The Use of Risk Contribution Analysis and Value Investing to Outperform Global Benchmarks

 
Ryan A. Hughes
UCLA Anderson School of Management
Originally Published: Jan 2014

(This whitepaper was originally written when Ryan Hughes graduated from the UCLA Anderson MBA program. This study was an independent, in-depth research study that acted as the launching pad for his future firm, Bull Oak Capital. Several changes to the firm's investment strategy has occurred since this whitepaper was written. However, many elements of this whitepaper still serve as the bedrock for Bull Oak's investment philosophy. Please reach out to Ryan with any investment strategy questions.)

 

Summary

By designing an investment strategy that combines a risk contribution method and a small cap value stock selection method, I have formulated a strategy that shows attractive risk-adjusted returns. From 11/2006 to 12/2013, the Bull Oak Conservative, Moderate, and Aggressive backtested strategies show net of fee, average annual returns of 86, 316, and 500 basis points higher than their respective benchmarks. This investment strategy is the result of a graduate research project under the direction of Dr. Hanno Lustig, the faculty director of the UCLA Master of Financial Engineering program. As such, I created Bull Oak Capital to capitalize on the promising results of the backtest performance. This paper describes the general methodology used to help achieve these objectives.

Chart 1: Bull Oak Diversified Strategies Backtested Cumulative Performance
11/1/2006 – 12/31/2013
Chart 1

The purpose of Bull Oak Capital is to offer a more comprehensive and intelligent strategy to both retail and institutional investors. Bull Oak strives to deliver the maximum net-of-fee real investment return for each of the three risk-tolerance portfolios. The firm’s Investment Strategy for each client employs six steps:

  • Identify the appropriate set of asset classes (ACs) for the current investing environment
  • Select the investment vehicles to represent each AC
  • Select the individual stocks to represent the small-cap AC (the Bull Oak Alpha Generator portfolio)
  • Use the Bull Oak Risk Contribution Model to allocate the ACs for the different portfolios (Conservative, Moderate, or Aggressive)
  • Determine the client’s risk tolerance and timeframe and execute the appropriate portfolio
  • Provide portfolio rebalancing and ongoing management

 

Section 1: Introduction

During my MBA program at UCLA Anderson, I launched a graduate research project to create an investment strategy that would outperform it’s benchmarks in the long-run, while “weathering” periods of high volatility and uncertainty - a common goal of many investment managers. Fortunately, I had the benefit of working with some of the brightest minds in finance, both in academia and in industry. The outstanding results of this project fueled the creation of Bull Oak Capital, an investment management firm focused on serving high net-worth individuals and institutional clients, such as pension funds, endowments, etc. The backtested performances of the Bull Oak Diversified Strategies (Conservative, Moderate, and Aggressive) have all significantly outperformed their respective benchmarks while maintaining lower volatility levels (see Chart 1 and Appendix 2). Critically, they also have done so while accounting for an assumed Bull Oak management fee of 1%.

Chart 2: Bull Oak Diversified Strategies Backtested Performance, Net of Fees
$1,000,000 Invested, 11/1/2006 – 12/31/2013

Chart 2

For a more detailed analysis on the backtested performance of the three Bull Oak Diversified Strategies, please refer to Appendix 1 - 3.

In my approach, I crafted two separate, but complementary, strategies that use the qualities present in risk parity portfolios (the Risk Contribution Method) and value investing (the Bull Oak Alpha Generator model).

The Risk Contribution Method (RCM) allocates broad asset classes by over/under-weighting an AC as its risk level falls/rises. The Bull Oak Alpha Generator (BOAG) model is a proprietary stock selection method that uses the equity return characteristics developed by Fama & French and others.[i] The BOAG model only represents a part of the overall portfolio strategy. However, it is a vital one as U.S. small caps have historically outperformed all other ACs (Fama and French 1992).

 

Section 2: Building the Bull Oak Investment Methodology

This research project sought to develop a smarter investment approach and framework when investing client’s assets. In pursuit of this framework, Bull Oak Capital improves money management by first focusing on the portfolio’s total risk by applying the Risk Contribution Method (RCM) model. After the overall AC weights are allocated using the RCM model, the Bull Oak Alpha Generator (BOAG) model is employed, which is a portion of the overall RCM model (see Chart 2 and Table 2).

The BULL OAK INVESTMENT METHODOLOGY: the RCM portfolio w/ BOAG

RCM Chart

*Chart is for illustrative purposes and is representative of a hypothetical Bull Oak RCM strategy. Asset classes and the proportional weightings in the strategies may change at any time without notice, subject to the discretion of Bull Oak Capital.

BOAG is a U.S. small cap (Equity) stock selection method that screens and invests in undervalued/oversold companies. These investments are typically deep value stocks that exhibit specific characteristics that indicate equity outperformance.

Table 2: List of Asset Classes Bull Oak Employs

Table 2

2.1 The Flaw of Modern Portfolio Theory and Why I Chose Not To Adopt It

Most professional investment managers implement a mean-variance optimization asset management model, otherwise known as Modern Portfolio Theory (MPT), developed by Markowitz (1952) and Sharpe (1964). The basic idea behind MPT is that there is a tradeoff between risk and return where riskier investments are expected to have a higher return. MPT offers how to build an optimal portfolio with the lowest possible risk by diversifying between assets. However, MPT theory works only when it rests on the following dubious assumptions; market returns are normally distributed, correlations between ACs are constant, all investors behave and invest rationally, and all investors can borrow at the risk-free rate.

However, most troubling to me, is that MPT requires predictions about the future returns of securities, ACs, and the overall portfolio. The Expected Return [E(r)] variable, which is required for MPT to work, is a random variable that a portfolio manager would expect to find if he/she could repeat it an infinite number of times. Since portfolio managers cannot “run” the scenario an infinite number of times, the manager “predicts” a reasonable number by evaluating historical pricing information. Therefore, the MPT model is fundamentally unreliable.

Estimating expected returns is extremely difficult to do. In fact, one could argue that it is impossible, especially as AC premiums change over time. When managers realize that they are unable to successfully implement the MPT framework, most default to a 60% equity/40% bond strategic portfolio. Consequently, most professional managers today administer this strategic 60/40 portfolio, which is why it has become the most commonly used strategy and industry benchmark.

But the frequency of this strategy’s adoption hides its major defect: most portfolio managers are unaware of the dominant equity risk a 60/40 portfolio carries with it. The 60/40 portfolio variant earns much of its return from exposure to equity risk and little from other sources of risk, making this portfolio fairly under-diversified (Chaves, Hsu, Li, Shakernia 2012). If a manager is unaware of where the portfolio risk is coming from, or how much risk each AC is contributing to the overall portfolio, then the client’s portfolio is vulnerable during periods of high volatility and uncertainty.

Rather than attempting to allocate and forecast the Expected Return of each AC, I find it much easier and more effective to allocate the amount of risk each AC contributes to the total portfolio. As a result, I’ve developed the Bull Oak Risk Contribution Method (RCM) model.

2.2 The Creation of the Bull Oak Risk Contribution Method (RCM)

The Bull Oak RCM model evaluates the risk level of each AC and weights each AC accordingly. For example, if the risk level of Equities were rising and Bonds falling, the RCM model would underweight Equities and overweight Bonds. By controlling how much risk each AC contributes to the overall portfolio, Bull Oak can control the overall risk level.

Risk contribution is the measurement of risk each individual AC contributes to the overall portfolio. Traditionally, volatility (the standard deviation of returns) has been the most common way a manager would evaluate risk. Each AC carries a particular amount of risk and all ACs in a portfolio contribute varying amounts. The most effective way a manager can control this is to weight each AC differently.

However, the problem with this approach is that if any of the ACs are highly correlated, diversifying among them will offer little to no risk-reduction benefits. Thus, the real risk that must be minimized are the covariance levels between ACs. In developing a true risk parity portfolio, where each AC contributes an equal amount of risk, there are several different methods one can use.[ii] The most effective of these is the Newton Method, the method Bull Oak Capital employ in its RCM model.

2.2.1 The RCM Model: Employing the Newton Method to Reduce Risk

The Newton Method, named after Sir Isaac Newton and Joseph Raphson, is a method for solving a system of nonlinear equations by repeating multiple iterations until the true solution converges (see Figure 1). While more procedural than its naïve counterpart, The Newton Method is quite effective and efficient. I provide only a high level overview on how the method is applied. The white paper by Chaves, Hsu, Li, Shakernia (2012) offers an excellent tutorial on how to implement it.

By using AC covariance levels as inputs, the algorithm finds the true solution, or optimized AC weights, by first “guessing” a solution reasonably close to the true root, x1. The function is then approximated by the tangent line at x1 and the corresponding root x2, which is closer to the true solution. This process is repeated until the true solution is found.

Figure 1: An Illustration of the Newton Method

Figure 1

The Newton Method can be solved as a function by first extending the method to vector, y:

Figure 1

where, J(y) is Jacobian of F(y).

Figure 1

Next, add the risk parity equation in order to solve in the form of a Jacobian matrix:

where, xi is the weight of each asset class, λ represents the constant to be found, and Ω is the covariance matrix of the ACs.

Since the Newton Method only solves for risk parity portfolios, I modified the model so that I can control the amount of risk each AC contributes to the overall portfolio. Thus, I created the RCM model, which allows me to correctly allocate the Conservative, Moderate, and Aggressive Diversified Strategies. By applying this tactic, the Diversified Strategies are able to accept an identified amount of risk while still able to react swiftly during periods of high volatility and uncertainty in the market.

Table 3: The Bull Oak Risk Contribution Method (RCM) Backtest Performance

Table 3

The RCM model demonstrates superior performance while achieving lower volatility levels. This is evident by the impressive Sharpe Ratios, , which is a measure of how much risk the portfolio is taking to achieve its returns. Additionally, the average duration of the three Diversified Strategies is shorter, measuring at just 4.14 years. Lastly, a very important metric to evaluate is the Max Drawdown. This metric measures the percentage loss from peak to trough during any period. During this backtested period, this number is a result of the poor performance many ACs faced during financial crisis, 2007-2009. However, due to adaptive nature of RCM, all three strategies experienced much shorter drawdowns; -8.81%, -22.30%, and -33.62% for the Conservative, Moderate, and Aggressive strategies, respectively. For further analysis of the RCM model, please refer to Appendix 3.

2.3 Bull Oak Alpha Generator (BOAG - Small Cap Strategy)

Many portfolio managers attempt to outperform well-known indices or benchmarks, such as the S&P 500 or the Russell 2000. This approach to money management is called active management. Passive management, on the other hand, is where a manager does not attempt to outperform, but instead invests in the indices themselves. Empirical research shows that active management rarely outperforms passive management (Rompotis 2009). Excess value is extremely difficult to capture in well-known markets, especially in markets where Wall St. analysts follow well-recognized companies, such as U.S. large cap stocks.[i] As a result, I do not try to outperform this and other well-known markets, because it is a futile effort. That being said, it is important to note that not all markets are as efficient.

The U.S. large cap market is semi-strong-form efficient, meaning that there is very little opportunity to consistently outperform the S&P 500 or Russell 1000. The U.S. small cap market, on the other hand, is weak-form efficient. In this AC, analyst coverage is low, information is slowly diffused throughout the market, and it takes time for the market to fully realize the intrinsic value of a company. This creates an opportunity where value can be captured.

Chart 3: Bull Oak Alpha Generator (BOAG) Backtest Results
Growth of $1,000,000 (2006-2013)

Chart 3

Works by Joel Greenblatt, Fama & French, Haugen & Baker, Daniel & Titman, and others have all proven that there exists certain characteristics that explain why a stock is more likely to outperform its peers. Using these characteristics, I developed the Bull Oak Alpha Generator (BOAG) model to identify deeply discounted stocks that are trading below their intrinsic worth. By identifying certain characteristics and capitalizing on market mispricing, BOAG is able to successfully separate the stars from the duds. As a result, the backtested results indicate that this method significantly outperforms the Russell 2000 index (see Chart 3).

The BOAG portfolio achieved impressive results, nearly 20% higher average returns than the Russell 2000 and a Sharpe Ratio of 0.86 (see Table 4). Additionally, while it’s volatility levels are higher, which is to be expected, its Max Drawdown is 6% and 8.35% better than PRFZ and the Russell 2000 Index, respectively. To view the month-by-month backtest performance of the BOAG portoflio, please see Appendix 5.

Table 4: Bull Oak Alpha Generator (BOAG) vs. Benchmarks

Table 4

 

Section 3: Finding Asset Classes

As technological innovations accelerate information diffusion and as the global economy becomes more interconnected, true diversification becomes more relevant. The best way to maximize portfolio returns is through diversification (Ibbotson & Kaplan, 2000). However, an interconnected economy translates into less diversification opportunities. Thus, it is critical to select ACs with scrutiny. First, I had to consider how to categorize the broad and sub-ACs. This exercise is more difficult than it appears as many practitioners disagree on the scope of ACs. In my opinion, the broad ACs are Equities, Bonds, and Alternatives. Under the broad ACs, I partitioned each into sub-ACs.

3.1 Equities

Equities have historically been a highly volatile and risky AC. However, it is well documented that they have delivered the largest returns, as they are directly exposed to the factors that drive economic expansion. In fact, stock performance is a leading indicator of GDP growth. No other AC (Bonds or Alternatives) has provided the returns that equities have (Faber 2013).

Equity sub-ACs behave differently based on the country where they are located. Developed International stocks are not nearly as volatile as Emerging Market stocks. Likewise, Emerging Market stocks are not as liquid as International Stocks, leading to wider bid/ask spreads. Based on thorough analysis, the Equity sub-ACs are:

U.S. Large Cap
U.S. Small-Mid Cap
Developed International Ex-U.S. Large Cap
Developed International Ex-U.S. Small-Mid Cap
Emerging Markets

3.2 Bonds

Bonds are income-generating debt securities with maturities typically ranging from 1 week to 30 years and longer. Most coupons paid by bonds are fixed, thus providing fairly stable returns during economic downturns. Unlike Equities, investment-grade Bonds perform rather well during economic contractions, as investors flee riskier assets for higher quality securities.

There are many different types of bonds and they behave quite differently. Therefore, I gave much consideration to categorizing this AC. Additionally, as duration risk becomes more apparent in bond portfolios, I categorized the major sub-ACs according to duration risk.

Based on thorough analysis, I identified the sub-ACs as:

U.S. Core Investment Grade Bonds
Core Total U.S. Bond Market
Short Term Core U.S. Bond

Treasuries
Treasury Long Duration
Treasury Intermediate Duration
Treasury Short Duration

Corporate Investment Grade
Corp Long Duration
Corp Intermediate Duration
Corp Short Duration

International Bonds
International Investment Grade
Foreign Developed Bond
Emerging Market Bonds

Miscellaneous
Floating Rate Bonds
High Yield Bonds
U.S. Mortgage Bond

I chose not to include Treasury Inflation Protected Securities (TIPS) under the Bond AC, as most managers typically do. TIPS coupon payments change over time as they are tied to the current inflation rate. Consequently, TIPS do not behave like normal Treasury bonds, or most bonds in general. I included TIPS under the Alternatives AC instead.

3.3 Alternatives

Alternatives are ACs that do not fit into the above-mentioned broad ACs. By including Alternatives into a portfolio, the biggest benefit is to realize the non-correlated returns. During the 2008 economic crisis, many Equities and Bonds were highly correlated. If a manager held only Equities and Bonds (like many 60/40 portfolio managers), then his/her clients performed poorly. By including Alternative ACs, the manager creates value by adding more diversification, which in turn dampens negative effects during periods of high volatility.

Based on thorough analysis, I have identified the sub-ACs as:

REITS – U.S. Real Estate Investment Trusts
TIPS – U.S. Treasury Inflation Protected Securities
Global Commodities
Currency Exchange Rates (added in 2015)

Many firms include other ACs in Alternatives, such as Private Equity, Hedge Funds, and Master Limited Partnerships. I chose not to include these sub-ACs because it either didn’t offer diversification benefits and/or it wasn’t cost effective.

3.3.1 Alternatives – Excluded Asset Classes

Private Equity (PE) is the practice of investing in non-public companies. Most PE firms charge hefty fees, often leaving invested partners with subpar real returns. Additionally, PE companies have very similar betas (risk exposure) that public firms have, offering little to no real diversification benefits. Most managers only look at the sequence of returns offered by PE managers to determine the covariance risk. Most PE cash disbursements returned to investors are spotty and irregular. Based on these sequences of returns, investment in PE looks as if it can offer diversification benefits for investors. However, this is not the case. If there is an economic downturn and consumer demand falls, private and public companies both will experience a decline in revenue, leading to a reduction in earnings. Both a private restaurant chain and public restaurant chain will feel the effects of a drop in consumer demand. Therefore, it is difficult to find any economic diversification benefits by investing in this asset class.

Hedge Funds boomed in the 1980s and 1990s, as impressive returns attracted billions of dollars and more start-up funds. Most investors seemed not to mind the 2 & 20 fee structure, so as long as the returns were outperforming the market. However, since the 2000s, the Hedge Fund Return Index (HFRI) has failed to impress, realizing lackluster returns. With an expensive fee structure and a poor performance history, I determined not to include it as a sub-AC.

Master Limited Partnerships are publicly traded partnerships that invest in oil and natural gas pipelines. As a partner in the pipeline, one would receive periodic income distributions in the form of royalties or liquidations. These are usually favorable ACs as they often receive favorable tax treatment. However, due to these tax treatments, Exchange Traded Funds (ETFs) that invest in MLPs, or track MLP indices, often have very high expense ratios and have significant tracking error. These ETFs are structured as corporations and they are required by law to pay income taxes on the MLP income, thus resulting in significant tracking error and subpar performance. With high fees, this is a poor sub-AC to include.

 

Section 4: Selecting Investment Vehicles

Bull Oak employs both passive and active management. When considering passive management, the goal was to select the most accessible, yet cost-effective vehicles available. Where active management is desired, the goal was to use a strategy that would outperform its benchmark, net of fees.

4.1 Passive Investment Vehicles

I chose to use passive ETFs to represent the sub-ACs where passive management is desired. The rise of ETFs has significantly changed the investing landscape, offering cost-effective access to otherwise inaccessible ACs. When selecting which ETFs to use, there were many costs to consider, both direct and hidden. Transaction costs are apparent at the custodian level and are often minimal. However, hidden costs exist and they should be accounted for. They are:

  • Expense ratio: An annual fee that the ETF charges its shareholders. This fee is deducted from the fund's average net assets, which is accrued on a daily basis. Currently, the average expense ratio is 0.20% across all Bull Oak strategies.
  • Liquidity: Lower-risk securities are more freely traded and therefore have higher trading volume and liquidity. The more actively traded a particular ETF is, the more liquid it is; therefore, ETFs that invest in actively-traded securities will be more liquid than those that do not. ETFs with fewer actively traded securities will be affected by a greater bid-ask spread.
  • Tracking Error: Passive ETFs are designed to track their appropriate index by investing in identical/similar securities. The tracking error is the difference between the return an investor receives and the benchmark it is attempting to imitate. If there is high tracking error, whether it is due to limited supply of a security or tax implications, there can be a significant “cost” that the investor may not immediately realize.

 

Section 5: Rebalancing and Ongoing Monitoring

The RCM method portfolio and the BOAG portfolio will not stay optimized over time unless it is rebalanced. As markets fluctuate, these portfolios will drift from optimum AC weights. Therefore, it is necessary to rebalance the RCM model quarterly and the BOAG model annually.

The RCM algorithm is run every quarter, drawing upon the most recent pricing data and risk levels. From this, the RCM model will weight each AC optimally based on the most recent risk levels that are available.

The BOAG model is rebalanced annually, selecting the most attractive stocks from the Russell 2000 Index. Bull Oak will sell the prior year securities in a tax efficient manner, paying attention to long-term capital gain holdings.

Section 6: Conclusion

Bull Oak Capital combines the best-in-class investment strategies described earlier with practical experience and portfolio guidance. Bull Oak strives to deliver the maximum net-of-fee real investment return for each of the three risk-tolerance portfolios. This is achieved by combining both the Risk Contribution Method and the Bull Oak Alpha Generator portfolios. Nevertheless, I will continue to sharpen Bull Oak’s investment methods as new ideas emerge and breakthroughs occur. Additionally, Bull Oak will continuously monitor and periodically rebalance the Bull Oak risk-tolerance portfolios to maximize returns while accounting for the total risk in each of the three risk-tolerance portfolios. It is my professional assessment that this process will result in outstanding long-term financial success for Bull Oak’s clients.

 

Section 7: Acronyms

AC: Asset Class
BOAG: Bull Oak Alpha Generator (a proprietary U.S. small cap investment strategy)
ETF: Exchange Traded Fund
GSCI: Goldman Sachs Commodity Index
MPT: Modern Portfolio Theory
MSCI ACWI: Morgan Stanley Composite Index – All-Country World Index (a global stock index)
RAFI: Research Affiliates Fundamental Index
RCM: Bull Oak’s Risk Contribution Method (a proprietary investment strategy)
REIT: Real Estate Investment Trust
RP: Risk Parity
TIPS: Treasury Inflation Protected Securities

 

Section 8: Acknowledgements

There were many people who helped throughout the entirety of this research program. All of them receive my sincerest gratitude, as the Bull Oak strategies would not be what they are today. First and foremost is to my research professor, Dr. Hanno Lustig, who took time out of his very busy schedule as the Director of the UCLA Masters of Financial Engineering program to assist me with the direction of this project. Dr. Dragos Munteanu, a very good friend of mine, helped me brainstorm and write a complex language code that I would never have been able to do on my own. Dr. Mahyar Kargar, another great friend, provided very astute and thoughtful feedback that required me to consider critical issues from many different viewpoints. Dr. Jason Hsu, co-founder and Chief Investment Officer at Research Affiliates, graciously provided his thoughts to my project and offered great suggestions that I currently employ in the model. And most importantly, my family deserves the greatest thanks of all. Thank you, Jill, Hayden, and Emily for allowing me to spend countless hours on campus or at Starbucks.

 

Section 9: Appendix

Appendix 1: Bull Oak Portfolios Backtest Overview Table, Net of Fees

Appendix 1

Appendix 2: Bull Oak Diversified Strategy Backtested Performance Summary

Appendix 2

Appendix 3: Risk Contribution Method Portfolios versus Benchmarks (w/o BOAG)

Appendix 3

Appendix 4: Different Views of the Russell 1000 - Fundamental Indexing vs. Market Cap Indexing 1962-2003

Appendix 4

Appendix 5: Bull Oak Alpha Generator (BOAG) Small Cap Backtest Table
$1,000 Invested, 1/1/2006 – 12/31/2013

Appendix 5

Section 10: References

Arnott, R., Hsu, J., Moore, P. 2004. Fundamental Indexation. Social Science Research Network 9-17.

Chaves, D., Hsu, J., Li F., and Shakernia O. 2012. Efficient Algorithms for Computing Risk Parity Portfolio Weights. Social Science Research Network 1-7.

Faber, M. 2007. A Quantitative Approach to Tactical Asset Allocation. Social Science Research Network

Fama, E., and K. French. 1992. The cross-section of expected stock returns. Journal of Finance 427-465.

Ibbotson, R., and Kaplan, P. 2000. Does Asset Allocation Policy Explain 40, 90, or 100 Percent of Performance? Financial Analysts Journal 26–3.

Mahajan, S. 2013. Algorithms for Constructing Equal Risk Contribution Portfolios. Applied Finance Project, UCLA Anderson.

Maillard, S., Roncalli T., and Teiletche J. 2010. The Properties of Equally Weighted Risk Contribution Portfolios. Journal of Portfolio Management 60–70.

Markowitz, H. 1952. Portfolio Selection. Journal of Finance.

Rompotis, G. 2009. Active vs. Passive Management: New Evidence from Exchange Traded Funds. Social Science Research Network 6-9.

Sharpe, W. 1964. Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risks. Journal of Finance

 

Endnotes

[i] Fama & French, Haugen & Baker, Daniel & Titman, and others have all provided empirical research to show that specific characteristics explain why a stock is more likely to outperform its peers. The most prevalent of these characteristics are the size of a company and the relative “value” of a company (book-to-market, P/FCF ratio, etc.).

[ii] The Newton Method is the superior and preferred method. I performed several different backtest studies where I evaluated the risk parity naïve method, the Newton method, the Power method, and a momentum risk parity method. Additionally, in “Algorithms for Constructing Equal Risk Contribution Portfolios” by Shipra Mahajan, several different methods, including methods I backtested, were evaluated and concluded that the Newton Method is the preferred method for large cap equity portfolios. 

[iii] U.S. large cap stocks are companies that have a market capitalization greater than $10B (e.g. Wal-Mart, Apple, etc.). Mid cap stocks are between $2.5B - $10B and small cap stocks are under $2.5B.

 

White Paper Disclosures

Nothing in this document should be construed as a solicitation or offer, or recommendation, to buy or sell any security. Investment management services are only provided to investors who become Bull Oak Capital clients pursuant to a written agreement, which investors are urged to read and carefully consider in determining whether such agreement is suitable for their individual facts and circumstances.

Bull Oak Capital presents the Risk Parity and Risk Contribution Method information starting in 1990, which is the earliest date that necessary data is available for all three of the broad asset classes being used.  Additionally, the Bull Oak Capital Investment Strategies (Aggressive, Moderate, and Conservative) presents the backtested results starting in November 2006, which is the earliest date all available security pricing and data is available. Backtested results use closing prices of the day for both securities and indices. Model is not manipulated in any way that would produce better-than-expected results – such as material changes in model directives, constraints, or optimization. We have not made any additional calculations to account for the periodic rebalancing, which we use as part of the allocation plan, nor have we deducted other expenses. For our calculations, we use the following: Global Stock (MSCI All-Country World Total Return Index), U.S. All Cap Stock (Russell 3000 Total Return Index), U.S. Small Cap Stock (Russell 2000 Total Return Index), U.S. Large Cap Stock (S&P 500 Total Return Index), Developed Foreign Stock (MSCI EAFE Total Return Index), Emerging Market Stock (MSCI Emerging Markets Total Return Index), Real Estate (FTSE/NAREIT North America Index), Commodities (S&P GSCI Total Return Index), TIPS (Barclays Capital U.S. TIPS Index), Core Global Investment Grade Bond (Barclays Capital Global Aggregate Bond Index), Core U.S. Investment Grade Bond (Barclays Capital U.S. Aggregate Bond Index), Corporate Bond (Barclays Capital U.S. Corporate Investment Grade Index), Core U.S. High Yield Bond (Barclays Capital U.S. High Yield Index),  Emerging Market Bond (Barclays Emerging Market Bond Index), Floating Rate Notes (Bank of America Merrill Lynch U.S. ABS Autos Float), Risk-Free Rate (U.S. T-Bill 3 Month Middle Rate). Comparisons to indices are provided for illustrative purposes only.

Bull Oak Capital’s service was not available to investors during the time period shown. The choices made by Bull Oak Capital to use certain indices may affect the performance calculations, and different choices would result in different performance estimates. The information is only an indication of the general performance of one type of allocation plan during the time period, and other allocation plans, based on different risk profile information, could have also been selected for comparison. No index is directly comparable to the performance of an asset class. Various strategies and assumptions may affect performance, such as ETF selection, ETF tracking error and expenses, and rebalancing of allocations. The use of a different rebalancing plan could create different results.

To convey genuine backtest results, a 1% annual management fee has been deducted from all 3 strategies (Conservative, Moderate, and Aggressive) during the entirety of the backtest performance period. Further, the 1% fee was deducted on a monthly basis (0.0833% per month).

Past performance is no guarantee of future results, and any hypothetical returns, expected returns, or probability projections may not reflect actual future performance. Actual investors on Bull Oak Capital may experience different results from the results shown. There is a potential for loss as well as gain that is not reflected in the hypothetical information portrayed. The performance results shown do not represent the results of actual trading using client assets but were achieved by means of the retroactive application of a model designed with the benefit of hindsight.

Bull Oak Capital, LLC