Portfolio Diversification
Diversification is a core principle in portfolio management that aims to reduce risk by spreading investments across different assets. The idea is that by holding a variety of assets, you decrease the impact that any single asset's poor performance can have on the overall portfolio. This is because not all assets move in the same direction or with the same magnitude at the same time.
Correlation is a statistical measure that describes how two assets move in relation to each other. It ranges from -1 to 1:
- A correlation of
1means both assets move perfectly in sync; - A correlation of
0means their movements are unrelated; - A correlation of
-1means the assets move in exactly opposite directions.
Understanding how assets are correlated is crucial for portfolio construction. When you combine assets with low or negative correlation, you can achieve a smoother, more stable overall portfolio performance, reducing risk without necessarily sacrificing returns.
1234567891011import numpy as np # Sample returns for two different assets asset_a_returns = [0.01, 0.02, -0.005, 0.03, 0.015] asset_b_returns = [-0.002, 0.018, 0.01, -0.004, 0.02] # Calculate correlation using numpy correlation_matrix = np.corrcoef(asset_a_returns, asset_b_returns) correlation = correlation_matrix[0, 1] print("Correlation between Asset A and Asset B:", round(correlation, 2))
When assets in a portfolio have negative or low correlation, the ups and downs of their returns tend to offset each other. This means that when one asset's value drops, the other might remain stable or even increase, helping to cushion the overall impact on your portfolio. As a result, the total volatility—or risk—of the portfolio can be lower than that of the individual assets. This is the main reason diversification works: combining assets that do not move together reduces the likelihood of experiencing large losses at the same time.
123456789101112131415161718192021import numpy as np # Assume equal investment in both assets weights = np.array([0.5, 0.5]) returns = np.array([asset_a_returns, asset_b_returns]) # Calculate average returns for each asset mean_returns = np.mean(returns, axis=1) # Portfolio expected return portfolio_return = np.dot(weights, mean_returns) # Calculate covariance matrix cov_matrix = np.cov(returns) # Portfolio variance portfolio_variance = np.dot(weights.T, np.dot(cov_matrix, weights)) # Portfolio standard deviation (risk) portfolio_risk = np.sqrt(portfolio_variance) print("Portfolio Expected Return:", round(portfolio_return, 4)) print("Portfolio Risk (Std Dev):", round(portfolio_risk, 4))
1. What is the main benefit of diversification in a portfolio?
2. How does correlation between assets affect portfolio risk?
3. What does a correlation coefficient of -1 mean?
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Diversification is a core principle in portfolio management that aims to reduce risk by spreading investments across different assets. The idea is that by holding a variety of assets, you decrease the impact that any single asset's poor performance can have on the overall portfolio. This is because not all assets move in the same direction or with the same magnitude at the same time.
Correlation is a statistical measure that describes how two assets move in relation to each other. It ranges from -1 to 1:
- A correlation of
1means both assets move perfectly in sync; - A correlation of
0means their movements are unrelated; - A correlation of
-1means the assets move in exactly opposite directions.
Understanding how assets are correlated is crucial for portfolio construction. When you combine assets with low or negative correlation, you can achieve a smoother, more stable overall portfolio performance, reducing risk without necessarily sacrificing returns.
1234567891011import numpy as np # Sample returns for two different assets asset_a_returns = [0.01, 0.02, -0.005, 0.03, 0.015] asset_b_returns = [-0.002, 0.018, 0.01, -0.004, 0.02] # Calculate correlation using numpy correlation_matrix = np.corrcoef(asset_a_returns, asset_b_returns) correlation = correlation_matrix[0, 1] print("Correlation between Asset A and Asset B:", round(correlation, 2))
When assets in a portfolio have negative or low correlation, the ups and downs of their returns tend to offset each other. This means that when one asset's value drops, the other might remain stable or even increase, helping to cushion the overall impact on your portfolio. As a result, the total volatility—or risk—of the portfolio can be lower than that of the individual assets. This is the main reason diversification works: combining assets that do not move together reduces the likelihood of experiencing large losses at the same time.
123456789101112131415161718192021import numpy as np # Assume equal investment in both assets weights = np.array([0.5, 0.5]) returns = np.array([asset_a_returns, asset_b_returns]) # Calculate average returns for each asset mean_returns = np.mean(returns, axis=1) # Portfolio expected return portfolio_return = np.dot(weights, mean_returns) # Calculate covariance matrix cov_matrix = np.cov(returns) # Portfolio variance portfolio_variance = np.dot(weights.T, np.dot(cov_matrix, weights)) # Portfolio standard deviation (risk) portfolio_risk = np.sqrt(portfolio_variance) print("Portfolio Expected Return:", round(portfolio_return, 4)) print("Portfolio Risk (Std Dev):", round(portfolio_risk, 4))
1. What is the main benefit of diversification in a portfolio?
2. How does correlation between assets affect portfolio risk?
3. What does a correlation coefficient of -1 mean?
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