Statistical Analysis for Investment Decisions
Understanding how to make informed investment decisions often requires more than just observing historical returns; you need to determine whether observed differences are statistically significant or could have occurred by chance. Hypothesis testing provides a formal way to test assumptions about financial data, such as whether one asset truly outperforms another. Confidence intervals allow you to estimate a range within which a true parameter, like the mean return, is likely to fall. Both are essential for investors seeking to make data-driven decisions and avoid common pitfalls like over-interpreting random fluctuations in returns.
123456789101112import numpy as np from scipy import stats # Simulated daily returns for two assets asset_a_returns = np.array([0.001, 0.002, -0.001, 0.003, 0.002, 0.000, 0.001]) asset_b_returns = np.array([0.000, 0.001, -0.002, 0.002, 0.001, -0.001, 0.000]) # Perform an independent t-test t_stat, p_value = stats.ttest_ind(asset_a_returns, asset_b_returns, equal_var=False) print("t-statistic:", t_stat) print("p-value:", p_value)
When you run a t-test using scipy.stats.ttest_ind, you compare the means of two independent samples—in this case, the returns of two different assets. The output includes a t-statistic, which measures the size of the difference relative to the variation in your sample data, and a p-value, which helps you judge statistical significance. If the p-value is small (commonly below 0.05), you have evidence to reject the null hypothesis that the two assets have the same mean return. Otherwise, you cannot confidently claim a difference.
A confidence interval, on the other hand, gives you a range of plausible values for a parameter such as the mean return. For example, a 95% confidence interval suggests that, if you repeated your sampling many times, 95% of those intervals would contain the true mean. This helps investors understand the uncertainty around their estimates and avoid overconfidence in point values.
123456789101112131415161718import numpy as np from scipy import stats # Simulated daily returns for an asset returns = np.array([0.001, 0.002, -0.001, 0.003, 0.002, 0.000, 0.001]) # Calculate sample mean and standard error mean_return = np.mean(returns) sem = stats.sem(returns) # Calculate 95% confidence interval for the mean confidence = 0.95 h = sem * stats.t.ppf((1 + confidence) / 2., len(returns)-1) lower_bound = mean_return - h upper_bound = mean_return + h print("Mean return:", mean_return) print("95% confidence interval:", (lower_bound, upper_bound))
1. What does a p-value indicate in hypothesis testing?
2. Why might an investor use a confidence interval?
3. Which scipy function is used for t-tests?
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Understanding how to make informed investment decisions often requires more than just observing historical returns; you need to determine whether observed differences are statistically significant or could have occurred by chance. Hypothesis testing provides a formal way to test assumptions about financial data, such as whether one asset truly outperforms another. Confidence intervals allow you to estimate a range within which a true parameter, like the mean return, is likely to fall. Both are essential for investors seeking to make data-driven decisions and avoid common pitfalls like over-interpreting random fluctuations in returns.
123456789101112import numpy as np from scipy import stats # Simulated daily returns for two assets asset_a_returns = np.array([0.001, 0.002, -0.001, 0.003, 0.002, 0.000, 0.001]) asset_b_returns = np.array([0.000, 0.001, -0.002, 0.002, 0.001, -0.001, 0.000]) # Perform an independent t-test t_stat, p_value = stats.ttest_ind(asset_a_returns, asset_b_returns, equal_var=False) print("t-statistic:", t_stat) print("p-value:", p_value)
When you run a t-test using scipy.stats.ttest_ind, you compare the means of two independent samples—in this case, the returns of two different assets. The output includes a t-statistic, which measures the size of the difference relative to the variation in your sample data, and a p-value, which helps you judge statistical significance. If the p-value is small (commonly below 0.05), you have evidence to reject the null hypothesis that the two assets have the same mean return. Otherwise, you cannot confidently claim a difference.
A confidence interval, on the other hand, gives you a range of plausible values for a parameter such as the mean return. For example, a 95% confidence interval suggests that, if you repeated your sampling many times, 95% of those intervals would contain the true mean. This helps investors understand the uncertainty around their estimates and avoid overconfidence in point values.
123456789101112131415161718import numpy as np from scipy import stats # Simulated daily returns for an asset returns = np.array([0.001, 0.002, -0.001, 0.003, 0.002, 0.000, 0.001]) # Calculate sample mean and standard error mean_return = np.mean(returns) sem = stats.sem(returns) # Calculate 95% confidence interval for the mean confidence = 0.95 h = sem * stats.t.ppf((1 + confidence) / 2., len(returns)-1) lower_bound = mean_return - h upper_bound = mean_return + h print("Mean return:", mean_return) print("95% confidence interval:", (lower_bound, upper_bound))
1. What does a p-value indicate in hypothesis testing?
2. Why might an investor use a confidence interval?
3. Which scipy function is used for t-tests?
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