewed?

Answer 4

standard deviation will overestimate risk;

Conversely, and of even greater concern, if the return distribution is negatively skewed, standard deviation will underestimate risk; and,

Question 5

When return distributions exhibit “fat tails

Answer 5

standard deviation will underestimate the likelihood of extreme events i.e. large gains and, more concerning, large losses occurring.