Previously, we talked about the advantages of structural diversification over the traditional 60/40 portfolio (see “Death of the 60/40 portfolio,”). But using structural diversification requires many strong assumptions, which may not work out as expected.

To see why, look at Figure 1 (below), which shows how our estimates and assumptions dictate the type of optimization we choose. The less we estimate, the more we have to assume, which exposes us to the risk that we’ve assumed something incorrectly (the left side of the figure). But the more we estimate, the greater the risk that we’ve estimated something incorrectly (the right side of the figure). Investors can choose their approach to asset allocation based on what they can confidently estimate dynamically through time, and based on how often they can rebalance to account for changing estimates. For instance, an institutional manager may have strong confidence in her ability to estimate, but if she’s only able to rebalance twice a year, she’s forced to assume more (and estimate less) than a similar manager who can rebalance monthly. An equal weight portfolio assumes all assets are likely to exhibit similar return and risk characteristics, and does not attempt to estimate any of them. Traditional mean-variance optimization requires estimates for returns, volatility and correlations. Estimating all of these parameters is difficult; worse, small errors in estimates can result in profoundly inappropriate portfolios.

If static portfolios like the structurally diversified policy portfolio require too many assumptions, and mean-variance optimal portfolios require too many difficult parameter estimates, perhaps it’s time for a compromise. A naive risk parity portfolio, which we’ll examine in-depth for this article, requires you to estimate risk, but not correlations or returns, and is a compellingly simple alternative.

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## FIGURE 1. WHICH PORTFOLIO OPTIMIZATION WOULD YOU CHOOSE?

## Naive risk parity

It’s difficult to accurately estimate returns and correlations. So consider using naive risk parity if:

- you’re confident you can measure the volatility of assets;
- you assume all assets in your investment universe are likely to deliver an equal amount of excess return per unit of risk (i.e., exhibit equal Sharpe ratios);
- you can’t confidently estimate those assets’ correlations.

Naive risk parity allocates assets in proportion to the inverse of their respective risk, with the goal that all assets in the portfolio contribute a similar amount of risk; higher-risk assets will receive lower portfolio weights, and lower-risk assets will receive higher weights. This approach is more robust than a simple equal-weight portfolio. That’s because, as Figure 2 (below) shows, in an equal-weight portfolio, the “lunatics run the asylum” because higher volatility assets come to dominate portfolio outcomes. Figure 2 illustrates the proportion of portfolio volatility contributed by a wide variety of asset classes (represented by ETF codes) through time.

Notice how the volatility contribution of IEF (Intermediate Treasury Bond ETF), represented in red, contributes much less to total portfolio risk over time than high-volatility assets like emerging market stocks (EEM), European stocks (IEV) and U.S. real estate (ICF).

If an asset class contributes little volatility, this limits the diversification potential of that asset in the portfolio—so, despite IEF’s low average correlation with other risky assets in the portfolio, its diversification potential is rendered ineffective. Think about a choir where the chorus drowns out the soloist.

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We want each asset to contribute an equal amount of risk to the portfolio. To facilitate this, each asset must be weighted in proportion to the inverse of its risk. Figure 3 (below) shows how a portfolio with the goal of equalizing asset-level volatility in the portfolio requires a large weight in Intermediate Treasuries (IEF), and relatively low weights in Emerging (EEM) and European (IEV) stocks through time.

## FIGURE 2. NOMINAL ASSET VOLATILITY CONTRIBUTION THROUGH TIME, 60-DAY ROLLING OBSERVATIONS

## FIGURE 3. EQUAL VOLATILITY WEIGHTING THROUGH TIME, 60-DAY ROLLING OBSERVATIONS

Data source for figures 2 and 3: Bloomberg

## Methodology: Naive risk parity

Let’s examine two simple ways of measuring and allocating through time based on asset level risk: volatility and variance. As variance is the square of volatility, variance weighting will overemphasize lower volatility assets in the portfolio, and result in a lower-risk portfolio in general.

**Volatility**, used in almost every formal risk model, is the standard deviation of log price changes. Alternatively, it is the standard deviation of price changes as a percentage, and this is the measure most used in practice. Many beginner quants incorrectly run the volatility analysis on the original price series—avoid that. To calculate volatility in Excel, use the STDEV(A1:A60) function, where the range A1:A60 contains asset returns (not prices) from time t=1 through t=60.**Variance**is the volatility measure squared, so we eliminate the square root sign from the equation above.

The Excel implementation for variance is VAR(A1:A60).

## Results and limitations of naive risk parity

It’s one thing to say naive risk parity is a compelling approach, but it’s another thing to prove it. To illustrate the concept, we tested the methodology on two asset class universes. The first, containing 10 broad asset classes drawn from regional equity indexes, bonds, commodities and real estate, is coherent and well-balanced. Note that, where possible, we have extended the history of ETFs back through time using their respective underlying total return indices.

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- Commodities (DB Liquid Commoties Index)
- Gold
- U.S. stocks (Fama/French top 30% by market capitalization)
- European stocks (Stoxx 350 Index)
- Japanese stocks (MSCI Japan)
- Emerging market stocks(MSCI EM)
- U.S. REITs (Dow Jones U.S. Real Estate Index)
- International REITs (Dow Jones Int’l Real Estate Index)
- Intermediate Treasuries (Barclays 7-10 year Treasury Index)
- Long Treasuries (Barclays 20+ year Treasury Index)

In contrast, the universe below, which consists of 35 different equity indexes along with REITs, gold, commodities, and one bond index, is profoundly overweight in equities, which swamps the diversification opportunity of alternative asset classes. This universe was included to demonstrate some of the limitations of naive risk parity, in anticipation of a future article that will resolve many of the weaknesses. We will call this universe our Dog’s Breakfast universe (below).

Results are compelling: returns are preserved above 8% on an annualized basis, while portfolio risk, as measured by volatility and maximum drawdowns, as well as VaR and CVaR, are substantially reduced. Sharpe ratios increase by 50% to 100%, and investors experience 89% to 95% positive rolling 12-month periods, up from 80% with the equal-weight portfolio. However, it’s clear from Figure 4 (below) that naive risk based optimizations are still vulnerable to meaningful drawdowns, even on our well-specified, 10-asset universe, during periods like 2008. Again, this is due to the fact that naive optimizations cannot control for periods when formerly uncorrelated assets become highly correlated—and highly volatile—under periods of extreme financial stress.

The Dog’s Breakfast universe, on the other hand, is poorly specified for a naive risk parity approach because the equity and equity-like assets completely swamp the ability for non-correlated assets like Treasury bonds and gold to exert their diversification benefits (see our tablet edition). As a result, the performance of naive portfolios is barely distinguishable from the simple equal weight version.

Naive risk parity has limited ability to leverage the diversification potential available from these two universes. So, next time, we’ll look at robust risk parity, which emphasizes the diversification potential of assets in the portfolio.

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## Dog’s Breakfast Universe

**(Alternative assets highlighted in blue)**

VTI – Total U.S. Stock Market

EIRL – Ireland

TUR – Turkey

ECH – Chile

THD – Thailand

EEM – Emerging Markets

QQQ – Nasdaq

DBC – Commodities

IFN – India

ACWI – All Cap World Index

IDX – Indonesia

VGK – Europe

GLD – Gold

RSX – Russia

GREK – Greece

RWX – Int’l real estate

EWZ – Brazil

IYR – U.S. real estate

EZA – South Africa

IEF – 7-10 year Treasuries

EWW – Mexico

EWM – Malaysia

EWY – South Korea

EWK – Belgium

EWT – Taiwan

EWL – Switzerland

EWU – United Kingdom

EWJ – Japan

EWQ – France

EWH – Hong Kong

EWS – Singapore

EWI – Italy

EWO – Austria

EWD – Sweden

EWP – Spain

EWG – Germany

EWN – Netherlands

EWA – Australia

EFA – EAFE

EWC – Canada

## Figure 4. Risk optimization results for 10-asset-class universe

Equal weight portfolio | Risk parity portfolio | Rp.var portfolio | |

Period | Jan. 1995-Jul. 2013 | Jan. 1995-Jul. 2013 | Jan. 1995-Jul. 2013 |

CAGR | 8.32 | 8.83 | 8.98 |

MaxDD | -43.84 | -27.8 | -14.04 |

MAR | 0.19 | 0.32 | 0.64 |

Sharpe | 0.53 | 0.79 | 1.09 |

DVR | 0.47 | 0.73 | 1.03 |

Volatility | 12.43 | 8.38 | 6.03 |

AvgDD | -1.59 | -1.18 | -0.91 |

VaR | -1.15 | -0.83 | -0.57 |

CVaR | -1.89 | -1.24 | -0.85 |

Exposure | 99.55 | 99.55 | 99.55 |

Pos. 12 Month | 81.02 | 89.36 | 95.23 |

Turnover | 50.9 | 100.08 | 168.08 |

Source: Bloomberg

**Adam Butler**, CFA, CAIA,

**Michael Philbrick**and

**Rodrigo Gordillo**, advisors at Butler|Philbrick| Gordillo & Associates with Dundee Goodman Private Wealth.

Originally published in Advisor's Edge Report

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