problem with standard deviation
does not distinguish between upside and downside risk
investors are concerned about downside risk.
although standard deviation does not distinguish between upside and downside risk, why is it still a reasonable measure of risk?
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.
The process of investment management/portfolio selectoin is dramatically simplified if asset returns are normally distributed
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.
If the return distribution is positively skewed and negatively skewed?
standard deviation will overestimate risk;
Conversely, and of even greater concern, if the return distribution is negatively skewed, standard deviation will underestimate risk; and,
When return distributions exhibit “fat tails
standard deviation will underestimate the likelihood of extreme events i.e. large gains and, more concerning, large losses occurring.