Assessing differences in mutual fund returns across fund types adjusted for market volatility through Pearson and Spearman Correlation

Project info

• Field of studyEconomics and Finance
• LevelUndergraduate thesis (S1)
• Method typeInferential Statistics
• Estimated build time± 3 working days
• Toolsscipy.stats pearsonr, spearmanr; pandas.DataFrame.corr
• PriceUS$16 - US$103

Research goal

Apply Pearson and Spearman Correlation to synthetic data to test differences in mutual fund returns across fund types adjusted for market volatility and conclude on statistical significance.

Variables

Example result

• -0.755Pearson r
• <0.001Pearson p-value
• -0.699Spearman rho
• <0.001Spearman p-value
• 0.571r squared
• 0.13595% CI width (r)

Correlation between Mutual fund return and Fund type: Pearson r = -0.755 (p < 0.001) and Spearman rho = -0.699; the relationship is negative and strong.

Computed from illustrative synthetic data, not from a real study.

About Pearson and Spearman Correlation

Pearson correlation measures the strength of the linear relationship between two numeric variables, while Spearman measures a monotonic rank-based relationship. They are used to explore relations among variables before or without a predictive model.

Steps

1. 1Draw a scatter plot to see the pattern
2. 2Check normality and outliers
3. 3Compute Pearson if linear and normal
4. 4Compute Spearman if ordinal, non-normal, or with outliers
5. 5Obtain the coefficient and p-value
6. 6Build a correlation matrix and heatmap when there are many variables

Assumptions to check

• Pearson: linear relation and roughly normal data
• Spearman: monotonic relation
• Independent observations without extreme outliers

Reading and reporting the results

Report the coefficient r or rho, p-value, and sample size, then interpret the strength. Remind readers that correlation does not prove causation.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.stats as st

rng = np.random.default_rng(28)
n = 120
fund_type = rng.normal(10, 2, n)
market_volatility = rng.normal(5, 1, n)
mutual_fund_return = 2 * fund_type + np.exp(0.3 * market_volatility) + rng.normal(0, 2, n)

r, p = st.pearsonr(fund_type, mutual_fund_return)
rho, p2 = st.spearmanr(market_volatility, mutual_fund_return)
print("Pearson X1-Y: r =", round(r, 3), "p =", round(p, 5))
print("Spearman X2-Y: rho =", round(rho, 3), "p =", round(p2, 5))

df = pd.DataFrame({"x1": fund_type, "x2": market_volatility, "y": mutual_fund_return})
corr = df.corr(method="spearman")
print(corr.round(2))

fig, ax = plt.subplots(1, 2, figsize=(10, 4))
ax[0].scatter(fund_type, mutual_fund_return, s=10); ax[0].set_xlabel("x1"); ax[0].set_ylabel("y")
im = ax[1].imshow(corr, vmin=-1, vmax=1, cmap="coolwarm")
ax[1].set_xticks(range(3)); ax[1].set_xticklabels(corr.columns)
ax[1].set_yticks(range(3)); ax[1].set_yticklabels(corr.columns)
plt.colorbar(im, ax=ax[1])
plt.tight_layout()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions