Risk Parity

Risk parity allocates capital so that each asset (or asset class) contributes the same amount of risk to the portfolio. Translated: weight inversely to volatility, then optionally lever the whole thing up to hit a target portfolio vol. The intuition is that a 60/40 stock/bond mix is actually 90/10 in risk terms because equities are 3× more volatile than bonds — so you're accidentally running an equity bet with a bond garnish.

The institutional grandfather is Bridgewater's All Weather fund (1996), which packaged the idea as a four-quadrant macro allocation balanced across growth and inflation regimes. Practitioner versions range from naive inverse-vol to full risk-budgeted optimisers.

# Naive inverse-volatility weighting
for each asset i:
  vol_i = rolling_std(returns_i, 60)
  weight_i = (1 / vol_i) / sum(1 / vol_j for j in universe)

# Optional: scale to target portfolio vol
portfolio_vol = sqrt(w' @ cov_matrix @ w)
leverage = target_vol / portfolio_vol
weights *= leverage  # may exceed 1.0 (uses margin)

The naive version assumes zero correlation between assets, which is wrong but tractable. The full version solves for weights that equalise marginal risk contributions accounting for the covariance matrix — same idea, more arithmetic, generally better in practice.

Diversified rising markets where stocks and bonds have negative correlation. The 1990s through the late 2010s were the golden era: equities compounded, bonds provided ballast and rallied during equity drawdowns, and the levered combination earned a higher Sharpe than either leg alone. Risk parity ate well from 2009 to 2021.

It also works structurally well in any environment where inflation is contained and central banks can ease into stress. Both stocks and bonds rally when the cost of capital falls — risk parity captures both legs.

When stocks and bonds crash together. 2022 was the textbook case: persistent inflation forced the Fed to hike into a slowdown, equities fell 18%, the long bond fell 30%, and risk parity portfolios — levered into the joint crash — drew down 20–30%. The diversification assumption failed exactly when it was supposed to help.

The deeper problem: risk parity treats historical volatility as a stationary input. When vol regimes shift faster than the rolling window can update, the weights are based on yesterday's reality. Bond vol in 2022 was 3× its 2010s baseline; the strategy was running on stale risk numbers for months.

• PSR-DSR gap large. Risk parity on a small universe (4 assets — typical: SPY, TLT, GLD, DBC) has limited candidate diversity. Quantis runs 4 variants for the candidate search; with only 4 underlying assets the variants collapse onto similar portfolios and DSR deflation hits hard. Expect PSR-DSR gaps of 30+ points and don't panic.
• CPCV fraction-positive often < 70%. Small-universe strategies fail more CPCV paths because the asset selection has no degrees of freedom — every path holds basically the same things. Below 60% is genuine concern; 60–70% is the structural floor for 4-asset portfolios.
• Beta < 0.6 to SPY (unlevered). Healthy unlevered risk parity has equity exposure but it's diluted. After leverage, beta can climb back above 1.0 — that's expected, not a bug.
• MaxDD lower than 60/40. The whole point. If your risk parity backtest shows MaxDD comparable to or worse than a plain 60/40, the leverage is wrong (probably too high) or the correlation regime in your sample broke the diversification.

• Backtesting only through 2009–2021. The strategy looks magical there because stocks and bonds were negatively correlated and both compounded. Run it through the 1970s (if you have the data) and 2022 to see the failure mode.
• Ignoring the cost of leverage. Risk parity hits target vol via futures or margin loans; financing costs eat the marginal return. A backtest at zero financing cost overstates real-world Sharpe by 0.2–0.4.
• Static rolling window. A 60-day vol estimate adapts to vol regime changes too slowly. Some implementations use shorter windows or blend short and long; check whether your backtest's vol estimator can keep up with regime breaks.

• Walk-forward vs CPCV → why small-universe strategies fail more CPCV paths and how to read the fraction-positive metric.
• Sharpe vs PSR vs DSR → the metrics that explain the PSR-DSR gap on small-universe portfolios.