Investors know that buying and selling securities is risky. The simple logic of the market – buy low, sell high – isn’t often easy to achieve. Modern Portfolio Theory (MPT) attempts to assess the maximum expected return of a portfolio given a specific amount of risk.

According to MPT, an optimal portfolio is based on asset allocation, diversification and appropriate rebalancing that results in a lack of correlation between various holdings in that portfolio. That, of course, is not enough. Thanks to risk.

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**Alpha and Beta**

Alpha and Beta are __risk ratios__ used to calculate, compare and predict returns. Alpha compares the performance of a security, portfolio or fund to a benchmark (such as the S&P 500). Beta measures the volatility of a security to a benchmark index.

The baseline number for Alpha is 0 (investment performed exactly according to market expectations). The baseline for Beta is 1 (security’s price is moving exactly with the market).

**R-squared**

R-squared measures the movement of a security in relation to a benchmark. A high R-squared shows that a portfolio’s performance is in line with the index. Financial advisors can use R-squared in tandem with beta to provide investors with a comprehensive picture of asset performance.

**Standard Deviation**

Standard deviation is a way to __quantify__ any variation from the average. Basically, it’s a measure of volatility. Unlike beta, standard deviation compares volatility to historical returns as opposed to a benchmark index.

The greater the standard deviation, the greater the variance between price and mean. A volatile stock has a high standard deviation. A stable stock has a standard deviation that is quite low.

**Sharpe Ratio**

This tool __measures__ the expected excess return of a security in relation to its volatility. In other words, it tells you how much additional return you could receive by holding riskier assets. A ratio of 1 or greater is considered to have a better risk to reward trade-off.

The Sharpe ratio for large market cap stocks, for example, should initially outperform safer bonds. In the long run, bonds will inevitably outperform stocks.

**Efficient Frontier**

Efficient __frontiers__ come from mean variance analysis. This is an attempt to create more efficient choices when it comes to investing. A typical investor would likely prefer high returns with low variance.

A security that lies below the efficient frontier is considered sub-optimal because it does not provide enough return for the risk. One that lies to the right is also sub-optimal because it has a high level of risk for the defined rate of return.

**Capital Asset Pricing Model**

The __relationship__ between risk and expected return results in CAPM. This theory helps investors measure the risk and expected return so they can appropriately price the asset or security. The expected return under CAPM will be higher when the investor is willing to bear greater risk.

CAPM is used widely to price risky securities, generating returns that are expected given asset risk and considering the cost of capital.

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**Value-at-Risk**

Value-at-Risk (VaR) __measures__ risk. Essentially it measures the maximum loss that can’t be exceeded given a certain level of confidence. This is calculated based on time, confidence level and a pre-determined amount of loss.

For example, if an investment has a 5% VaR, the investor faces a 5% chance of losing the entire investment in each month. VaR is rather simplistic but is still a popular measure in portfolio management.