Software Engineer and Finance Blogger
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  • Wealthfront released a whitepaper that describes an example risk parity strategy. A backtest is performed to show that it outperforms a traditional 60/40 stocks/bonds strategy and popular commercially available funds
  • A risk parity strategy equalizes the risk contribution of each asset in a portfolio. Extra money is borrowed and invested into the portfolio to reach a desired rate of return

This article attempts to unravel the theory behind risk parity strategies and how they work through easy to understand terms. Specifically, it'll describe what an asset's risk contribution to a portfolio means, how it relates to a portfolio's volatility, and how leverage is important to a risk parity strategy.

Understanding the risk parity strategy

The fundamental theory behind risk parity strategies is that assets in a portfolio should be balanced by risk, not by dollars. In other words, instead of allocating more $$$ to riskier assets to achieve a performance target, a risk parity strategy balances assets by risk contribution and then uses leverage to achieve the performance target.

For someone unfamiliar with finance, the above paragraph probably sounds like a bunch of mumble jumble. Here's an English translation: the performance of an investment portfolio is largely dictated by the risk it carries. The riskier its assets are, the higher the portfolio's upside potential. For example, compare a 100% savings account portfolio with a 100% stocks portfolio; the former has low risk and low returns, while the latter has high risk and a greater chance of large returns. "Traditional" portfolios increase risk by concentrating money in riskier assets, while risk parity portfolios have fixed asset allocations in order to equalize risk contributions. To increase risk, a risk parity portfolio uses leverage (i.e. borrows extra money to invest).

Leverage means borrowing money to put in an investment. The more money you borrow, the more volatile (i.e. risky) the investment becomes. For example, if you have $1 invested in AMZN and AMZN's price doubles, you've earned $1. However, if you borrow another $1 and invest $2 in AMZN, when its price doubles, you've earned $2. On the flipside, if you're leveraged by 2x and AMZN falls in price, you lose money twice as fast.

To get a more nuanced understanding of risk parity strategies, you need to understand: * How to define risk for financial assets * How to define an asset's risk contribution to a portfolio * Why does equalizing risk contribution even matter? * How can leverage be used to increase risk in a risk parity strategies

How do you define risk?

There are many ways to define risk for a financial asset. A popular way, and one that is also relevant to risk parity strategies, is to normalize the covariance of an asset's price (with the overall market) by the variance of the overall market.

In simple terms, this risk measurement method measures how likely an asset's price will move with the market. The less likely it is to move with the market, the less risky it is.

When an asset "moves with the market", it means that the asset's price increases as the market's valuation increases, and vice versa when its price decreases.

How do you define an asset's risk contribution to a portfolio?

Now that we have a good idea of how to measure a financial asset's overall risk, we can apply this to portfolios. An asset's risk contribution to a portfolio can be defined as its covariance with the overall portfolio normalized by the variance of the overall portfolio.

Again, in simple terms, this risk contribution measurement method measures how likely an asset's price will move with the portfolio. The less likely it is to move with the portfolio, the less risk it contributes to the portfolio.

Note that an asset's risk contribution is affected by both its covariance with other assets in the portfolio and its allocation size. For example, an asset representing 100% of a portfolio will move exactly with the portfolio, thus contributing 100% of the risk.

Why does equalizing risk contributions even matter?

The risk parity approach to constructing a portfolio is based on the Modern Portfolio Theory (MPT) formalized by American economist Harry Markowitz in his 1952 paper, "Portfolio Selection".

This framework simplifies an investor's decisions into two dimensions: expected return and risk. If the investor only cares about expected returns, s/he would put 100% of their money into a stock with the highest expected return. However, MPT reasons that investors are also risk adverse, and so would rather invest in stocks with the highest expected return adjusted by risk.

As such, a risk parity portfolio, like all MPT portfolios, aims to maximize its risk-adjusted return. It turns out, when you just focus on equalizing risk contributions, ignore expected returns, and use leverage to scale the overall portfolio's volatility, you can achieve a higher level of risk-adjusted return than other types of portfolios.

For this to occur, two things need to hold true:

  • Retrospectively, the actual risk-adjusted return of low-risk assets must exceed the actual risk-adjusted return of high-risk assets so that using leverage works. If this isn't true, an investor would've been better off directly investing in high-risk assets and not using leverage. An investor often won't have a good idea of what the actual risk-adjusted return of an asset is because it's hard to estimate expected returns. The difficult part lies in estimating whether its currently best to use a risk parity strategy or not. Historically, risk-adjusted returns of low-risk assets has been higher than risk-adjusted returns of high-risk assets.
  • The cost of leverage (i.e. borrowing money) needs to be sufficiently low so that the gains realized from investing the borrowed money exceeds the cost of borrowing.

Constructing a portfolio using MPT (i.e. maximizing risk-adjusted returns) is hard because it requires a lot of guesstimation and extrapolation from historical data. As we all know, past performance is not an indicator of future outcomes. Calculating expected returns for an asset is especially hard since there could be an infinite number of events that could skew actual outcomes, such as a coronavirus outbreak. One of the redeeming qualities of the risk parity approach is its disregard for expected returns.

Why is leverage necessary?

Leverage is necessary for a risk parity strategy since you'll often find one a risk parity portfolio skews heavily towards low-risk-low-return assets like bonds. To meet a desired performance level (e.g. "I want a 7% annualized return rate"), you need to scale up the size of the portfolio through leverage. Imagine that you have a $1 million portfolio that earns 3% annually. If you borrowed an extra $1 million, you'd have a $2 million portfolio earning 3% annually. 3% of $2 million is 6% of $1 million. As such, using leverage here has doubled your returns from an initial $1 million.

However, leverage also comes with added risk. You lose money extra fast when the price of the portfolio's assets fall.

Back to the Wealthfront whitepaper

Parametizing a risk parity strategy

Since a risk parity strategy forces assets to be allocated such that their risk contributions are equalized, the portfolio manager doesn't have control over asset allocation percentages. The parameters that they have control over are the assets in the portfolio, the portfolio's volatility target, how an asset's risk contribution is specifically calculated, and how often the calculation is performed and the portfolio rebalanced.

For Wealthfront, they chose 7 asset classes for their portfolio: US Equities, Foreign Developed Equities, Emerging Market Equities, US Bonds, Emerging Market Bonds, Energy Stocks, and REITs

Their portfolio volatility target is 12% and they rebalanced the portfolio monthly.

To calculate risk contribution, they "construct a forecast of the one-month asset class variance-covariance matrix using a rolling, backward-looking window of daily returns." This matrix is used to calculate allocations for each asset such that their risk contributions are equal.

Total Return Swap for leverage

Borrowing money cheaply can be hard. The whitepaper states: "Unfortunately it is very difficult to find a lender who will offer financing at a reasonable rate if the portfolio grows to be very large." To apply leverage to their risk parity strategy, Wealthfront describes a financial contract called a Total Return Swap (TRS).

In a TRS, Wealthfront gives a bank collateral and in return gets access to capital several times larger than the collateral. Wealthfront is then able to use this capital to construct a portfolio.

Collateral: something given to a lender's custody as security for repayment of a loan. Collateral is forfeited in the event the loan can't be paid.

In a TRS, Wealthfront doesn't have custody of the portfolio's assets. The bank does. However, if the assets appreciate, the bank will pay Wealthfront the difference. If the assets depreciate, Wealthfront pays the bank the difference. Throughout the swap's lifespan, Wealthfront also has to pay an interest rate on the funds "borrowed".

TRS interest rates are typically very low. They also allow portfolio managers to periodically rebalance portfolios and adjust the amount of leveraged. As such, they can be efficiently use to implement a risk parity strategy.

Wealthfront's backtest

To backtest a strategy is to apply it on historical data and measure its performance. Wealthfront backtests its example risk parity strategy with a classic 60/40 Equity/Bond strategy from 1996 to 2017. The risk parity strategy achieved an annualized return of 11.3% whereas the 60/40 strategy saw an annualized return of 7.7%. In 20 years, that's an 8.5x return vs a 4.4x return.

Wealthfront also compared this risk parity strategy's backtest performance to popular commercially available funds like Bridgewater's All Weather Fund and AQR's Risk Parity Blend and showed that it outperforms these funds as well. However, we have to keep in mind that hindsight is 20/20.