Risk parity: how equal risk weights are calculated, the leverage and the 2022 losses

Put 60% of a portfolio in stocks and 40% in bonds, give stocks a volatility of 15% a year and bonds 5%, set the correlation between them at 0.2, and the stock half produces 91.8% of the portfolio's swings. The bonds, with 40% of the money, produce 8.2%. Estimates for real 60/40 and similar portfolios run from roughly 90% to more than 95%, depending on the period and the indexes used.

Risk parity is a method of portfolio construction in which each asset class contributes the same share of total risk, usually measured as volatility. Bonds move less than stocks, so a risk parity portfolio holds far more bonds than stocks by dollar amount. Most versions then use futures or borrowing to raise the whole portfolio to the risk level of a conventional stock and bond mix.

How much of a 60/40 portfolio's risk comes from stocks

A holding's risk contribution is its weight multiplied by the change in portfolio volatility when that weight rises by a small amount. The contributions of all holdings add up exactly to the portfolio's volatility, which is what allows a statement such as "stocks carry 92% of the risk".

For the 60/40 example, the inputs are a stock variance of 0.0225 (15% squared), a bond variance of 0.0025 (5% squared) and a covariance of 0.0015 (0.2 × 15% × 5%). The arithmetic runs in four lines:

1. Portfolio variance: 0.36 × 0.0225 + 0.16 × 0.0025 + 2 × 0.6 × 0.4 × 0.0015 = 0.00810 + 0.00040 + 0.00072 = 0.00922. Its square root is a volatility of 9.60%.
2. Covariance of stocks with the portfolio: 0.6 × 0.0225 + 0.4 × 0.0015 = 0.0141. Stock contribution: 0.6 × 0.0141 ÷ 0.0960 = 8.81 percentage points.
3. Covariance of bonds with the portfolio: 0.6 × 0.0015 + 0.4 × 0.0025 = 0.0019. Bond contribution: 0.4 × 0.0019 ÷ 0.0960 = 0.79 points.
4. The two contributions add up to 9.60, and 8.81 ÷ 9.60 = 91.8%.

Holding the volatilities fixed, the stock share depends on the correlation:

A negative correlation lowers total volatility and pushes the stock share toward 100%, because the bonds then offset part of the stock moves and their own net contribution shrinks close to zero.

The equal risk contribution rule for two assets

Risk parity sets every contribution equal. With two assets the solution has a closed form. Setting the two contributions equal gives w₁²σ₁² + w₁w₂ρσ₁σ₂ = w₂²σ₂² + w₁w₂ρσ₁σ₂, where ρ is the correlation. The correlation term appears on both sides and cancels, which leaves w₁σ₁ = w₂σ₂: each weight is proportional to the inverse of the asset's volatility.

For stocks at 15% and bonds at 5%, that gives 5 ÷ 20 = 25% in stocks and 15 ÷ 20 = 75% in bonds. At a 0.2 correlation, this portfolio has a volatility of 5.81%, and each asset contributes about 2.9 points of it.

Simple risk parity backtests apply the inverse volatility rule to any number of assets. The 2012 leverage aversion study built its portfolios that way, using three years of monthly returns to estimate each volatility, and AQR's 2010 white paper used a 12-month estimate. With three or more assets, inverse volatility and equal risk contribution give different answers.

A worked three-asset example with stocks, bonds and commodities

The inputs below are round numbers close to the long-run volatilities of global stocks, US bonds and the S&P GSCI commodity index, which were 15.71%, 5.36% and 19.24% a year from 1973 to 2010. The correlations are assumptions chosen for the example.

Inverse volatility weights come to 21.1% stocks, 63.2% bonds and 15.8% commodities. With these correlations they leave stocks with 37.5% of the risk, bonds with 30.0% and commodities with 32.5%. Stocks are correlated with both other assets, so they carry more than a third.

No closed form exists for three assets with unequal correlations, so the weights come from a solver. A short Python script that repeatedly sets each weight to σ_p² ÷ (3 × (Σw)_i), rescales the weights to sum to 100% and stops when they no longer change returns this portfolio:

The covariance of stocks with the portfolio is 0.0225 × 0.1888 + 0.0015 × 0.6540 + 0.0090 × 0.1571 = 0.006644, where 0.0090 is the stock and commodity covariance (0.3 × 15% × 20%). Multiplied by the 18.88% weight and divided by the 6.135% volatility, it gives 2.045 points. Bonds give 0.6540 × 0.001918 ÷ 0.06135 = 2.045, and commodities give 0.1571 × 0.007985 ÷ 0.06135 = 2.045. The three contributions add up to the portfolio's volatility.

Against inverse volatility, the solver takes 2.2 points of weight out of stocks, the asset most correlated with the others, and moves it to bonds, which are uncorrelated with commodities.

Leverage and what it costs

Unlevered, the three-asset portfolio has a volatility of 6.1%, against 9.6% for the 60/40 mix built from the same stock and bond inputs. To reach the 60/40 risk level, every position is multiplied by 9.60 ÷ 6.135 = 1.565. The levered portfolio holds 29.6% in stocks, 102.4% in bonds and 24.6% in commodities, 156.5% of capital in total, with the extra 56.5% financed by borrowing or, more often, by futures contracts that require only a margin deposit.

Borrowed money pays a short-term interest rate, and futures prices build a similar financing cost into the contract. The two-asset version above needs 1.65 times leverage, so 65% of capital is financed. At the 3-month Treasury bill rate of 0.15% in January 2022, financing that 65% cost about 0.1% of capital a year. At 5.34% in October 2023, it cost about 3.5% a year, before any spread a lender adds.

The leverage aversion study's simulations make no adjustment for financing spreads or for the cost of forced deleveraging, and measure returns in excess of Treasury bills. In a robustness appendix, the levered risk parity portfolio still beat the market portfolio when financed at LIBOR, the most expensive rate tested.

Why safer assets may pay more per unit of risk

One theory for why risk parity should earn more per unit of risk comes from Clifford Asness, Andrea Frazzini and Lasse Pedersen, in "Leverage aversion and risk parity", published in the Financial Analysts Journal in January 2012. Many investors cannot or will not borrow. To reach a higher expected return, they buy riskier assets such as stocks, which bids up their prices and lowers their future return per unit of risk. Safer assets are left offering a higher return per unit of risk, and an investor able to apply leverage can collect it. The same argument within a single asset class underlies the low-volatility anomaly and betting against beta.

The paper's long US sample, 1926 to 2010, set each asset's weight at the inverse of its volatility and rebalanced monthly:

In a broader sample from 1973 to 2010, with global stocks, US bonds, credit and commodities, levered risk parity returned 6.15% a year over T-bills against 4.31% for the value-weighted market at the same 10.10% volatility, a Sharpe ratio of 0.61 against 0.43. Bonds rallied for most of the three decades before 2010, and the paper answers that objection with the full 1926 to 2010 sample, over which bond yields made a near complete round trip. The authors work at AQR Capital Management, which runs risk parity funds, and the journal printed that disclosure with the article.

The All Weather strategy and the origin of the term

Harry Markowitz described efficient portfolios in 1952, and James Tobin showed in 1958 that investors should hold a combination of one diversified portfolio and cash. Liquid futures markets and cheaper financing later let large portfolios extend that combination into borrowing.

Bridgewater Associates launched its All Weather strategy in 1996, originally for Ray Dalio's trust assets. The design holds four sub-portfolios with the same risk, each built to do well in one environment relative to what markets expect:

• inflation rising
• inflation falling
• growth rising
• growth falling

The first pension fund to adopt it started with a 200 million dollar allocation. Bridgewater, founded by Dalio in 1975, appears in our list of hedge funds among the global macro managers.

Edward Qian of PanAgora Asset Management wrote "Risk parity portfolios: efficient portfolios through true diversification" in September 2005, nine years after All Weather's launch, and he is credited with defining the term.

AQR's 2010 white paper built a "simple risk parity" portfolio from three indexes, the MSCI World, a US government bond index and the S&P GSCI, with each weight set by a 12-month volatility forecast. From January 1971 to December 2009 the simulated portfolio returned 11.2% a year against 9.6% for a 60/40 mix, both at 10.1% volatility, for a Sharpe ratio of 0.45 against 0.28. It lagged in two of the periods the paper singled out: in the Fed's surprise rate increases of February and March 1994 it lost 9.0% against 5.8% for 60/40, and in the stock rally from September 1982 to March 1984 it gained 38.0% against 48.0%.

The 2013 taper tantrum

On May 22, 2013, Fed Chairman Ben Bernanke told Congress's Joint Economic Committee that the Fed was prepared to increase or reduce the pace of its asset purchases. Bond yields rose through the second quarter on speculation that the purchases would be tapered by the end of the year, and German, UK and Japanese government bonds fell along with Treasuries.

The AQR Risk Parity Fund, a mutual fund with more than 930 million dollars in assets at the end of 2013, invested through futures and swaps across global stocks, bonds, currencies, credit and commodities. Its Class I shares returned 0.12% for 2013, while a 60/40 benchmark of the S&P 500 and the Barclays US Aggregate returned 17.57%. By asset class:

• equities added 5.89 percentage points
• credit added 2.67 points
• nominal bonds took away 3.42 points, most of it in the second quarter
• inflation-linked bonds took away 5.02 points

The fund targeted about 10% annual volatility. In June, as volatility rose, its drawdown control policy cut the risk target and exposures dropped sharply, so the fund reduced positions during the sell-off. The target was raised again later in the year, and the fund's beta to the S&P 500 went from 0.41 at the end of 2012 to 0.65 at the end of 2013.

2022: stocks, bonds and inflation-linked bonds fell together

In 2022 the Federal Reserve raised rates by 4.25 percentage points in nine months. From the first quarter through the third, the RPAR Risk Parity ETF lost 28.48% of its net asset value and the more leveraged UPAR Ultra Risk Parity ETF lost 37.53%. The tightening pushed down almost every asset class at the same time, including the long Treasuries and long inflation-protected bonds that make up much of a risk parity portfolio. A 60% S&P 500 and 40% Bloomberg US Aggregate mix lost 15.79% over the full year, and our 60/40 portfolio guide covers why stocks and bonds fell together.

Calendar-year returns at net asset value, from the funds' 2025 annual report:

From its launch on December 12, 2019 to the end of 2025, RPAR returned 3.83% a year. Over the same period a 60/40 mix of the S&P 500 and the Bloomberg US Aggregate returned 9.65% a year and the S&P 500 alone 15.32%. RPAR's net assets fell from 1.63 billion dollars at the end of 2021 to 563 million dollars at the end of 2025, a decline that reflects both losses and redemptions.

Risk parity ETFs and funds

The three US-listed ETFs below use risk parity or All Weather allocations. Our comparison of ETFs and mutual funds covers how the two structures differ in expenses, taxes and trading costs.

RPAR Risk Parity ETF (RPAR)

Launched December 12, 2019. Seeks exposures similar to the Advanced Research Risk Parity Index across global equities, US Treasuries, commodities and TIPS, with gold and commodity producer stocks in the commodity sleeve. Net expenses were 0.48% in 2025, 0.50% before a fee waiver. At the end of 2025, its securities plus the notional value of its Treasury futures came to about 120% of its 563 million dollars of net assets.

UPAR Ultra Risk Parity ETF (UPAR)

Launched January 3, 2022. Same four asset classes with more leverage. Net expenses were 0.64% in 2025. At the end of 2025, securities plus stock and Treasury futures came to about 168% of its 64 million dollars of net assets.

State Street Bridgewater All Weather ETF (ALLW)

Launched March 6, 2025 as the SPDR Bridgewater All Weather ETF and renamed on March 1, 2026. Total expenses were 0.80% annualized in the period to October 31, 2025. On that date it held inflation-linked Treasuries, stock ETFs, government bond and stock index futures in several countries, gold futures and commodity index swaps, for positions worth about 1.86 times its 651 million dollars of net assets. From launch to October 31, 2025 it returned 14.38%, against 18.43% for the MSCI ACWI index.

Criticisms of risk parity

• Results depend on the test period. In 2012 tests of value-weighted, 60/40, unlevered and levered risk parity portfolios, start and end dates changed the results even over periods of decades, transaction costs could reverse the ranking when leverage was used, and a statistically significant premium did not ensure outperformance over a realistic holding period.
• Bond-heavy weights. Equal risk weighting puts most of the capital in bonds, and levered versions hold more than 100% in them. In the three-asset example above, bonds reach 102.4% of capital after leverage. Rising rates hit that position directly, as in 2013 and 2022.
• Volatility understates tail losses. Risk parity equalizes volatility, which treats gains and losses alike. In the 1926 to 2010 sample, levered risk parity had a skewness of -0.36 against 0.20 for 60/40. Negative skewness means a longer tail of large monthly losses than of large gains.
• Correlations change. The weights depend on estimated correlations. When stocks and bonds fall together, as they did in 2022, the bond sleeve loses money in the same months as the stock sleeve.
• Volatility targets cut positions in sell-offs. A portfolio that holds its volatility constant reduces positions when volatility rises. The AQR fund's exposures dropped sharply in June 2013, during the second-quarter bond sell-off.
• Financing costs rise with rates. The cost of leverage moved from about 0.1% to about 3.5% of capital a year for a 1.65 times levered portfolio between January 2022 and October 2023.

This article is general information, not investment advice.

Frequently asked questions

What is risk parity in simple terms?

Risk parity is a way of building a portfolio so that each asset class, typically stocks, bonds, commodities and inflation-linked bonds, contributes the same share of the portfolio's total volatility. Because bonds move less than stocks, a risk parity portfolio holds more money in bonds, and most versions use futures or borrowing to lift the portfolio back to the risk level of a conventional stock and bond mix.

How do you calculate risk parity weights?

With two assets, each weight is proportional to the inverse of the asset's volatility and the correlation drops out: stocks at 15% volatility and bonds at 5% give 25% stocks and 75% bonds. With three or more assets, the weights come from a numerical solver that adjusts them until each asset's weight times its covariance with the portfolio, divided by the portfolio's volatility, is the same for every asset.

Is there a risk parity ETF?

Yes. The RPAR Risk Parity ETF has traded since December 2019 and charged net expenses of 0.48% in 2025. The UPAR Ultra Risk Parity ETF, launched in January 2022, applies more leverage to the same four asset classes for 0.64%. The State Street Bridgewater All Weather ETF (ALLW), launched in March 2025 under the SPDR name, charged total expenses of 0.80% annualized in its first reporting period.

Why do risk parity funds use leverage?

An unlevered risk parity portfolio holds mostly bonds, so its volatility and expected return are lower than those of a 60/40 mix. In a three-asset example with stocks at 15% volatility, bonds at 5% and commodities at 20%, the equal risk portfolio has a volatility of 6.1% against 9.6% for 60/40. Scaling every position by 1.565 brings it to the same 9.6%, with total positions of 156.5% of capital.

What does parity mean in risk parity?

Parity means equality. In risk parity, the equal quantity is each asset class's contribution to total portfolio risk, usually measured as volatility. Dollar amounts end up unequal: in a three-asset example with stocks, bonds and commodities, bonds take 65.4% of the capital so that their share of the risk matches that of each of the other two.