# Correlation

Source: https://www.yieldcurve.pro/corr

This tool measures how Treasury bonds at each maturity co-move with the S&P 500. For six Treasury ETFs — SHV (0–1 Yr), SHY (1–3 Yr), IEI (3–7 Yr), IEF (7–10 Yr), TLH (10–20 Yr), and TLT (20+ Yr) — it computes the Pearson correlation between that ETF's daily returns and SPY's daily returns over a rolling window. The chart plots all six correlations on a single curve, ordered by tenor from shortest to longest.

The shaded band shows ±1 standard deviation of historical correlations at today's inflation level — specifically, today's reading of the chosen breakeven rate. To build it: split the full range of the breakeven series into 30 equal-width buckets, find the bucket containing today's breakeven rate, then compute the mean and standard deviation of every historical correlation that fell in that same bucket. The band answers a precise question: when breakeven inflation sat where it sits today, how dispersed were stock–bond correlations?



**Controls**

* **Horizon** — the rolling-window length: 1 Mo, 3 Mo, 6 Mo, or 1 Yr of trading days. A 1 Mo window reacts fast to regime shifts but carries more noise. A 1 Yr window is stable but lags turning points.
* **Inflation** — the breakeven series used to define inflation buckets. The 5 Yr breakeven is more volatile, so its buckets are sparser and the ±1σ band wider. The 10 Yr breakeven is more stable, concentrating more observations per bucket and producing a tighter band.

**How to Read It**

* **Line above zero** — bonds at that maturity move with stocks (poor diversifier).
* **Line below zero** — bonds hedge equity risk.
* **Shaded band** — the typical range of correlations when breakeven inflation matched today's breakeven rate. Points outside the band are unusual for the current inflation environment.
* **Downward-sloping curve** — longer-duration bonds are better equity hedges than shorter-duration bonds.

**Use Cases**

* Identify which Treasury maturity best diversifies equities given today's breakeven rate.
* Compare short-duration (SHV, SHY) versus long-duration (TLH, TLT) hedging behavior.
* Pair with [Portfolio](https://www.yieldcurve.pro/portfolio) to size bond allocations based on current correlation structure.

**Why Breakevens Instead of CPI?**

Stock-bond correlation shifts are driven by inflation *expectations*, not past prints. When markets fear future inflation, bonds sell off alongside stocks; when they fear deflation, bonds rally as stocks fall. Breakeven rates measure the expectation that drives this mechanism. CPI tells you what already happened — and publishes monthly with a lag. Breakevens update daily as markets digest each data release, giving ~250 observations per year versus 12 for CPI. That frequency matters: with 30 inflation buckets, CPI would leave most buckets nearly empty.

**Notes**

* Breakeven rates are daily, market-implied inflation expectations derived from TIPS pricing.
* ETF data starts circa 2002; breakevens from 2003. The effective start date depends on the lookback window.
* The ±1σ band uses 30 equal-width buckets spanning the full historical range of the chosen breakeven series.