An annualized return is the rate of return you would expect to receive per year given a partial year’s return (e.g., 1 month) or cumulative multi-year return (e.g., 3 years) after taking into account the effects of compounding.  The formula for annualizing a return is: Ra = (1+ Ru)^(1/n) – 1, where:
  • Ra = annualized return
  • Ru = unannualized return
  • n = number of years over which the cumulative return is calculated

Example 1: You make a 1% return in January.  Your annualized return would be 12.7%.

Example 2: You make a 35% return over 3 years.  Your annualized return would be 10.5%.

Unannualized Return Calculation Annualized Return
Ru = 1% (1 month return) Ra = (1+1%)^(1/(1/12)-1 12.7%
Ru = 35% (over 3 years) Ra = (1+35%)^(1/3)-1 10.5%
Volatility is a term widely used in Finance to describe the dispersion of returns for a stock or portfolio around its mean (or average).  Volatility is commonly associated with the “riskiness” of an investment.  For example, the higher the volatility of a stock’s returns, the higher its perceived riskiness. Volatility is synonymous with standard deviation, the statistical concept used to measure variability of a data set.
Normal Distribution
Portfolio volatility is a function of the volatilities of and correlations between the individual securities in the portfolio. Volatility is calculated as the square root of the portfolio variance. Mathematically, the expression used to calculate portfolio variance is:
Variance Formula
  • σi is the standard deviation of security i
  • ωi is the weight of security i
  • ρi,j is the correlation between securities i and j
Efficiency Ratio is a measure of reward-to-risk and is similar in concept to the Sharpe Ratio. Like the Sharpe Ratio, Efficiency ratio allows you to assess whether the expected return potential of a portfolio justifies its risk.
The Sharpe Ratio is a measure of a portfolio’s risk-adjusted performance. Named after Nobel Laureate, Bill Sharpe, the ratio is calculated by subtracting the risk-free rate (e.g., 10-year U.S. Treasury bond or 3 month Treasury bill) from the rate of return for a portfolio and dividing the result by the volatility of the portfolio returns.

The Sharpe Ratio can be used to differentiate two investments with identical returns but different levels of volatility (risk). The investment with lower risk will have a higher Sharpe ratio than the other, indicating that it is a better overall investment (higher risk-adjusted return).
Correlation measures how two securities move in relation to one another. Correlation is commonly expressed as a coefficient between -1 and +1.

A correlation of +1 means the two securities move in the exact same direction. Likewise a coefficient of -1 means the two securities move in the exact opposite direction. A coefficient of 0 means the two are uncorrelated and will move completely random to one another. Generally, a coefficient of 0.7 and higher indicates strong correlation.

Example: The monthly returns of AMR (American Airlines) and UAUA (United Airlines) had a correlation of 0.71 from the period February 2006 to November 2009.

AMR/UAUA Correlation graph


The Market Model (also referred to as the Single-Index Model) is the most basic and widely understood of all factor models. The Market Model is based on the assumption that the returns on an individual security can be explained entirely by its relationship with the returns on the market portfolio (for example, a market index such as the S&P 500).

The relationship with the market portfolio is called its “beta”. Securities with high betas (above 1) will tend to move higher than the market when it rises and lower than the market when it falls.
The Fama-French Three Factor Model is an extension to the Market Model and adds two additional factors to explain the returns of securities: size premium and book-to-market (or value) premium. The model was developed by Eugene Fama and Ken French, two academic professors, as a result of prior research studies and observations that small cap stocks and stocks with high book-value-to-price ratios (value stocks) tended to do better than the market as a whole.
The Carhart Four Factor Model is an extension of the Fama French three-factor model with the addition of a fourth factor: Momentum.

The addition of the Momentum factor came as a result of a number of studies that showed that strategies involving buying stocks that have done well in the past 1-4 quarters and selling those that have done well over the same period, generates significant positive returns over 3-12 month holding periods.
Pair trading is a “market neutral” trading strategy where traders identify highly-correlated securities, look for opportunities where the correlation diverges, then bets the “spread” between the two will eventually converge – generally by shorting the outperforming stock and buying the underperforming one.

Guidelines on Notation in Performance and Metrics

The change in price from the previous day’s close to the next day’s close (updated at the end of each day).
A rolling one month calculation starting from today’s date and going backward 30 previous days.
A rolling one year calculation starting from today’s date and going back to the same date one year ago.
A rolling three month calculation starting from today’s date and going backward 90 previous days.
The average intraday volatility for a security based on the trailing 90 days
The time period beginning from the day you purchased the stock or fund and ending today.
Year to-Date is the time period starting January 1st and ending today.