Risk Parity Library: Leverage Aversion and Risk Parity (Asness, Frazzini, & Pedersen, 2012)

Welcome to the latest installment in the Risk Parity Library, a series where I summarize some of the most important papers and books in the Risk Parity world. My goal is to save DIY investors a little time, highlight the key ideas, and point you toward the next step in your investing education. If you want to understand not just what Risk Parity is but why it works, this paper belongs near the top of your reading list.

Read the Original:

It originally appeared in the Financial Analysts Journal, Vol. 68, No. 1 (January/February 2012), pp. 47-59 (13 pages).

This is one of the foundational papers in the Risk Parity literature for two reasons.

First, it provides perhaps the strongest theoretical explanation for why Risk Parity works. Earlier research had shown that diversified, risk-balanced portfolios often outperformed traditional allocations, but the underlying reason remained somewhat unclear. Asness, Frazzini, and Pedersen argue that the missing ingredient is leverage aversion—the fact that many investors are either unwilling or unable to borrow.

That one assumption helps explain why Risk Parity has historically worked. If most investors refuse to use leverage, they’ll chase higher expected returns by buying riskier assets instead. That pushes the prices of risky assets higher and their future expected returns lower, while leaving safer assets relatively underpriced. Risk Parity turns this behavior on its head by owning more of the safer assets and using modest leverage to reach the desired level of portfolio risk.

Second, the authors test this theory across multiple decades, asset classes, and countries. They conclude that Risk Parity’s historical success is unlikely to be the product of data mining or a lucky historical period. It’s one of the strongest empirical cases for Risk Parity you’ll find.

The paper opens by comparing a simple Risk Parity portfolio with both a traditional 60/40 portfolio and the value-weighted market portfolio over the period from 1926–2010. Even this straightforward implementation substantially outperformed both on a risk-adjusted basis.

The natural question becomes:

Why does Risk Parity outperform?

That’s what the rest of the paper sets out to answer.

Before introducing their own theory, the authors review the foundations of Modern Portfolio Theory and the Capital Asset Pricing Model (CAPM).

CAPM assumes investors can freely borrow money to increase exposure to the optimal (tangency) portfolio. In reality, many investors cannot—or simply won’t—use leverage.

That’s where the authors depart from classical finance.

Readers unfamiliar with these concepts may want to review CAPM, the Efficient Frontier, and the Capital Market Line before tackling this section. You could start with my summary of Markowitz’s famous paper, if you like.

Building on earlier work by Frazzini and Pedersen (2010), the authors argue that low-beta assets should earn higher risk-adjusted returns than high-beta assets.

A quick reminder:

• Beta measures how closely an asset moves with the stock market.

• High-beta assets (such as equities) tend to rise and fall more than the market.

• Low-beta assets (such as long-term Treasuries) tend to move much less.

The key phrase is risk-adjusted return.

If safer assets produce more return per unit of risk, investors willing to use leverage can simply own more of them, potentially producing better overall portfolios than investors who simply load up on risky assets.

This is the heart of the paper.

Because many investors dislike leverage, they try to increase expected returns by overweighting risky assets instead.

That increased demand pushes risky asset prices higher, which lowers their future expected returns.

Meanwhile, safer assets become relatively neglected. Their prices remain lower than they otherwise would be, which means their expected returns become unusually attractive relative to their risk.

As the authors write:

“Because some investors choose to overweight riskier assets in order to avoid leverage, the price of riskier assets is elevated... In contrast, the safe assets... trade at low prices. Hence, investors who are able and willing to apply leverage can earn high risk-adjusted returns by... overweighting safer assets.”

This is the fundamental economic rationale behind Risk Parity.

The empirical section alone makes the paper worth reading.

The authors test Risk Parity across three completely different datasets:

1. U.S. stocks and bonds (1926–2010)

2. Global stocks, U.S. bonds, credit, and commodities (1973–2010)

3. Stocks and bonds across 11 countries (1986–2010)

This broad approach matters. If the same idea works across different markets, different time periods, and different asset classes, it’s much harder to dismiss the results as luck or data mining.

Across all three datasets, Risk Parity consistently produced superior risk-adjusted performance.

Some highlights:

• Even though the 1926–2010 period strongly favored equities, the more bond-heavy Risk Parity portfolio still outperformed.

• Levered Risk Parity generated meaningfully higher Sharpe ratios than both the market portfolio and a traditional 60/40 allocation.

• Perhaps most impressively, Risk Parity beat the 60/40 portfolio on a Sharpe ratio basis in all eleven countries included in the international study (see the graph on Page 55).

Taken together, these results make a compelling case that Risk Parity’s success is not tied to one market, one country, or one lucky historical period.

The authors conclude that leverage aversion provides a coherent explanation not only for Risk Parity’s success across asset classes, but also for the long-observed tendency of lower-beta securities to outperform on a risk-adjusted basis within individual asset classes.

Because the same theory successfully predicts outcomes across so many different markets and datasets, they argue that Risk Parity’s historical outperformance is unlikely to be a statistical accident.

The paper closes with one of the strongest endorsements of Risk Parity in the academic literature (p. 56):

“Our finding that RP investing is yet another instance of this theory working out of sample greatly enhances our confidence that Risk Parity’s superiority to traditional methods of strategic asset allocation is real and important and not a figment of the data.”

If you’re only going to read a handful of academic papers on Risk Parity, this should be one of them.

Earlier papers established that Risk Parity worked. This paper goes much further by explaining why it should work in the first place. The authors then test that explanation across nearly a century of data, multiple asset classes, and eleven countries.

Whether you ultimately decide to invest using Risk Parity or not, the idea of leverage aversion is one of the most useful concepts in modern investing. It provides a simple explanation for why investors systematically overpay for risky assets and underappreciate safer ones—and why combining safer assets with sensible leverage can sometimes produce better portfolios than simply buying more stocks.

For anyone trying to understand the intellectual foundations of Risk Parity, this paper is essential reading.