- 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%|
- 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
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).
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.
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 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.