Knowledge Tree
Standard deviation
Facts (26)
Sources
Chapter 8 – Risk and Return – Fundamentals of Finance pressbooks.pub 13 facts
measurementIn a hypothetical portfolio construction example, Stock A has an expected return of 8% and a standard deviation of 15%, while Stock B has an expected return of 8% and a standard deviation of 20%, with a correlation of 0.2 between their returns.
claimIn portfolio management, calculating the expected return and standard deviation of a portfolio comprising two stocks with a positive but low correlation results in a lower overall portfolio risk compared to holding either stock individually.
measurementA low-risk bond typically has an expected return of 3% and a standard deviation of 2%.
measurementA growth stock typically has an expected return of 12% and a standard deviation of 25%, which indicates a wider range of potential outcomes.
claimThe standard deviation of a portfolio can be lower than the weighted average of individual asset risks due to the benefits of diversification.
claimStandard deviation measures the variability or volatility of investment returns relative to the expected return, which quantifies the investment's risk.
formulaThe formula for standard deviation (σ) is σ = √Σ Pi (Ri - E(R))^2, where Pi is the probability of outcome i, Ri is the return of outcome i, and E(R) is the expected return.
claimExpected return is defined as an average anticipated return based on probabilities, while standard deviation is defined as a measure of the variability of returns around that average.
claimThe standard deviation of a portfolio is determined by the standard deviations of the individual assets (e.g., Stock A at 10%, Stock B at 15%), their respective weights (e.g., 50% each), and the correlation coefficient between them (e.g., 0.3).
claimA higher standard deviation in investment returns indicates that the returns are more spread out, which signifies greater investment risk.
claimRisk-averse investors evaluate investment options by comparing expected returns against standard deviation (risk), typically preferring lower risk for a given level of return.
procedureThe procedure to calculate the standard deviation of investment returns (σ) involves five steps: (1) subtract the expected return from each possible return to find the deviation for each outcome, (2) square each deviation, (3) multiply each squared deviation by the probability of its corresponding outcome, (4) sum all the weighted squared deviations, and (5) take the square root of the result.
claimFor individual assets, both standard deviation and beta are relevant metrics for assessing risk, depending on whether the asset is viewed in isolation or as part of a portfolio.
The Relationship Between Risk and Return in Different Asset Classes bi-sam.com Mar 18, 2025 6 facts
measurementBetween 1926 and 2023, Large-Cap Stocks had a historical average annual return of 10.2% and a volatility (standard deviation) of 19.8%.
measurementBetween 1926 and 2023, Emerging Markets stocks had a historical average annual return of 11.6% and a volatility (standard deviation) of 28.7%.
measurementInvestment risk is typically measured using standard deviation to measure volatility, beta to measure market sensitivity, and maximum drawdown to measure the largest peak-to-trough decline.
measurementBetween 1926 and 2023, Mid-Cap Stocks had a historical average annual return of 11.7% and a volatility (standard deviation) of 22.5%.
measurementBetween 1926 and 2023, Small-Cap Stocks had a historical average annual return of 11.9% and a volatility (standard deviation) of 25.1%.
measurementBetween 1926 and 2023, International Developed stocks had a historical average annual return of 9.1% and a volatility (standard deviation) of 22.1%.
Next Generation Investment Risk Management: Putting the 'Modern ... financialplanningassociation.org 5 facts
claimEfficient frontiers calculated using shortfall probability and those calculated using standard deviation are generally similar, with portfolios optimal under standard deviation often being near-optimal under shortfall probability.
claimStandard deviation measures the dispersion of returns around an average, but it fails to capture an investor's actual risk of losing money or failing to meet specific financial objectives.
claimConservative portfolios that appear on the efficient frontier when using standard deviation as a risk measure often fall into the inefficient interior of the frontier when using shortfall probability as the risk measure.
perspectiveThe authors of 'Next Generation Investment Risk Management' argue that risk should be measured in the same way investors intuitively think about it—as the chance of significant loss or the failure to meet a financial objective—rather than simply as standard deviation, which is the amount of dispersion around the average return.
claimStandard deviation as a risk measure is flawed because it does not distinguish between deviations above the mean (positive returns) and deviations below the mean (negative returns).
Risk Factors, Expected Returns, and Investment Instruments analystprep.com Aug 5, 2024 1 fact
claimMean-variance optimization, which relies on standard deviation, is often unsuitable for alternative investments because these assets frequently suffer from infrequent valuation, erratic correlations, and extended lock-up periods.
Risk Return Trade Off - Meaning, Importance and Example bajajfinserv.in 1 fact
claimStandard deviation measures the historical fluctuation of a fund's returns, where a high standard deviation indicates unpredictability and a low standard deviation suggests steadier performance.