Вивчайте Sharpe Ratio and Performance Evaluation | Risk Analysis and Portfolio Management

Understanding how to measure and compare the performance of investment portfolios is critical in finance. The Sharpe Ratio is one of the most widely used metrics for this purpose. It provides a way to evaluate how much excess return you receive for the extra volatility endured by holding a riskier asset compared to a risk-free asset. The Sharpe Ratio is calculated using the following formula:

[ \text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p} ]

where:

R_p is the average return of the portfolio;
R_f is the risk-free rate of return;
σ_p is the standard deviation of the portfolio's returns.

By standardizing excess returns by the amount of risk taken, the Sharpe Ratio allows you to compare the performance of different portfolios or strategies on a level playing field. This is especially useful when you want to determine whether higher returns are due to smart investment choices or simply taking on more risk.


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import numpy as np

# Example portfolio returns (in decimal form, e.g., 0.01 for 1%)
portfolio_returns = np.array([0.01, 0.015, -0.005, 0.02, 0.012])
risk_free_rate = 0.003  # 0.3% risk-free rate

# Calculate average portfolio return and standard deviation
avg_return = np.mean(portfolio_returns)
std_dev = np.std(portfolio_returns, ddof=1)

# Calculate Sharpe Ratio
sharpe_ratio = (avg_return - risk_free_rate) / std_dev

print(f"Sharpe Ratio: {sharpe_ratio:.2f}")

When you interpret the Sharpe Ratio, a higher value typically means better risk-adjusted performance. In other words, a portfolio with a higher Sharpe Ratio is delivering more return per unit of risk taken. However, it is important to recognize the limitations of the Sharpe Ratio. It assumes that returns are normally distributed and that risk is fully captured by standard deviation, which may not always be the case in real-world financial markets. The Sharpe Ratio can also be distorted if the returns contain outliers or if the risk-free rate is not chosen appropriately. Therefore, you should use the Sharpe Ratio alongside other metrics and qualitative analysis to get a complete picture of portfolio performance.


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import numpy as np

# Portfolio A and Portfolio B returns
returns_a = np.array([0.012, 0.017, -0.003, 0.022, 0.011])
returns_b = np.array([0.02, -0.01, 0.025, 0.018, 0.005])
risk_free_rate = 0.003

# Calculate Sharpe Ratios
sharpe_a = (np.mean(returns_a) - risk_free_rate) / np.std(returns_a, ddof=1)
sharpe_b = (np.mean(returns_b) - risk_free_rate) / np.std(returns_b, ddof=1)

print(f"Sharpe Ratio for Portfolio A: {sharpe_a:.2f}")
print(f"Sharpe Ratio for Portfolio B: {sharpe_b:.2f}")

if sharpe_a > sharpe_b:
    print("Portfolio A has better risk-adjusted performance.")
else:
    print("Portfolio B has better risk-adjusted performance.")

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Suggested prompts:

What are some alternatives to the Sharpe Ratio for evaluating portfolio performance?

Can you explain how to choose an appropriate risk-free rate?

What are the main limitations of using the Sharpe Ratio in real-world investing?

Свайпніть щоб показати меню

[ \text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p} ]

where:

R_p is the average return of the portfolio;
R_f is the risk-free rate of return;
σ_p is the standard deviation of the portfolio's returns.


              1234567891011121314
            
import numpy as np

# Example portfolio returns (in decimal form, e.g., 0.01 for 1%)
portfolio_returns = np.array([0.01, 0.015, -0.005, 0.02, 0.012])
risk_free_rate = 0.003  # 0.3% risk-free rate

# Calculate average portfolio return and standard deviation
avg_return = np.mean(portfolio_returns)
std_dev = np.std(portfolio_returns, ddof=1)

# Calculate Sharpe Ratio
sharpe_ratio = (avg_return - risk_free_rate) / std_dev

print(f"Sharpe Ratio: {sharpe_ratio:.2f}")


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import numpy as np

# Portfolio A and Portfolio B returns
returns_a = np.array([0.012, 0.017, -0.003, 0.022, 0.011])
returns_b = np.array([0.02, -0.01, 0.025, 0.018, 0.005])
risk_free_rate = 0.003

# Calculate Sharpe Ratios
sharpe_a = (np.mean(returns_a) - risk_free_rate) / np.std(returns_a, ddof=1)
sharpe_b = (np.mean(returns_b) - risk_free_rate) / np.std(returns_b, ddof=1)

print(f"Sharpe Ratio for Portfolio A: {sharpe_a:.2f}")
print(f"Sharpe Ratio for Portfolio B: {sharpe_b:.2f}")

if sharpe_a > sharpe_b:
    print("Portfolio A has better risk-adjusted performance.")
else:
    print("Portfolio B has better risk-adjusted performance.")

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Секція 2. Розділ 4

Sharpe Ratio and Performance Evaluation

1. What does a higher Sharpe Ratio indicate?

2. Which variable in the Sharpe Ratio formula represents the risk-free rate?

3. Why is it important to consider risk-adjusted returns?

Sharpe Ratio and Performance Evaluation

1. What does a higher Sharpe Ratio indicate?

2. Which variable in the Sharpe Ratio formula represents the risk-free rate?

3. Why is it important to consider risk-adjusted returns?