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Asset Allocation

Contribution to Risk: An Insightful Metric for Portfolio Construction

Robert Harlow, Quantitative Analyst and Portfolio Manager
Aaron Stonacek, ASA, CFA, Solutions Analyst

Important Information for model portfolios
The information presented herein for the model portfolios is hypothetical in nature and is shown for illustrative, informational purposes only. This material is not intended to forecast or predict future events, but rather to demonstrate T. Rowe Price’s capability to manage assets in this style. It does not reflect the actual returns of any portfolio and/or strategy and does not guarantee future results. Certain assumptions have been made for modeling purposes and are unlikely to be realized. No representation or warranty is made as to the reasonableness of the assumptions made or that all assumptions used in modeling analysis presented have been stated or fully considered. Changes in the assumptions may have a material impact on the information presented. Data shown for the model portfolios is as of July 2017 and represents the manager’s analysis of those strategies as of that date and is subject to change over time. The results of the model portfolios are developed with the benefit of hindsight and have inherent limitations. These results do not reflect actual trading. The model portfolios are not actively managed and do not reflect the impact that material economic, market or other factors may have on weighting decisions. If the weightings change, results would be different. Management fees, transaction costs, taxes, potential expenses, and the effects of inflation are not considered and would reduce returns. Actual results experienced by clients may vary significantly from the hypothetical illustrations shown. This information is not intended as a recommendation to buy or sell any particular security, and there is no guarantee that results shown will be achieved.

Executive Summary

  • When developing their strategic asset allocations, investors often use a range of diagnostic tools to analyze the impact that a given position could have on portfolio outcomes. These estimates are typically based on a given set of portfolio exposures, the expected returns and volatilities of the asset classes involved, and the expected correlations among those asset classes.
  • In this paper, we explore the use of an additional metric—contribution to risk (CTR)—that can help investors and analysts measure the expected contribution of each allocation to potential loss within a portfolio.
  • CTR serves as a risk disaggregation measure, estimating the contribution to total portfolio volatility expected from each individual asset class. By analyzing their portfolios in this manner, investors can determine the sensitivity of the portfolio optimization process to small changes in their modeling assumptions.
  • We examine CTR across two common portfolio construction methods: a standard multi-asset balanced portfolio and a portfolio constructed using a risk parity approach. We also show how expected portfolio volatility and the sources of that volatility can change in market environments that are more stressful than an investor’s original assumptions.

The Evolution of Risk Disaggregation

Future asset class returns, volatilities, and cross-correlations are unknown and unknowable ex-ante; however, investors seeking to design efficient portfolios will often make assumptions about the expected values of these variables. While each asset class contributes to the total risk of a portfolio, these contributions are not equal across asset classes and can change significantly with small changes in the underlying assumptions. The magnitude of these changes also can differ across asset classes. Stocks are more volatile than bonds, for example, but contributions to total risk from bond allocations tend to be more sensitive to estimation error.

CTR Defined

CTR is the percentage contribution to expected total portfolio volatility from each position in an investor’s portfolio. It is a function of the current allocation, volatility and cross-correlation assumptions. A useful interpretation of CTR is expected percentage contribution to portfolio loss from a particular position. For this reason, CTR is often used as a measure of diversification.

CTR Under a Balanced Portfolio Approach

Based on a portfolio’s asset allocation and the volatility and correlation assumptions behind those allocations, investors can calculate an insightful breakout of risk using the CTR metric. We illustrate this process by applying it to two hypothetical portfolios. Our first example can be considered a typical multi-asset balanced portfolio, allocated 60% to equities (split between U.S. and international stocks) and 40% to fixed income or cash instruments (Figure 1).1

FIGURE 1: A Hypothetical Balanced Portfolio

Source: T. Rowe Price
The above details are indicative and are for illustrative purpose only. These are subject to change without further notice.

Using the allocation, correlation, and volatility assumptions shown in Figure 2, we can calculate the risk contribution made by each portfolio holding using the CTR metric. As is commonly observed, the risk contributed by equities is much higher relative to their weight in the portfolio compared with the contribution from fixed income and cash (Figure 3). About 97% of total portfolio volatility can be attributed to the 60% allocation to equities, given the assumptions in Figure 2.

FIGURE 2: Baseline Assumptions

Asset Class Weight Volatility U.S. Large-Cap Equities Core Fixed Income International Equities Cash
U.S. Large-Cap Equities 45% 18% 1.00
Core Fixed Income 35 6.5 -0.11 1.00
International Equities 15 20 0.93 0.05 1.00
Cash 5 0 0.00 0.00 0.00 1.00

Source: T. Rowe Price
The above details are indicative and are for illustrative purpose only. These are subject to change without further notice.

FIGURE 3: Asset Allocation and CTR for a Balanced Portfolio

Source: T. Rowe Price
The above details are indicative and are for illustrative purpose only. These are subject to change without further notice.

CTR Under a Risk Parity Approach

As noted above, almost all of the expected risk in a balanced portfolio comes from equities. This relationship has led some investors to adopt a risk-based approach to portfolio construction, in which allocation weights are set so that each asset class contributes a relatively equal amount to total portfolio risk. The resulting “risk parity” portfolio differs from a balanced portfolio by increasing allocations to less volatile assets. An investor desiring an equal contribution to risk from fixed income, international equity, and U.S. equity allocations might design the hypothetical portfolio shown in Figure 4.

FIGURE 4: Asset Allocation and CTR in a Risk Parity Portfolio

*Percentage does not total 100% due to rounding.
Source: T. Rowe Price
The above details are indicative and are for illustrative purpose only. These are subject to change without further notice.

As expected, the risk parity approach increases the fixed income allocation relative to the balanced portfolio. Contributions to portfolio volatility are evenly distributed across the asset classes, given the initial assumptions. However, we will see that as these assumptions are changed, the CTRs for each asset class will drift from parity.

Impact of Estimation Error in a CTR Framework

In addition to decomposing portfolio risk, CTR also can be used to test the sensitivity of portfolio risk to shifts in capital market expectations. Since the CTR metric relies on asset allocation, volatility, and correlation assumptions, changes in these variables will result in nonlinear shifts in CTR itself. To illustrate these portfolio sensitivities, we modeled the three scenarios described in Figure 5.2

FIGURE 5: Capital Market Scenarios

Scenario Model Effect Market Conditions
Correlation Shock All asset class correlations increase. In stressful market situations, return correlations between asset classes tend to increase.
Volatility Shock Fixed income volatility assumption increases two percentage points. Central banks ending easing programs could result in rising bond volatility.
Exposure Shock U.S. and international equity exposures increase five percentage points, and bond exposure falls 10 percentage points. A portfolio that is not rebalanced may experience a large allocation drift during equity bull markets.

Source: T. Rowe Price

Under each of these scenarios, we compared the resulting portfolio asset allocations and CTRs with those of the hypothetical portfolios shown above—i.e., with both a traditional 60/40 balanced portfolio and a risk parity portfolio.

As shown in Figure 6 and Figure 7, the contribution to total portfolio risk from fixed income increases significantly in both portfolios when asset class cross-correlations increase (scenario one). This suggests the fixed income/equity correlation assumption is a particularly significant variable in portfolio optimization and construction. Even a small shift in that assumption will have a broad effect on portfolio structure and estimated portfolio risk.

FIGURE 6: Asset Allocation and CTR Scenarios for a Balanced Portfolio

Source: T. Rowe Price
The above details are indicative and are for illustrative purpose only. These are subject to change without further notice.

FIGURE 7: Asset Allocation and CTR Scenarios for a Risk Parity Model Portfolio

*Percentage does not total 100% due to rounding.
Source: T. Rowe Price
The above details are indicative and are for illustrative purpose only. These are subject to change without further notice.

Additionally, the risk parity portfolio is particularly sensitive to changes in the volatility assumptions for low-volatility asset classes (scenario two). This is due in part to the large relative allocations to those asset classes that stem from the risk parity approach.

In scenario three, we see that negligence in portfolio rebalancing can further increase the risk exposure contributed by equity allocations. In the risk parity portfolio, a 16% reduction in the fixed income allocation (from 64% to 54% of the total portfolio) reduces the fixed income CTR by 52% (a decrease from 33% to 16% of the total portfolio). These scenarios, and others, can be tested in this manner during the portfolio design process to expose the most critical assumptions.


  • The CTR metric is a tool that allows investors and managers to understand the contribution to total portfolio volatility made by each asset class in the portfolio, as well as the sensitivity of each modeling assumption to the overall portfolio outcome.
  • This scenario testing capability can provide useful insights and modeling capabilities during portfolio construction and strategic asset allocation exercises.
  • Risk-based portfolios are significantly more sensitive to parameter estimation changes than balanced portfolios.

Price Perspective

Contribution to Risk: An Insightful Metric for Portfolio Construction

Contribution to Risk: An Insightful Metric for Portfolio Construction
Figures A1 and A2 show the CTRs for each asset class in the three shock scenarios tested. Figure A1 uses the balanced portfolio as the baseline, while Figure A2 uses the risk parity portfolio.

1 In the allocations shown in Figure 1, U.S. large-cap equity is represented by the S&P 500 Index, international equity is represented by the Morgan Stanley Capital International All Country World Index, core fixed income is represented by the Bloomberg Barclays U.S. Aggregate Bond Index, and cash is represented by the 30-Day Treasury Bill. [Return to Text]

2 Please see the appendix on page 5 for the volatility and correlation assumptions used in each scenario. [Return to Text]

Important Information

This material is being furnished for general informational purposes only. The material does not constitute or undertake to give advice of any nature, including fiduciary investment advice, and prospective investors are recommended to seek independent legal, financial and tax advice before making any investment decision. T. Rowe Price group of companies including T. Rowe Price Associates, Inc. and/or its affiliates receive revenue from T. Rowe Price investment products and services. Past performance is not a reliable indicator of future performance. The value of an investment and any income from it can go down as well as up. Investors may get back less than the amount invested.

The material does not constitute a distribution, an offer, an invitation, a personal or general recommendation or solicitation to sell or buy any securities in any jurisdiction or to conduct any particular investment activity. The material has not been reviewed by any regulatory authority in any jurisdiction.

Information and opinions presented have been obtained or derived from sources believed to be reliable and current; however, we cannot guarantee the sources’ accuracy or completeness. There is no guarantee that any forecasts made will come to pass. The views contained herein are as of the date noted on the material and are subject to change without notice; these views may differ from those of other T. Rowe Price group companies and/or associates. Under no circumstances should the material, in whole or in part, be copied or redistributed without consent from T. Rowe Price.

The material is not intended for use by persons in jurisdictions which prohibit or restrict the distribution of the material and in certain countries the material is provided upon specific request.

It is not intended for distribution to retail investors in any jurisdiction.

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T. ROWE PRICE, INVEST WITH CONFIDENCE and the Bighorn Sheep design are, collectively and/or apart, trademarks or registered trademarks of T. Rowe Price Group, Inc.


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