1. What is Standard Deviation of Returns?

Standard deviation of returns measures the dispersion or volatility of investment returns around their mean. It quantifies the risk associated with an investment, with higher values indicating greater volatility and uncertainty.

2. How Does the Calculator Work?

The calculator uses the standard deviation formula:

Where:

• \( \sigma \) — Standard deviation (%)
• \( p \) — Probability of each return (unitless)
• \( r \) — Individual return (%)
• \( E(r) \) — Expected return (%)

Explanation: The formula calculates how much individual returns deviate from the expected return, weighted by their probabilities, providing a measure of investment risk.

3. Importance of Standard Deviation in Finance

Details: Standard deviation is a fundamental risk measure in portfolio management, helping investors understand the volatility of their investments and make informed decisions about risk tolerance and asset allocation.

4. Using the Calculator

Tips: Enter returns as percentages (comma separated) and their corresponding probabilities (also comma separated). The sum of probabilities should equal 1 for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What does a high standard deviation indicate?
A: A high standard deviation indicates greater volatility and higher investment risk, as returns are more spread out from the average.

Q2: How is standard deviation different from variance?
A: Variance is the average of squared deviations from the mean, while standard deviation is the square root of variance, making it more interpretable as it's in the same units as the original data.

Q3: What is considered a "good" standard deviation?
A: This depends on investment goals and risk tolerance. Conservative investors prefer lower standard deviation, while aggressive investors may accept higher volatility for potentially higher returns.

Q4: Can standard deviation be negative?
A: No, standard deviation is always non-negative as it's derived from squared differences.

Q5: How does diversification affect standard deviation?
A: Proper diversification typically reduces portfolio standard deviation as different assets don't move perfectly together, reducing overall volatility.