How Investment Risk Is Quantified

While diversification and asset allocation can improve returns, systematic and unsystematic risks are inherent in investing. However, along with the efficient frontier, statistical measures and methods, including value at risk (VaR) and capital asset pricing model (CAPM) are useful ways to measure risk. Understanding these tools can help an investor differentiate high-risk investments from stable ones.

Modern Portfolio and Efficient Frontier

Investing in financial markets can carry significant risks. Modern portfolio theory (MPT) assesses the maximum expected portfolio return for a given amount of portfolio risk. Within the framework of MPT, an optimal portfolio is constructed on the basis of asset allocation, diversification, and rebalancing. Asset allocation, together with diversification, is the strategy of dividing a portfolio among various asset classes. Optimal diversification involves holding multiple instruments that aren't positively correlated. 

Alpha and Beta Ratios

When it comes to quantifying value and risk, two statistical metrics—alpha and beta—are useful for investors. Both are risk ratios used in MPT and help to determine the risk/reward profile of investment securities.

Alpha measures the performance of an investment portfolio and compares it to a benchmark index, such as the S&P 500. The difference between the returns of a portfolio and the benchmark is referred to as alpha. A positive alpha of one means the portfolio has outperformed the benchmark by 1%. Likewise, a negative alpha indicates the underperformance of an investment.

Beta measures the volatility of a portfolio compared to a benchmark index. The statistical measure beta is used in the CAPM, which uses risk and return to price an asset. Unlike alpha, beta captures the movements and swings in asset prices. A beta greater than one indicates higher volatility, whereas a beta under one means the security will be more stable.

For example, Amazon (AMZN), with a beta coefficient (5Y monthly) of 1.15 as of July 2021, represents a less risky investment than Carnival Corp (CCL), which has a beta of 2.32. A savvy financial advisor or fund manager would likely avoid high alpha and beta investments for risk-averse clients.

Capital Asset Pricing Model

CAPM is an equilibrium theory built on the relationship between risk and expected return. The theory helps investors measure the risk and the expected return of an investment to price the asset appropriately. In particular, investors must be compensated for the time value of money and risk. The risk-free rate is used to represent the time value of money for placing money in any investment.

Simply put, the mean return of an asset should be linearly related to its beta coefficient—this shows that riskier investments earn a premium over the benchmark rate. Following a risk-to-reward framework, the expected return (under a CAPM model) will be higher when the investor bears greater risks.

R-Squared

In statistics, R-squared represents a notable component of regression analysis. The coefficient R represents the correlation between two variables—for investment purposes, R-squared measures the explained movement of a fund or 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 the beta to provide investors with a comprehensive picture of asset performance.

Standard Deviation

By definition, the standard deviation is a statistic used to quantify any variation from the average return of a data set. In finance, standard deviation uses the return of an investment to measure the investment’s volatility. The measure differs slightly from beta because it compares volatility to the historical returns of the security rather than a benchmark index. High standard deviations are indicative of volatility, while lower standard deviations are associated with stable assets.

The Sharpe Ratio

One of the most popular tools in financial analysis, the Sharpe ratio is a measurement of the expected excess return of an investment in relation to its volatility. The Sharpe ratio measures the average return in excess of the risk-free rate per unit of uncertainty to determine how much additional return an investor can receive with the added volatility of holding riskier assets. A Sharpe ratio of one or greater is considered to have a better risk-to-reward tradeoff.

Efficient Frontiers

The efficient frontier, which is a set of ideal portfolios, does its best to minimize an investor’s exposure to such risk. Introduced by Harry Markowitz in 1952, the concept identifies an optimal level of diversification and asset allocation given the intrinsic risks of a portfolio.

Efficient frontiers are derived from mean-variance analysis, which attempts to create more efficient investment choices. The typical investor prefers high expected returns with low variance. The efficient frontier is constructed accordingly by using a set of optimal portfolios that offer the highest expected return for a specific risk level.

Value at Risk

The value at risk (VaR) approach to portfolio management is a simple way to measure risk. VaR measures the maximum loss that cannot be exceeded at a given confidence level. Calculated based on time period, confidence level, and predetermined loss amount, VaR statistics provide investors with a worst-case scenario analysis. 

If an investment has a 5% VaR, the investor faces a 5% chance of losing the entire investment in any given month. The VaR methodology isn’t the most comprehensive measure of risk, but it remains one of the most popular measures in portfolio management due to its simplistic approach.

The Bottom Line

Investing in financial markets is inherently risky, but some investments are riskier than others. Many individuals use financial advisors and wealth managers to increase returns and reduce the risk of investments. These financial professionals use statistical measures and risk/reward models to differentiate volatile assets from stable ones. Modern portfolio theory uses five statistical indicators—alpha, beta, standard deviation, R-squared, and the Sharpe ratio—to do this. Likewise, the capital asset pricing model and value at risk are widely employed to measure the risk to reward tradeoff with assets and portfolios.