Risk management is a crucial process used to make investment decisions. The process involves identifying and analyzing risk in an investment and deciding whether or not to accept that risk given the expected returns for the investment. Some common measurements of risk include standard deviation, Sharpe ratio, beta, value at risk (VaR), conditional value at risk (CVaR), and R-squared.

### Key Takeaways

- Risk management is the analysis of an investment's returns compared to its risk with the expectation that a greater degree of risk is supposed to be compensated by a higher expected return.
- Risk - or the probability of a loss - can be measured using statistical methods that are historical predictors of investment risk and volatility.
- Commonly used risk management techniques include standard deviation, Sharpe ratio, and beta.
- Value at Risk and other variations not only quantify a potential dollar impact but assess a confidence interval of the likelihood of an outcome.
- Risk management also oversees systematic risk and unsystematic risk, the two broad types of risk impacting all investments.

## Standard Deviation

Standard deviation measures the dispersion of data from its expected value. The standard deviation is commonly used to measure the historical volatility associated with an investment relative to its annual rate of return. It indicates how much of the current return is deviating from its expected historical normal returns. For example, a stock that has high standard deviation experiences higher volatility and is therefore considered riskier.

### When To Use Standard Deviation

Standard deviation is most useful in conjunction with an investment's average return to evaluate the dispersion from historical results.

### Standard Deviation Formula

Standard deviation is calculated by dividing the square root of the sum of squared differences from an investment's mean by the number of items contained in the data set.

An alternative to the standard deviation is the semi-deviation, a measurement tool that only assesses part of an investmentâ€™s risk profile. The semi-deviation is calculated similarly to the standard deviation but can be used to specifically look at only the downside or risk of loss potential of an investment as only half the distribution curve is determined.

## Sharpe Ratio

The Sharpe ratio measures investment performance by considering associated risks. To calculate the Sharpe ratio, the risk-free rate of return is removed from the overall expected return of an investment. The remaining return is then divided by the associated investmentâ€™s standard deviation. The result is a ratio that compares the return specific to an investment with the associated level of volatility an investor is required to assume for holding the investment. The Sharpe ratio serves as an indicator of whether an investment's return is worth the associated risk.

One variation of the Sharpe ratio is the Sortino ratio which removes the effects of upward price movements on standard deviation to focus on the distribution of returns that are below the target or required return. The Sortino ratio also removes the risk-free rate of return in the numerator of the formula.

### When To Use Sharpe Ratio

The Sharpe ratio is most useful when evaluating differing options. This measurement allows investors to easily understand which companies or industries generate higher returns for any given level of risk.

### Sharpe Ratio Formula

The Sharpe ratio is calculated by subtracting the risk-free rate of return from an investment's total return. Then, divide this result by the standard deviation of the investment's excess return.

Another variation of the Sharpe ratio is the Treynor Ratio which integrates a portfolioâ€™s beta or with the rest of the market. Beta is a measure of an investment's volatility compared to the general market. The goal of the Treynor ratio is to determine whether an investor is being compensated fairly for taking additional risk above the market. The Treynor ratio formula is calculated by dividing the investmentâ€™s beta from the return of the portfolio less the risk-free rate.

## Beta

Beta measures the amount of systematic risk an individual security or sector has relative to the entire stock market. The market is always the beta benchmark an investment is compared to, and the market always has a beta of one.

If a security's beta is equal to one, the security has exactly the same volatility profile as the broad market. A security with a beta greater than one means it is more volatile than the market. A security with a beta less than one means it is less volatile than the market.

### When To Use Beta

Beta is most useful when comparing an investment against the broad market.

### Beta Formula

Beta is calculated by dividing the covariance of the excess returns of an investment and the market by the variance of the excess market returns over the risk-free rate.

Beta can also be used to measure the scale of volatility a security has compared to the market. For example, suppose a security's beta is 1.5. The security is considered 50% more volatile than the market. Beta is helpful when comparing across securities - at a glance, beta easily identifies that an investment with a beta of 1.5 is more volatile than an investment with a beta of 1.3.

## Value at Risk (VaR)

Value at Risk (VaR)** **is a statistical measurement used to assess the level of risk associated with a portfolio or company. The VaR measures the maximum potential loss with a degree of confidence for a specified period. For example, suppose a portfolio of investments has a one-year 10 percent VaR of $5 million. Therefore, the portfolio has a 10 percent chance of losing $5 million over a

one-year period.

### When To Use Value at Risk

VaR is most useful when wanting to assess a specific outcome and the likelihood of that outcome occurring.

There are several different methods for calculating Value at Risk, each of which with their own formula:

- The historical simulation method is the simplest as it takes prior market data over a defined period and applies those outcomes to the current state of an investment.
- The parametric method or variance-covariance method is more useful when dealing with larger data sets.
- The Monte Carlo method is best suited for the most complicated simulations and assumes the probability of risk for each risk factor is known.

### Conditional Value at Risk (CVaR)

Conditional Value at Risk (CVaR) is another risk measurement used to assess the tail risk of an investment. Used as an extension to the VaR, the CVaR assesses the likelihood, with a certain degree of confidence, that there will be a break in the VaR. It seeks to assess what happens to investment beyond its maximum loss threshold. This measurement is more sensitive to events that happen at the tail end of a distribution.

### When To Use Conditional VaR

CVaR is most useful for investors wanting to know maximum potential losses for outcomes less statistically likely to occur.

For example, suppose a risk manager believes the average loss on an investment is $10 million for the worst one percent of possible outcomes for a portfolio. Therefore, the CVaR or expected shortfall is $10 million for this one percent portion of the investmentâ€™s distribution curve. The VaR loss for this investment will likely be lower than $10 million as the CVaR loss often exceeds the distribution boundary of the VaR simulation.

## R-squared

R-squared is a statistical measure that represents the percentage of a fund portfolio or a security's movements that can be explained by movements in a benchmark index. For fixed-income securities and bond funds, the benchmark is the U.S. Treasury Bill. The S&P 500 Index is the benchmark for equities and equity funds.

R-squared values range from zero to one and are commonly stated as a percentage (0% to 100%). An R-squared value of 0.9 means 90% of the analysis accounts for 90% of the variation within the data. Risk models with higher R-squared values indicate that the independent variables being used within the model are explaining more of the variation of the dependent variable.

### When To Use R-Squared

R-Squared is most useful when attempting to determine why the price of an investment changes. It's a byproduct of a financial model that clarifies what variables determine the outcome of other variables.

### R-Squared Formula

The formula to find R-Squared is to divide the unexplained variance (the sum of the squares of residuals) by the total variance (the total sum of squares). Then, subtract this quotient from 1.

Mutual fund investors are often recommended to avoid actively managed funds with high R-squared ratios which are generally criticized by analysts as being "closet" index funds. In these cases, with each basket of investments acting very similar to each other, it makes little sense to pay higher fees for professional management when you can get the same or close results from an index fund.

## Categories of Risks

Risk management is divided into two broad categories: systematic and unsystematic risk. Every investment is impacted by both types of risk, though the risk composition will vary across securities.

### Systematic Risk

Systematic risk is associated with the overall market. This risk affects every security, and it is unpredictable and undiversifiable. However, systematic risk can be mitigated through hedging. For example, political upheaval is a systematic risk that can affect entire financial sectors such as the bond, stock, and currency markets. All securities within these sectors would be adversely impacted.

### Unsystematic Risk

The second category of risk, unsystematic risk, is specifically associated with a company or sector. It is also known as diversifiable risk and can be mitigated through asset diversification. This risk is only inherent to a specific stock or industry, and every security has a different level of unsystematic risk. If an investor buys an oil stock, the investor assumes all risks associated specifically with the oil industry and the company itself.

To protect against unsystematic risk, the investor may look to take the opposite side of, or hedge, his position by buying a put option on crude oil or on the company, or he may look to mitigate the risk through diversification by buying stock in an unrelated company or industry. The ultimate goal is to reduce portfolio-wide exposure to the oil industry and the specific company.

## Why Is Risk Management Important?

Risk management - specific to investing - is important because it evaluates potential upsides and downsides to securities. Instead of solely focusing on the projected returns of an investment, it considers the potential loss of capital and informs the investor of the unfavorable outcomes that may occur with an investment.

## How Do You Measure the Risk of an Investment?

There's a multitude of ways to measure risk. Beta is a measurement that compares the risk or volatility of an investment against the general market. Standard deviation measures the dispersion of performance from an investment's average. The Sharpe Ratio measures whether an investment's returns are faily compensating an investor for the associate level of risk assumed.

## What Are the Two Major Types of Risk?

The two major types of risk are systematic risk and unsystematic risk. Systematic risk impacts everything - it is the general, broad risk assumed when investing. Unsystematic risk is more specific to a company, industry, or sector. You're stuck with systematic risk, but you have complete control over how much unsystematic risk you want to carry.

## The Bottom Line

Many investors tend to focus exclusively on investment returns with little concern for investment risk. The risk measures we have discussed can provide some balance to the risk-return equation. The good news for investors is that these indicators are automatically calculated and readily available on a number of financial websites. These metrics are also incorporated into many investment research reports.

When considering a stock, bond, or mutual fund investment, volatility risk and risk management are additional items to evaluate when considering the quality of an investment.