Few Useful Terms

Risk Free Return:
Before understanding Risk free assets, let us understand what a risky asset is. A risky asset is one which gives uncertain future returns. This uncertainty can be measured by the variance or the standard deviation of the expected future returns.
Risk free assets are assets whose expected risk is fully certain and thus the standard deviation of such expected returns comes to zero.

Alpha:
The α (alpha) of a security or fund is its outperformance over the return adjusted for risk, with risk measured by β (beta).
α= (r - rf) - (β×(rm - rf))
where rf is the risk free rate
rm is the (forecast) market rate of return
and rm the return on a fund or security r.


Beta :
The Beta coefficient, in terms of finance and investing, is a measure of a stock's (or portfolio's) volatility in relation to the rest of the market. Beta is calculated for individual companies using regression analysis.
The beta coefficient is a key parameter in the capital asset pricing model (or CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio.
• Beta < 0: Negative Beta - not likely.
• Beta = 0: Cash in the bank.
• Beta Between 0 and 1: Low-volatility
• Beta = 1: Matching the market.
• Beta > 1: More volatile than the market.
Example of use: A fund with a beta of 1 is deemed to have the same volatility as the S&P 500; therefore a fund with a beta of 4 is four times more volatile than the S&P 500, and a fund with a beta of .25 is 25% as volatile as the S&P 500.

This means that a fund with a beta of 4 would rise 40% if the S&P 500 rose 10% (the same is true of a drop).

The three basic interpretations of Beta are as follows:
Econometric Beta: The primary risk factor for the CAPM. Relevant to pricing and not valuation.
Graphical Beta: The slope coefficient of the characteristic line.
Statistical Beta: The measure of systematic risk in the CAPM.

Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the asset's sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his or her willingness to take risk.

Variance :
Variance measures the variability (volatility) from an average. Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security.

Standard Deviation
The standard deviation is a measure of how spread out a set of numbers is. It is the square root of variance.
The most common use of the standard deviation in finance is to measure the risk of holding a security or portfolio.

Covariance
The covariance of two variables (numbers measuring something) is a measure of the relationship between them. It closely related to the correlation and calculated as an intermediate step in calculating the correlation.
The covariance of two numbers is the arithmetic mean, over all values of x1, and the corresponding values of x2, of:
(x1 - μ1)(x2 - μ2)
where x1 is the value of one variable
x2 is the value of the other variable
μ1 is the arithmetic mean of of x1 and
μ2 is the arithmetic mean of of x2.
The correlation of x1 and x2 is:
(cov(x1,x2))/(σ1σ2)
where cov(x1,x2) is the covariance of x1 and x2
σ1 is the standard deviation of x1 and
σ2 is the standard deviation of x2.

Coefficient of correlation
A coefficient of correlation is a mathematical measure of how much one number (such as a share price) can expected to be influenced by changes in another (such as an index). It is closely related to covariance (see below).
A correlation coefficient of 1 means that the two numbers are perfectly correlated: if one grows so does the other, and the change in one is a multiple of the change in the other.
A correlation coefficient of -1 means that the numbers are perfectly inversely correlated. If one grows the other falls. The growth in one is a negative multiple of the growth in the other.
A correlation coefficient of zero means that the two numbers are not related.
A non-zero correlation coefficient means that the numbers are related, but unless the coefficient is either 1 or -1 there are other influences and the relationship between the two numbers is not fixed. So if you know one number you can estimate the other, but not with certainty. The closer the correlation coefficient is to zero the greater the uncertainty, and low correlation coefficients means that the relationship is not certain enough to be useful.