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 the capital asset valuation model (CAPM), are useful ways to measure risk. Understanding these tools can help an investor differentiate between high-risk and stable investments.

Modern portfolio and efficient frontier

Investing in financial markets can carry significant risks. Modern Portfolio Theory (MPT) assesses the maximum expected return of the portfolio for a given amount of portfolio risk. In the MPT framework, an optimal portfolio is built on the basis of asset allocation, diversification, and rebalancing. Asset allocation, along with diversification, is the strategy of dividing a portfolio among several asset classes. Optimal diversification involves holding multiple instruments that are not positively correlated.

Key takeaways

  • Investors can use models to help differentiate between risky and stable investments.
  • Modern portfolio theory is used to understand a portfolio’s risk relative to its performance.
  • Diversification can reduce risk and optimal diversification is achieved by building a portfolio of uncorrelated assets.
  • Efficient Frontier is a set of portfolios optimized in terms of asset allocation and diversification.
  • Beta, standard deviations, and VaR measure risk, but in different ways.

Alpha and beta relationships

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

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

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

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

Capital asset valuation model

CAPM is an equilibrium theory built on the relationship between risk and expected return. The theory helps investors measure the risk and expected return of an investment to properly value the asset. 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 to place money in any investment.

Simply put, the average return on 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-reward framework, the expected return (under a CAPM model) will be higher when the investor assumes greater risks.


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 relative to a benchmark. A high R squared shows that a portfolio’s performance is in line with the index. Financial advisers can use R-squared in conjunction with the beta version to provide investors with a complete picture of asset performance.

Standard deviation

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

Sharpe’s relationship

One of the most popular tools in financial analysis, the Sharpe index is a measure of an investment’s expected excess return relative to its volatility. The Sharpe index 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 having riskier assets. A Sharpe ratio of one or more is considered to have a better risk-reward trade-off.

Efficient borders

The efficient frontier, which is a set of ideal portfolios, does everything possible 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 options. 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 level of risk.

Risk and volatility are not the same. Volatility refers to the speed of the investment’s price movement and risk is the amount of money that can be lost on an investment.

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. VaR statistics, calculated based on time period, confidence level, and predetermined loss amount, provide investors with a worst-case analysis.

If an investment has a VaR of 5%, the investor faces a 5% probability of losing the entire investment in a given month. The VaR methodology is not the most comprehensive measure of risk, but it is still one of the most popular measures in portfolio management due to its simplistic approach.

The bottom line

Investing in financial markets is inherently risky. Many people use financial advisers and wealth managers to increase profitability and reduce investment risk. 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 index to do this. In addition, the equity and value-at-risk pricing model is widely used to measure the risk of rewarding compensation with assets and portfolios.

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Mark Holland

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