Oppiskele Sharpe Ratio and Performance Evaluation | Risk Analysis and Portfolio Optimization

The Sharpe ratio is a fundamental metric in finance used to evaluate the performance of an investment portfolio by adjusting returns for risk. It provides a standardized way to compare portfolios with different risk levels by measuring the excess return per unit of risk. The formula for the Sharpe ratio is:

Sharpe Ratio = (Portfolio Return − Risk-Free Rate) / Portfolio Standard Deviation

In this formula, the portfolio return represents the average return of the portfolio over a given period, the risk-free rate is the return of an investment considered free of risk (such as a U.S. Treasury bill), and the portfolio standard deviation measures the volatility or risk of the portfolio's returns. By subtracting the risk-free rate, the Sharpe ratio focuses on the additional return generated for taking on extra risk, making it a key metric for comparing the performance of different investment strategies.


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import numpy as np
import pandas as pd

# Simulated portfolio returns (daily)
returns = pd.Series([0.001, 0.002, -0.001, 0.003, 0.0005, -0.002, 0.0015])

# Annualize the mean and standard deviation (assuming 252 trading days)
mean_return = returns.mean() * 252
std_return = returns.std(ddof=1) * np.sqrt(252)

# Assume risk-free rate is 2% annually
risk_free_rate = 0.02

# Calculate Sharpe ratio
sharpe_ratio = (mean_return - risk_free_rate) / std_return
print(f"Sharpe Ratio: {sharpe_ratio:.2f}")

When interpreting Sharpe ratio values, a higher Sharpe ratio generally means that a portfolio offers better risk-adjusted returns. A Sharpe ratio above 1 is often considered good, above 2 very good, and above 3 excellent, but these thresholds can vary depending on market conditions and asset classes. However, the Sharpe ratio has limitations. It assumes returns are normally distributed and does not account for extreme events or changes in volatility over time. Additionally, the choice of risk-free rate and the time period analyzed can significantly affect the result. Therefore, while the Sharpe ratio is a useful tool for comparison, it should be used alongside other performance metrics and qualitative analysis.


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import matplotlib.pyplot as plt

# Simulated annualized returns and standard deviations for three portfolios
portfolios = {
    "Portfolio A": {"mean_return": 0.12, "std_return": 0.15},
    "Portfolio B": {"mean_return": 0.09, "std_return": 0.10},
    "Portfolio C": {"mean_return": 0.15, "std_return": 0.20},
}

risk_free_rate = 0.02

# Calculate Sharpe ratios
sharpe_ratios = {}
for name, stats in portfolios.items():
    sr = (stats["mean_return"] - risk_free_rate) / stats["std_return"]
    sharpe_ratios[name] = sr

# Visualize Sharpe ratios
plt.bar(sharpe_ratios.keys(), sharpe_ratios.values(), color=["skyblue", "salmon", "lightgreen"])
plt.ylabel("Sharpe Ratio")
plt.title("Sharpe Ratio Comparison of Portfolios")
plt.show()

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Osio 3. Luku 6

Kysy tekoälyä

Kysy mitä tahansa tai kokeile jotakin ehdotetuista kysymyksistä aloittaaksesi keskustelumme

Suggested prompts:

Can you explain how to interpret the Sharpe ratio values in the context of these portfolios?

What are some limitations of using the Sharpe ratio for portfolio comparison?

Can you suggest other metrics to use alongside the Sharpe ratio for evaluating investments?

Pyyhkäise näyttääksesi valikon

Sharpe Ratio = (Portfolio Return − Risk-Free Rate) / Portfolio Standard Deviation


              12345678910111213141516
            
import numpy as np
import pandas as pd

# Simulated portfolio returns (daily)
returns = pd.Series([0.001, 0.002, -0.001, 0.003, 0.0005, -0.002, 0.0015])

# Annualize the mean and standard deviation (assuming 252 trading days)
mean_return = returns.mean() * 252
std_return = returns.std(ddof=1) * np.sqrt(252)

# Assume risk-free rate is 2% annually
risk_free_rate = 0.02

# Calculate Sharpe ratio
sharpe_ratio = (mean_return - risk_free_rate) / std_return
print(f"Sharpe Ratio: {sharpe_ratio:.2f}")


              12345678910111213141516171819202122
            
import matplotlib.pyplot as plt

# Simulated annualized returns and standard deviations for three portfolios
portfolios = {
    "Portfolio A": {"mean_return": 0.12, "std_return": 0.15},
    "Portfolio B": {"mean_return": 0.09, "std_return": 0.10},
    "Portfolio C": {"mean_return": 0.15, "std_return": 0.20},
}

risk_free_rate = 0.02

# Calculate Sharpe ratios
sharpe_ratios = {}
for name, stats in portfolios.items():
    sr = (stats["mean_return"] - risk_free_rate) / stats["std_return"]
    sharpe_ratios[name] = sr

# Visualize Sharpe ratios
plt.bar(sharpe_ratios.keys(), sharpe_ratios.values(), color=["skyblue", "salmon", "lightgreen"])
plt.ylabel("Sharpe Ratio")
plt.title("Sharpe Ratio Comparison of Portfolios")
plt.show()

Oliko kaikki selvää?

Kiitos palautteestasi!

Osio 3. Luku 6

Sharpe Ratio and Performance Evaluation

1. What does a higher Sharpe ratio indicate about a portfolio's performance?

2. Why is the risk-free rate included in the Sharpe ratio calculation?

3. Which pandas method can be used to calculate the mean and standard deviation of returns?

Sharpe Ratio and Performance Evaluation

1. What does a higher Sharpe ratio indicate about a portfolio's performance?

2. Why is the risk-free rate included in the Sharpe ratio calculation?

3. Which pandas method can be used to calculate the mean and standard deviation of returns?