What’s the question?
Diversification is the only free lunch in finance, but it only works when holdings respond to different economic forces. A portfolio split evenly across eight sector ETFs appears diversified, yet if those sectors move in lockstep, the portfolio behaves like a single concentrated bet. The core question is empirical: which U.S. equity sectors provide genuine return independence, and which are redundant from a risk perspective?
A correlation matrix quantifies this. Each cell contains the Pearson correlation coefficient between two sectors’ daily return series, ranging from -1 (perfect inverse movement) to +1 (perfect co-movement). Values near zero indicate statistical independence — the ideal condition for diversification. Collapsing such a matrix into a single count of independent bets, and tracking that count through time, is the approach of an eigenvalue study of nine sector funds.
The approach
Eight SPDR sector ETFs serve as proxies for the major segments of the U.S. equity market: Technology (XLK), Financials (XLF), Healthcare (XLV), Energy (XLE), Consumer Discretionary (XLY), Consumer Staples (XLP), Industrials (XLI), and Utilities (XLU). One year of daily returns is fetched for each, pivoted into a wide-format DataFrame (one column per sector), and the pairwise Pearson correlation is computed across all 28 unique pairs. The three highest and three lowest correlations are extracted to identify the most redundant and most diversifying combinations.
import xfinlink as xfl
import pandas as pd
import numpy as np
xfl.set_api_key("your_key") # free at https://xfinlink.com/signup
tickers = ["XLK","XLF","XLV","XLE","XLY","XLP","XLI","XLU"]
labels = {"XLK":"Tech","XLF":"Financials","XLV":"Healthcare","XLE":"Energy",
"XLY":"ConsDisc","XLP":"ConsStaples","XLI":"Industrials","XLU":"Utilities"}
df = xfl.prices(tickers, period="1y", fields=["return_daily"])
returns = df.pivot_table(index="date", columns="ticker", values="return_daily").dropna()
corr = returns.corr().round(3)
corr.index = [labels[t] for t in corr.index]
corr.columns = [labels[t] for t in corr.columns]
print("=== Sector Correlation Matrix (1Y Daily Returns) ===")
print(corr.to_string())
pairs = []
for i, c1 in enumerate(corr.columns):
for j, c2 in enumerate(corr.columns):
if i < j: pairs.append((c1, c2, corr.iloc[i, j]))
pairs.sort(key=lambda x: x[2])
print("\nLeast correlated (best diversifiers):")
for c1, c2, v in pairs[:3]: print(f" {c1} <-> {c2}: {v:.3f}")
print("\nMost correlated:")
for c1, c2, v in pairs[-3:]: print(f" {c1} <-> {c2}: {v:.3f}")Output:
=== Sector Correlation Matrix (1Y Daily Returns) ===
Energy Financials Industrials Tech ConsStaples Utilities Healthcare ConsDisc
Energy 1.000 0.059 0.061 -0.049 0.100 0.093 0.023 -0.013
Financials 0.059 1.000 0.615 0.448 0.194 0.126 0.419 0.613
Industrials 0.061 0.615 1.000 0.572 0.285 0.347 0.473 0.632
Tech -0.049 0.448 0.572 1.000 -0.152 0.061 0.164 0.624
ConsStaples 0.100 0.194 0.285 -0.152 1.000 0.410 0.426 0.198
Utilities 0.093 0.126 0.347 0.061 0.410 1.000 0.270 0.136
Healthcare 0.023 0.419 0.473 0.164 0.426 0.270 1.000 0.359
ConsDisc -0.013 0.613 0.632 0.624 0.198 0.136 0.359 1.000
Least correlated (best diversifiers):
Tech <-> ConsStaples: -0.152
Energy <-> Tech: -0.049
Energy <-> ConsDisc: -0.013
Most correlated:
Financials <-> Industrials: 0.615
Tech <-> ConsDisc: 0.624
Industrials <-> ConsDisc: 0.632What this tells us
Energy is the standout diversifier in this matrix. Its highest correlation with any other sector is 0.100 (Consumer Staples), and it is slightly negative with both Technology (-0.049) and Consumer Discretionary (-0.013). Adding energy exposure to a portfolio dominated by growth sectors provides genuine risk reduction, not merely the appearance of it.
The Technology-Consumer Staples pair at -0.152 is the only meaningfully negative correlation in the entire matrix. These two sectors respond to opposing economic conditions: technology benefits from risk appetite and growth expectations, while consumer staples attract capital during defensive rotations. This inverse relationship makes them natural hedges within an equity-only portfolio.
At the other extreme, Financials, Industrials, and Consumer Discretionary form a tightly correlated cluster with all pairwise correlations above 0.61. These three sectors are all proxies for the same underlying factor — economic growth expectations. Holding all three does not meaningfully diversify; it triples down on a single macroeconomic bet.
So what?
For portfolio construction, the actionable finding is that sector selection matters more than sector count. An eight-sector portfolio where half the weight sits in the Financials-Industrials-ConsDisc cluster is less diversified than a four-sector portfolio that pairs Technology with Consumer Staples and adds Energy. The correlation matrix provides the empirical basis for those allocation decisions. Before adding a new sector position, check its correlation against existing holdings — if it exceeds 0.5 with anything already in the portfolio, the marginal diversification benefit is limited. A comparison of sector correlations in calm and stressed markets checks whether figures like these hold in a sell-off.