Does “Sharpe Parity” work better than “Risk Parity?”

Does “Sharpe Parity” work better than “Risk Parity?”

January 27, 2015 Research Insights, Tactical Asset Allocation Research
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(Last Updated On: April 24, 2017)

Strategies employing risk parity have been favored by mutual funds and other market participants the past few years. The attraction of risk parity strategies are two-fold: 1) the great story associated with the approach and 2) the favorable historical performance over the past 30 years. However, there is an argument that historical risk parity performance has been driven by leveraged exposure to Treasury Bonds, which have been on an epic tear the past ~30 years.

Nonetheless, good stories such as risk parity never die on Wall Street, they merely adapt and overcome. This white paper by UBS highlights skepticism around risk parity and presents a different, but related asset allocation method: Sharpe Parity.

Risk Parity Background

As you may recall, risk parity identifies weights that equalize “risk” across asset classes. Let’s first review a simple risk parity example.

Here is a visual interpretation of how risk parity works. If we allocate to a 60/40 stock/bond portfolio on a dollar-weighted basis, on a risk-contribution basis, we might be getting 90% of our risk from stocks and 10% of our risk from bonds.

Risk parity comes to the so-called rescue.

Risk parity suggests that we rejigger the dollar-weighted 60/40 portfolio in such a way that the risk contributions end up being 50% driven by bond exposure and 50% driven by stock exposure. In other words, our “risk contributions” are at parity, hence the title “risk parity.”

risk parity

How does this work in practice using the most basic version of risk parity outlined in the Asness, Frazzini, and Pedersen paper:

risk parity formula
Source: Leverage Aversion and Risk Parity (2012), Financial Analysts Journal, 68(1), 47-59

But UBS Doesn’t like Risk Parity. Why?

As per their own research:

  1. Risk parity ignores return and focuses only on risk;
  2. Risk parity uses volatility as the sole measure of risk, while neglecting other credit-related risks, such as default risk and illiquidity;
  3. Risk parity encounters huge drawdowns if bonds and equity sell off together;
  4. A low nominal return world makes recovery from risk parity drawdowns difficult.

UBS proposes a new asset allocation strategy, which shares some concepts with risk parity, but in their approach risk parity’s “standard deviation” is replaced with an estimate for an asset’s Sharpe Ratio. Here’s an explanation of the concept:

Think about it this way: if asset X has a Sharpe ratio of 2 it means that we have two units of return for 1 unit of risk, while asset Y with a Sharpe ratio of 1 gives us only 1 unit of return for the same amount of risk. In that case we construct a portfolio with the weight for asset X being double the weight of asset Y.

Strategy Background

This approach makes some sense, as it seems to account for return as well as risk. This approach is also in line with modern portfolio concepts such as mean-variance analysis, where investors want to maximize marginal Sharpe Ratios to create the so-called “tangency portfolio” that all MBA 101 students know and love.

But how does “Sharpe Parity” stand up to empirical scrutiny? In order to address this question, we compare 4 asset allocation approaches: Equal-weight allocation, an equal-weight allocation with a Simple Moving Average rule, simple Risk Parity, and Sharpe Ratio Parity.

  1. Equal-weight (EW_Index): monthly rebalanced equal-weight portfolios.
  2. Simple Moving Average (EW_Index_MA): calculate a simple moving average each month (12 month average); if the MA rule is triggered (when the current price > 12 month moving average), buy risk, or else, allocate to the risk-free asset.
  3. Risk Parity: follow the simple risk parity algorithm; use a look-back period of 36 months for the “standard” risk parity model.
  4. Sharpe Parity: use a look-back period of 36 months for the Sharpe Parity model; if an asset has a negative Sharpe Ratio, this asset’s weight will be 0; note that if all the assets’ Sharpe Ratios are negative, the strategy will allocate 100% to the risk-free asset.

Data Description

To test these 4 strategies, we apply them to the “IVY 5” asset classes:

  • SP500 = SP500 Total Return Index
  • EAFE = MSCI EAFE Total Return Index
  • REIT = FTSE NAREIT All Equity REITS Total Return Index
  • GSCI = GSCI Index
  • LTR = Merrill Lynch 7-10 year Government Bond Index

IVY 5 concept

Our simulated historical performance period is from 1/1/1980 to 7/31/2014. Results are gross, and thus do not include the effects of fees. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Data was obtained via Bloomberg. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see the disclosures at the end of this document for additional information.

Monthly Rebalance Performance

  • Sharpe Parity has a slightly higher CAGR. However on a risk-adjusted basis, Equal Weight MA and Risk Parity outperform the Sharpe Parity system, as reflected in their higher sharpe and sortino ratios.
  • The simple moving average technique has the lowest drawdown and the best overall risk-adjusted performance.
Risk parity vs sharpe parity_1
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Please see disclosures for additional information. Additional information regarding the construction of these results is available upon request.

Does Lookback period matter?

Next, we change the look-back period from 36 months to 3 months, which is identical to the lookback period used in the UBS whitepaper.

Here’s the result:

  • Sharpe Parity based on a 3 months lookback period has larger CAGR, but also has larger drawdowns, on a monthly, worst case, and cumulative basis. Sharpe and sortino ratios are worse than the 36 month lookback version.
Risk parity vs sharpe parity_2
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Please see disclosures for additional information. Additional information regarding the construction of these results is available upon request.


Based on these results, it seems hard to conclude that Sharpe Parity, particularly with a 3 month look-back period, offers a clear-cut advantage over traditional Risk Parity approaches. In fact, on a risk-adjusted basis, it compares poorly. Based on this analysis, it would appear that simple equal-weight portfolios with trend-following rules have worked better than more complicated risk parity or sharpe parity systems.

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Definitions of common statistics used in our analysis are available here (towards the bottom)

About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray received a PhD, and was a finance professor at Drexel University. Dr. Gray’s interest in entrepreneurship and behavioral finance led him to found Alpha Architect. Dr. Gray has published three books: EMBEDDED: A Marine Corps Adviser Inside the Iraqi Army, QUANTITATIVE VALUE: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, and DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His numerous published works has been highlighted on CBNC, CNN, NPR, Motley Fool, WSJ Market Watch, CFA Institute, Institutional Investor, and CBS News. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.

  • IlyaKipnis

    Not surprising, honestly. Simply, how stable is a Sharpe Ratio estimate over a small time frame? Over a longer time period, momentum (aka the return aspect of the Sharpe) is mean-reverting, and over a short time period, can the estimate really be trusted? Probably not. In any case, simply being greedy with the Sharpe ratio without any attention to correlations seem to be asking for a wallop when things go wrong (which they will).

  • yg

    I agree: a 3-month lookback period is probably too short and a 36-month is certainly too long. Could the author provide results using a 12-month period, also consistent with the 12m MA strategy?

  • New2CA

    Interesting exercise. How do I reconcile your findings versus Deo & Nakisa’s paper? On their paper, the Sharpe parity performed so much better than max Sharpe (tangency portfolio) and everything else. I notice that 1) you are using Ivy 5 asset classes while Deo & Nakisa were using 8 asset classes, 2) you are using Jan/1980 – July/2014 historical simulation period while Deo & Nakisa were using Dec/2002 – Dec/2013. Sharpe parity has the tendency of allocating high percentage of portfolio to assets with strong momentum. This can be very painful at market turning points (e.g. 1Q/2000 when Sharpe parity would have allocate high percentage of portfolio to QQQ).
    Also, some clarifications, please. Your “equal weight” means 20% each to Ivy 5. Is this the case? Your EW_Index_MA is similar to Mebane Faber’s Journal of Wealth Management approach (he used 200 day MA while you use 12 month MA). Is this the case?
    Thanks for your work and attention to my questions.

  • I don’t think there is a reconciliation except to say that the results associated with Sharpe Parity lack robustness…not a good thing…

    Yes, equal-weight means 20% across the board. And yes, as per the hyperlink above, we are talking about the Meb Faber system with MA rule.

    Hope that answer your questions and thanks for reading. Best of luck