How Much Risk Is In Your Portfolio?

by: EB Investor


Investors should never take more risk than is warranted to accomplish their investment goals.

Too often risk management is an afterthought, and when it is measured through risk tolerance questionnaires it is commonly miscalculated.

A focus on risk-adjusted returns, that follows the science of investing may be a superior way to manage assets for the long run.

A Quantitative Analysis of Risk and Return

Across all of my work, one of the main themes I have tried to emphasize is minimizing the level of risk an investor needs to take in order to reach their goals. Many investors follow one of two approaches to deal with risk. They either follow an active approach to fixed income such as that pursued by the popular PIMCO Total Return fund (MUTF:PTTRX), or they buy the Barclays Aggregate Bond (NYSEARCA:AGG) benchmark itself. My objective for this piece is to alert investors to the risks lurking in their portfolio, and offer a more intelligent way to manage risk that gives you the potential to avoid losses. One of the best ways to outperform over the long run is to lose less during stressful market events. This way investors are adding to gains, rather than trying to make up for losses.

Understanding Risk

Many investors, and a good deal of the personal finance periodicals, measure risk as the standard deviation of an asset. In reality measuring the standard deviation of an asset in the short term is a meaningless data point for investors seeking to achieve long term goals. Instead investors should be concerned with avoiding the permanent impairment of capital within a portfolio model. When constructing a portfolio with multiple assets you want to make sure the correlation of those assets is negative. Pairing together uncorrelated assets not only reduces the probability that an investor will experience the permanent impairment of capital, but the standard deviation will also be reduced as well. Reductions in the standard deviations of market returns are again meaningless to the portfolio construction process, but could have powerful behavioral effects on investors. A smoother ride may reduce the likelihood of investors bailing out on their long term plan at the wrong times.

In their paper "Tail Risk Constraints and Maximum Entropy," Geman, Geman and Taleb, make the argument that when building a portfolio the major concern is protection against the left tails. The authors continue with a definition of the constraints under traditional Value at Risk or VaR measures.

"We describe the shape and investigate other properties of the resulting so-called maxent distribution. In addition to a mathematical result revealing the link between acceptable tail loss (Value-at-Risk-VaR) and the expected return in the Gaussian mean-variance framework, our contribution is then twofold: 1) an investigation of the shape of the distribution of returns from portfolio construction under more natural constraints than those imposed in the mean-variance method, and 2) the use of stochastic entropy to represent residual uncertainty."

The authors conclude

"...most papers dealing with entropy in the mathematical finance literature have used minimization of entropy as an optimization criterion. For instance, Fritelli (2000) exhibits the unicity of a 'minimal entropy martingale measure' under some conditions and shows that minimization of entropy is equivalent to maximizing the expected exponential utility of terminal wealth. We have, instead, and outside any utility criterion, proposed entropy maximization as the recognition of the uncertainty of asset distributions. Under VaR and Expected Shortfall constraints, we obtain in full generality a "barbell portfolio" as the optimal solution, extending to a very general setting the approach of the two-fund separation theorem."

While the authors work is mathematically dense, the notion of the barbell approach emerges from the research. This creates a rather different approach for investors and practitioners, when creating a portfolio that achieves a desirable risk and return profile.

Investors increase the safety of their portfolio by taking more risk with less money. Investors can protect their portfolio against left tail risk, by simply holding a diversified evidence-based portfolio of uncorrelated assets, and taking only the risk that is necessary to reach their objectives. The fullest and most extreme expression of this would be for investors to limit their risk to equities, and tilting the portfolio towards small cap and value. By using the science of investing and taking an evidence-based approach investors can actually hold a lower allocation to equities without reducing the projected return profile. Additionally, holding allocations to alternative asset classes may further diversify systematic risks of the portfolio model and thus create a portfolio that allows investors to achieve their objectives while placing a lower percentage of their wealth at risk.

Below I have constructed two example portfolios. In the first portfolio I have designed a traditional 60%/40% allocation model which includes many more asset classes. By tilting towards the sources of outperformance, we can reduce the equity allocation to 50% while actually increasing the return taking an extreme approach to tilting the portfolio towards the sources of outperformance using the Fama French Five Factor Model. We can continue to tilt further and increase the return while decreasing the risk, with proper portfolio management. The theory behind this strategy is taking more risk with less money and constructing a portfolio that remains protected against left tail risks, thus reducing the probability of permanent impairment of capital towards 0%. Seeing as left tail risks are by definition catastrophic and unpredictable, we can not completely reach 0%.



DFA Core Equity II



DFA US Large Cap Value III



DFA US Small Cap Value



DFA Core International



DFA International Value



DFA International Small Cap Value






DFA Em Value



DFA EM Small Cap



DFA Intermediate Government



DFA World Ex US Government











DFA Small Cap Value



DFA International Small Cap Value



DFA Emerging Markets Small Cap



DFA Intermediate Government









The Problem with Traditional Client Risk Assessment

When sitting down with a client, financial advisors will typically engage in a risk assessment with clients. This is meant to assess the level of risk the client is willing to take to accomplish their goals. Yet most clients will over-estimate how comfortable they are with risk; being driven by greed, they will seek to maximize their return. Conversely at times of maximum pessimism, being driven by maximum fear, they will be driven to abandon their long term plan, seeking safety. This instability in assessing client risk tolerance creates a behavior anomaly that could lead to serious consequences for the client's ability to achieve their long run goals. Therefore, assessing a client's risk tolerance requires a more robust scientific approach. Sometimes quantifying for investors the actual losses in a given scenario puts it into perspective - losing 50% may sound bad but losing $500,000 of a $1,000,000 portfolio sounds worse. Sometimes just quantifying what that means to not only the portfolio, but to their ability to fund long run goals, will give the client a chance to reassess their risk tolerance.

Investors who misjudge their risk tolerance and take on more risk than is necessary may spend years just getting back to even. Therefore, a real assessment of risk is necessary. Below I have conducted a simple analysis using just equity and traditional fixed income, splitting the equity as 50% US and 50% international. I calculated the level of drawdown and the gain needed to return to even, as a way to illustrate the result of miscalculating your risk tolerance. For the model, I assumed a portfolio drawdown during a left tail event of -41%, and used a gain of 5% for traditional fixed income which we will explore more in-depth below.





Fixed Income





























Why Investment Grade Bonds Don't Manage Risk

I believe both of the popular approaches of buying a bond index or pursuing an intermediate bond active manager, leave investors exposed to excessive losses in the event of a left tail risk event. While a more intensive analysis of the mathematics would be required to arrive at a deeper understanding of true risk within a portfolio, I believe we can sufficiently prove the ineffectiveness of traditional bond strategies, both active and indexed, by simply testing their effectiveness against live data.



60%/40% Drawdown

$ Drawdown

Gain Needed to Get Back to Even


PIMCO Total Return






TCW Total Return






Metwest Total Return






Barclays Aggregate Bond Index






Looking at the data set we see that many intermediate term bond funds, failed to provide adequate cushion during the 2008 financial crisis, opening the portfolio to serious risks. But the real takeaway was the level of correlation with traditional stock strategies. This highly correlated asset class is thus not reducing risk in the portfolio the way investors thought, exposing the portfolio to larger drawdowns, and thus requiring a larger gain just to get back to even. Avoiding losses should be the paramount objective of any portfolio manager acting as a fiduciary. But how should we manage risk?

Using Fixed Income to Manage Risk

Given the data from the 2008 financial crisis that we examined above, we see that traditional bond strategies do a poor job of diversifying systematic risks, and providing investors with a true uncorrelated asset class to protect from excessive drawdowns. However, the type of fixed income an investor chooses to hold matters.

For investors whose objective in holding fixed income is to reduce the overall volatility of the portfolio and prevent portfolio losses in the event of a downturn in risk assets, holding only the highest quality fixed income will provide a true risk management asset. Let's view this through the 2008 live data to test the hypothesis using a portfolio of various maturities that averages a maximum of 10 years in duration. Investors willing to take on more equity risk may want to dial up duration risk to offset that risk, or may want to dial it down, if they are comfortable having more equity risk without a hedge or are overly concerned about rising rates. It is all dependent on individual investor goals and preferences.




Fixed Income Portfolio Duration


2008 Return

Vanguard Long Term Treasury



Vanguard Intermediate Term Treasury



Vanguard Extended Duration US Treasury



DFA Intermediate Government



Vanguard Short Term Treasury



An Evidence-Based Approach to Managing Risk

The main purpose of risk management is to avoid the permanent impairment of capital during a left tail risk event. Investors would be wise to follow an evidence-based approach to portfolio management which includes the implementation of the science of investing, this includes a more scientific approach to managing risk. Investors can more intelligently manage risk through not only high quality fixed income, but by using negatively correlated alternatives, as well as limiting the level of risk assets using a different approach to portfolio construction and risk management. Let's assess the various tools for risk management:

High Quality Fixed Income

To the extent that investors need to take risk, it should be done on the equity side of the portfolio. The fixed income side of the portfolio should be composed of nothing other than the highest quality fixed income. In most of the portfolios I build, I am looking to employ the science of investing and follow the Fama-French methodology of maximizing the term and quality factors. In this case we are looking for safety and therefore are willing to accept a lower yield as a result. We generally aim to target an intermediate duration between 5 and 10 years, but investors can customize duration to meet their objectives.

Uncorrelated Alternative Assets

Uncorrelated alternative assets can offer a powerful tool for portfolio managers and investors to customize their risk-return profile. In addition, many of these tools will also act as a hedge on inflation.

Real Estate

I laid out the case for real estate last week. Adding a global evidence-based real estate strategy has the power to increase return while lowering risk in the portfolio, acting as a powerful diversifier.


Commodities have powerful diversification and total return benefits for investors. Utilizing an evidence-based commodities strategy such as DFA Commodities Strategy (MUTF:DCMSX) can act as a powerful uncorrelated alternative holding as part of a larger portfolio strategy.

Managed Futures

Managed futures funds can be a powerful hedge within a larger portfolio model. Because the portfolio manager can take long and short positions, their hedging ability to the larger portfolio model can be powerful in a left tail risk event. In 2008 the Credit Suisse Managed Futures Index was up 23.03%.

Style Premia

Style premia investing is possibly the greatest alternative holding for any evidence-based investor, because it is the fullest expression of the science of investing. Larry Swedroe wrote an excellent piece on how this type of fund adds value, and I suggest investors who want to learn more check it out. AQR Capital Management is a leader in the alternatives space, and they run the AQR Style Premia fund (MUTF:QSPRX). The funds objective from their website:

"We invest long and short across six different asset groups: Stocks of major developed markets, country indices, bond futures, interest rate futures, currencies and commodities. We employ market-neutral, long-short strategies across these asset groups based on four investment styles:

Value - the tendency for relatively cheap assets to outperform relatively expensive ones

Momentum - the tendency for an asset's recent relative performance to continue in the future

Carry - the tendency for higher-yielding assets to provide higher returns than lower-yielding assets

Defensive - the tendency for lower-risk and higher-quality assets to generate higher risk-adjusted returns

Each of these styles has historically had low correlations to one another, so we expect them to be profitable at different times for different reasons. Thus, a portfolio combining all four of them seeks to benefit from their expected low correlations to one another and could help provide a more robust, dependable stream of returns."

Portfolio Construction

Finally, risk can be managed through a systematic approach to portfolio construction that seeks to limit the level of risk to what is required to achieve an investor's long run goals, and allocate the rest of an investor's wealth to a mix of uncorrelated assets that creates a far smoother risk-return profile more in line with an absolute return strategy.


Finally, let's assess the rules of portfolio construction and risk management that I have covered here:

An investor with a portfolio worth "X," needs to maximize the return of the portfolio while minimizing the risks of attaining that return. Thus a rigorous program for risk management is required. Merely purchasing stocks and traditional investment grade bonds is not good enough. Therefore, a more robust risk management methodology is required.

1. Investors need not take any more risk than is warranted to realize their financial goals.

2. Investors seeking to maximize return without regard to risk are speculating on the future value of risk assets, leaving one open to extensive losses.

3. Traditional methods of managing risk tend to be ineffectual because they are based on faulty behavioral assessments.

4. Investors following an evidence-based approach to portfolio construction with a rigorous program for risk management may achieve market-beating returns with less risk.

5. Traditional risk management techniques assume a greater level of risk than is necessary to achieve long term outperformance.

Investors don't need to hit home runs, and should instead focus on hitting singles, tilting their portfolio towards the sources of outperformance, limiting their risk taking to the amount required and relying on safer uncorrelated assets for the rest of their portfolio. Constructing the portfolio model with risk in mind should ensure the ability of investors to stick with their plan over the long run, and ultimately achieve their long term investment goals.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: This article is for informational purposes only and is not an offer to buy or sell any security. It is not intended to be financial advice, and it is not financial advice. Before acting on any information contained herein, be sure to consult your own financial advisor. I have used DFA Funds in client accounts.