Portfolio risk versus returns: the statistics

Caveat: This is an advanced investing topic. Past performance does not predict future performance.

Portfolio returns are expected to follow a normal distribution. Deviations from this pattern are a form of investment risk, described below.

Tails
(insert image - Gaussian distribution showing tails, etc.)
 * Fat tails
 * Long tails
 * Left tale risk
 * Right tale opportunity

Barbell strategy
Bonds: An investment strategy that concentrates holdings in both very short-term and extremely long-term maturities. When plotted on a timeline, the shape appears as a barbell. The reasoning behind this strategy is that it allows one portion of the portfolio to achieve high yields while the other portion minimizes risk.

Stocks: An investment strategy that concentrates holdings in both large-cap and small-cap funds, which minimizing mid-cap funds. When plotted against market capitalization (market "cap"), the shape appears as a barbell.

Swans

 * Understanding all the talk about "tails", forum discussion starting point about The Black Swan (Taleb book)
 * White swan
 * Gray swan
 * Black swan

Statistics discussions

 * Median of a distribution and how skewness affects the relationship between the mean and the median
 * Correlations and confidence intervals

Log-normal distributions
The proper distribution for a normal model would be a log-normal distribution... The reason for the log-normal distribution is that changes are relative to other changes. The probability that the market drops by 20% in the second half of the year is relatively independent of what happened in the first half of the year, but it is a larger point loss if the first half of the year was a bull market.
 * Why for annual returns the log normal distribution, rather than the normal distribution, should be used

To do
The first four moments of a distribution: Investors define volatility to be the standard deviation. For example, William F. Sharpe defines the Return per Unit of Risk (Sharpe Ratio) as some Return divided by the Standard Deviation.
 * Expected (mean) return
 * Standard deviation (volatility)


 * Skewness
 * Kurtosis