Question 1

What is portfolio risk and how is it measured?

Accepted Answer

Portfolio risk measures the uncertainty of investment returns, typically quantified by volatility (standard deviation). It represents how much your portfolio value might fluctuate. A portfolio with 15% volatility might experience returns ranging from -15% to +15% around the average return in most years. Portfolio risk depends on: asset allocation, individual asset volatilities, and correlations between assets.

Question 2

How do you calculate portfolio volatility?

Accepted Answer

Portfolio volatility is calculated using: σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂), where w = asset weights, σ = asset volatilities, and ρ = correlation. For a 60/40 stock/bond portfolio with 18% stock volatility, 6% bond volatility, and 0.2 correlation, the portfolio volatility is approximately 11.3%, demonstrating how diversification reduces risk below the weighted average of 13.2%.

Question 3

What is diversification benefit?

Accepted Answer

Diversification benefit is the risk reduction achieved by holding multiple uncorrelated assets. It's the difference between the weighted average of individual asset volatilities and the actual portfolio volatility. For example, if stocks (18% vol) and bonds (6% vol) are combined 60/40, the undiversified risk would be 13.2%, but the actual portfolio volatility might be only 11%, providing a 2.2% diversification benefit.

Question 4

What is the Sharpe Ratio and why is it important?

Accepted Answer

The Sharpe Ratio measures risk-adjusted returns: (Portfolio Return - Risk-Free Rate) / Portfolio Volatility. It shows how much excess return you earn per unit of risk. A Sharpe ratio above 1.0 is good, above 2.0 is very good, above 3.0 is excellent. For example, a portfolio returning 8% with 10% volatility and 2% risk-free rate has a Sharpe of 0.6, while one returning 10% with 12% volatility has a Sharpe of 0.67—the second is better risk-adjusted.

Question 5

What is correlation and how does it affect portfolio risk?

Accepted Answer

Correlation measures how two assets move together, ranging from -1 (perfect opposite) to +1 (perfect together). Lower or negative correlations provide better diversification. Stocks and bonds typically have 0.1-0.3 correlation (slightly positive), which helps reduce portfolio risk. Combining assets with 0 correlation cuts risk significantly; negative correlation provides even more diversification. This is why bonds traditionally diversify stock portfolios.

Question 6

What is an optimal asset allocation for risk management?

Accepted Answer

Optimal allocation depends on age, goals, and risk tolerance. Common guidelines: Age-based: 110 minus age in stocks (at 40, hold 70% stocks). Conservative: 40/60 stocks/bonds (low risk). Moderate: 60/40 stocks/bonds (balanced). Aggressive: 80/20 stocks/bonds (high growth). Very aggressive: 90/10+ stocks (maximum growth). Near-retirees: 30/50/20 stocks/bonds/cash. Adjust based on personal circumstances, time horizon, and market conditions.

Question 7

What is maximum drawdown and how is it calculated?

Accepted Answer

Maximum drawdown is the largest peak-to-trough decline in portfolio value. For stocks, it's often 2-3x annual volatility. A portfolio with 15% volatility might experience drawdowns of 30-45% during severe downturns (like 2008). Understanding max drawdown helps assess if you can emotionally handle losses. If 30% drawdown would cause panic selling, your portfolio is too risky. Estimate: Max Drawdown ≈ 2.5 × Portfolio Volatility.

Question 8

How does Modern Portfolio Theory relate to portfolio risk?

Accepted Answer

Modern Portfolio Theory (MPT), developed by Harry Markowitz, demonstrates that combining assets with low correlation reduces portfolio risk below weighted average risk. MPT introduced the efficient frontier—the set of portfolios offering maximum return for each risk level. Key insights: diversification is the only free lunch in finance, risk should be measured relative to the entire portfolio (not individual assets), and optimal portfolios maximize Sharpe ratio.

Question 9

How often should I rebalance to maintain target risk level?

Accepted Answer

Rebalancing frequency depends on strategy and costs. Annual rebalancing: sufficient for most investors, tax-efficient. Semi-annual: captures more opportunities. Quarterly: for active managers. Threshold-based: rebalance when allocation drifts 5%+ from target. Tax considerations: rebalance tax-advantaged accounts first to avoid capital gains. Studies show annual or 5% threshold rebalancing performs similarly with lower costs than frequent rebalancing.

Question 10

What are alternative assets and how do they affect portfolio risk?

Accepted Answer

Alternative assets (real estate, commodities, private equity, hedge funds) can improve diversification due to low correlation with stocks/bonds. Real estate (REITs): 0.4-0.6 stock correlation. Gold: -0.1 to 0.2 stock correlation (inflation hedge). Private equity: less liquid but potentially higher returns. Recommended allocation: 5-15% alternatives for diversification. However, alternatives often have higher fees, less liquidity, and require larger minimums—consider costs vs. benefits.

Question 11

How to calculate portfolio risk?

Accepted Answer

To calculate portfolio risk: 1) Determine asset weights (w₁, w₂, etc.) and individual asset volatilities (σ₁, σ₂, etc.), 2) Find correlations between assets (ρ), 3) Apply portfolio risk formula: σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂), 4) For multiple assets, extend the formula to include all pairs. Example: 60% stocks (18% vol) + 40% bonds (6% vol) with 0.2 correlation: σp = √(0.6²×0.18² + 0.4²×0.06² + 2×0.6×0.4×0.18×0.06×0.2) = 11.3%. Our calculator automates this calculation.

Question 12

How to calculate risk of a portfolio?

Accepted Answer

To calculate risk of a portfolio: Use the portfolio variance formula: Portfolio Variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ, then take the square root for standard deviation (volatility). Steps: 1) Get asset weights (must sum to 100%), 2) Get individual asset volatilities (standard deviations), 3) Get correlations between assets, 4) Calculate portfolio variance, 5) Take square root for portfolio volatility. Example: 60/40 stock/bond portfolio with 18% and 6% volatilities, 0.2 correlation = 11.3% portfolio risk. Lower correlation reduces portfolio risk below weighted average.

Question 13

What is a portfolio volatility calculator?

Accepted Answer

A portfolio volatility calculator computes the standard deviation of portfolio returns, measuring how much portfolio value fluctuates. It calculates: Portfolio volatility (standard deviation), Portfolio variance, Diversification benefits, Risk reduction from correlation. Enter asset allocations (weights), individual asset volatilities, and correlations between assets. The calculator uses Modern Portfolio Theory formulas to determine portfolio risk. Lower volatility means less risk. Example: 60% stocks (18% vol) + 40% bonds (6% vol) = ~11% portfolio volatility (lower than 13.2% weighted average due to diversification).

Question 14

What is a standard deviation of portfolio calculator?

Accepted Answer

A standard deviation of portfolio calculator calculates portfolio volatility (standard deviation of returns). Portfolio standard deviation measures return uncertainty. Formula: σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ). The calculator shows: Portfolio standard deviation (volatility), How diversification reduces risk, Impact of correlation on portfolio risk, Comparison to undiversified risk. Enter asset weights, individual standard deviations, and correlations. Lower standard deviation = lower risk. Example: Portfolio with 15% standard deviation means returns typically range ±15% around the average.

Question 15

What is a portfolio standard deviation calculator?

Accepted Answer

A portfolio standard deviation calculator computes the volatility of portfolio returns. Standard deviation measures how much returns deviate from the average. The calculator determines: Portfolio standard deviation (volatility percentage), Portfolio variance (standard deviation squared), Risk reduction from diversification, Impact of asset correlations. Enter your asset allocation percentages, individual asset volatilities, and correlations. The calculator uses variance-covariance formulas to compute portfolio risk. Lower standard deviation indicates more stable, less risky portfolio returns.

Question 16

What is a portfolio variance calculator?

Accepted Answer

A portfolio variance calculator computes portfolio variance, which is the square of standard deviation (volatility). Portfolio variance formula: σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ. The calculator shows: Portfolio variance, Portfolio standard deviation (square root of variance), Diversification benefits, Risk metrics. Variance measures return dispersion. Higher variance = higher risk. Enter asset weights, individual variances (or volatilities), and correlations. Portfolio variance accounts for how assets move together (correlation), which affects overall portfolio risk.

Question 17

What is an investment risk calculator?

Accepted Answer

An investment risk calculator measures the risk level of investment portfolios. It calculates: Portfolio volatility (standard deviation), Maximum potential losses (drawdown), Risk-adjusted returns (Sharpe ratio), Diversification benefits. Enter your asset allocation, expected returns, volatilities, and correlations. The calculator helps you: Understand portfolio risk level, Compare different asset allocations, Optimize risk-return tradeoff, Assess if risk matches your tolerance. Risk is typically measured as volatility (standard deviation of returns). Higher volatility = higher risk but potentially higher returns.

Question 18

What is a standard deviation portfolio calculator?

Accepted Answer

A standard deviation portfolio calculator computes portfolio volatility (standard deviation of returns). Standard deviation measures return uncertainty and risk. Formula: σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ). The calculator shows: Portfolio standard deviation percentage, How asset correlations affect risk, Diversification benefits, Risk level classification. Enter asset weights, individual standard deviations, and correlations. Standard deviation tells you how much returns typically vary. Example: 12% standard deviation means returns usually fall within ±12% of the average return.

Question 19

What is portfolio risk calculation?

Accepted Answer

Portfolio risk calculation determines the uncertainty of portfolio returns, typically measured as volatility (standard deviation). The calculation involves: 1) Portfolio Variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ, 2) Portfolio Standard Deviation = √Variance, 3) Where w = weights, σ = volatilities, ρ = correlation. Example: 60% stocks (18% vol) + 40% bonds (6% vol) with 0.2 correlation. Variance = 0.6²×0.18² + 0.4²×0.06² + 2×0.6×0.4×0.18×0.06×0.2 = 0.0128. Standard deviation = √0.0128 = 11.3%. This shows how diversification reduces risk below the 13.2% weighted average.

Question 20

What is a modern portfolio theory calculator?

Accepted Answer

A modern portfolio theory (MPT) calculator applies Harry Markowitz's theory to optimize portfolios. MPT shows that combining assets with low correlation reduces portfolio risk. The calculator determines: Efficient frontier (optimal risk-return combinations), Portfolio volatility for different allocations, Sharpe ratio (risk-adjusted returns), Optimal asset allocation. Enter expected returns, volatilities, and correlations for different assets. MPT demonstrates that diversification is the only 'free lunch' in investing—you can reduce risk without sacrificing expected returns by combining uncorrelated assets.

Question 21

What is an efficient portfolio calculator?

Accepted Answer

An efficient portfolio calculator finds portfolios on the efficient frontier—combinations offering maximum return for each risk level. Efficient portfolios: Maximize return for given risk, Minimize risk for given return, Have optimal Sharpe ratios, Are well-diversified. The calculator shows: Efficient frontier curve, Optimal asset allocations, Risk-return tradeoffs, Recommended portfolios. Enter expected returns, volatilities, and correlations for different assets. The calculator identifies portfolios that can't be improved—you can't get higher returns without taking more risk, or lower risk without accepting lower returns.

Question 22

What is portfolio risk formula?

Accepted Answer

The portfolio risk formula calculates portfolio volatility (standard deviation): σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂). Where: σp = portfolio standard deviation (risk), w₁, w₂ = asset weights (must sum to 1), σ₁, σ₂ = individual asset volatilities, ρ₁₂ = correlation between assets (-1 to +1). For multiple assets, extend to include all pairs. Example: 60% stocks (18% vol) + 40% bonds (6% vol), 0.2 correlation: σp = √(0.6²×0.18² + 0.4²×0.06² + 2×0.6×0.4×0.18×0.06×0.2) = 11.3%. Lower correlation reduces portfolio risk below weighted average.

Question 23

What is risk of a portfolio formula?

Accepted Answer

The risk of a portfolio formula calculates portfolio standard deviation: σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ). This measures portfolio volatility. Steps: 1) Calculate portfolio variance: σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ, 2) Take square root for standard deviation. The formula accounts for: Individual asset risks (σ₁, σ₂), Asset weights (w₁, w₂), Correlation (ρ) between assets. Lower correlation provides diversification benefit, reducing portfolio risk below the weighted average of individual risks. This is the core insight of Modern Portfolio Theory.

How to Calculate Portfolio Risk - Portfolio Volatility & Standard Deviation Calculator

Risk Analysis

How to Calculate Portfolio Risk - Step by Step Guide & Formula

Portfolio Risk Formula

Main Formula:

Step-by-Step: How to Calculate Portfolio Risk

Step 1: Determine Asset Weights

Step 2: Get Individual Asset Volatilities

Step 3: Find Asset Correlations

Step 4: Calculate Portfolio Variance

Step 5: Calculate Portfolio Standard Deviation

Portfolio Risk Calculation Example

Example: 60/40 Stock/Bond Portfolio

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Portfolio Risk Formula - Complete Guide

Main Portfolio Risk Formula:

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