Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as Co-Chair, Center for Applied Quantitative Finance, Risk Research and Quantitative Solutions at SAS. Don’s focus at SAS is quantitative finance, credit risk, asset and liability management, and portfolio management for the most sophisticated financial services firms in the world.

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Petroleo Brasileiro S.A.: A Market Review of Petrobras Bonds

10/30/2013 10:33 AM

Petroleo Brasileiro S.A. (“Petrobras”) (PBR) (PBRQF) is the largest company in the southern hemisphere by market capitalization and the largest company in South America by revenues. The Petroleo Brasileiro S.A. investor information website explains the firm’s world-wide operations in detail. In this note, we turn to the U.S. dollar bonds issued by Petroleo Brasileiro S.A. affiliates Petrobras Global Finance B.V. and Petrobras International Finance Co., both with the guarantee of the parent. We describe the bonds of both legal entities as being bonds issued by Petroleo Brasileiro S.A. for brevity.

We seek to bring a bond market perspective to the outlook for Petroleo Brasileiro S.A. as a complement to analysis based on a common stock holder’s perspective. Today’s note incorporates Petroleo Brasileiro S.A. bond price data as of October 29, 2013.  A total of 581 trades were reported on 6 fixed-rate non-call bond issues of Petrobras Global Finance B.V. and 12 fixed-rate non-call bond issues of Petrobras International Finance Co.  Total trading volume was $195.4 million. We used all of this data in this note.

Institutional investors around the world are required to prove to their audit committees, senior management, and regulators that their investments are in fact “investment grade.” For many investors, “investment grade” is an internal definition; for many banks and insurance companies “investment grade” is also defined by regulators. We consider whether or not a reasonable U.S. bank investor would judge Petroleo Brasileiro S.A. to be “investment grade” under the June 13, 2012 rules mandated by the Dodd-Frank Act of 2010, which requires that credit rating references be eliminated from U.S. government regulations.  The complete text of the relevant regulatory rulings in this regard is given at the end of this note.

Assuming the recovery rate in the event of default would be the same on all bond issues, a sophisticated investor who has moved beyond legacy ratings seeks to maximize revenue per basis point of default risk from each incremental investment, subject to risk limits on macro-factor exposure on a fully default-adjusted basis. In this note, we also analyze the maturities where the credit spread/default probability ratio is highest for Petroleo Brasileiro S.A.

Term Structure of Default Probabilities

Maximizing the ratio of credit spread to matched-maturity default probabilities requires that default probabilities be available at a wide range of maturities. The graph below shows the current default probabilities for Petroleo Brasileiro S.A. ranging from one month to 10 years on an annualized basis. For maturities longer than ten years, we assume that the ten year default probability is a good estimate of default risk. The default probabilities range from 0.61% at one month to 0.32% at 1 year and 0.39% at ten years.

We also explain the source and methodology for the default probabilities below.

Summary of Recent Bond Trading Activity

The National Association of Securities Dealers launched the TRACE (Trade Reporting and Compliance Engine) in July 2002 in order to increase price transparency in the U.S. corporate debt market. The system captures information on secondary market transactions in publicly traded securities (investment grade, high yield and convertible corporate debt) representing all over-the-counter market activity in these bonds. We used the 18 bond issues mentioned above in this analysis.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Petroleo Brasileiro S.A. bonds. These curves reflect the noise in the TRACE data, as some of the trades are small odd-lot trades. The lowest curve, in dark blue, is the yield to maturity on U.S. Treasury bonds (TLT)(TBT), interpolated from the Federal Reserve H15 statistical release for that day, which matches the maturity of the traded bonds of the Petroleo Brasileiro S.A. The next curve, in the lighter blue, shows the yields that would prevail if investors shared the default probability views outlined above, assumed that recovery in the event of default would be zero, and demanded no liquidity premium above and beyond the default-adjusted risk-free yield.  The orange line graphs the lowest yield reported by TRACE on that day on Petroleo Brasileiro S.A. bonds. The green line displays the value-weighted average yield reported by TRACE on the same day.  The red line is the maximum yield in each Petroleo Brasileiro S.A. bond issue recorded by TRACE.

The graph shows an increasing “liquidity premium” as maturity lengthens for the bonds of Petroleo Brasileiro S.A. This is a pattern seen usually with firms of good credit quality.  We explore this premium in detail below.

The high, low and average credit spreads at each maturity are graphed below for Petroleo Brasileiro S.A. We have done nothing to smooth the data reported by TRACE, which includes both large lot and small lot bond trades. For the reader’s convenience, we fitted a polynomial that explains the average spread as a function of years to maturity.

Using default probabilities in addition to credit spreads, we can analyze the number of basis points of credit spread per basis point of default risk at each maturity.  For Petroleo Brasileiro S.A., the credit spread to default probability ratio ranges from 3.5 to 10 times at maturities under 3 years to a range generally between 8 and 9 times at longer maturities. The ratios of spread to default probability for all traded bond issues are shown here:

The credit spread to default probability ratios are shown in graphic form below for Petroleo Brasileiro S.A. in this chart.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended October 25, 2013 (the most recent week for which data is available), the credit default swap trading volume on Petroleo Brasileiro S.A. was 33 trades for $221.8 million. The number of credit default swap contracts traded on Petroleo Brasileiro S.A. in the 155 weeks ended June 28, 2013 is summarized in the following chart. Petroleo Brasileiro S.A. CDS volume ranked 528th among all reference names traded world-wide during this period.

The weekly trading volume for the 155 weeks ended June 28, 2013 is graphed here:

On a cumulative basis, the default probabilities for Petroleo Brasileiro S.A. range from 0.32% at 1 year to 3.82% at 10 years.

Over the last decade, the 1 year and 5 year annualized default probabilities for Petroleo Brasileiro S.A. have been much more stable than the same probabilities for major financial institutions during the financial crisis. The 1 year default probability peaked at slightly under 1.80% in early 2009.  The 5 year default probability peaked at slightly under 0.60% on an annualized basis at the same time.

As explained at the end of this note, the firm’s default probabilities are estimated based on a rich combination of financial ratios, equity market inputs, and macro-economic factors.  Over a long period of time, macro-economic factors drive the financial ratios and equity market inputs as well. If we link macro factors to the fitted default probabilities over time, we can derive the net impact of macro factors on the firm, including both their direct impact through the default probability formula and their indirect impact via changes in financial ratios and equity market inputs. The net impact of macro-economic factors driving the historical movements in the default probabilities of Petroleo Brasileiro S.A. has been derived using historical data beginning in January 1990.  A key assumption of such analysis, like any econometric time series study, is that the business risks of the firm being studied are relatively unchanged during this period. With that caveat, the historical analysis shows that Petroleo Brasileiro S.A. default risk responds to changes in 2 domestic U.S. risk factors and 9 international risk factors among the 40 world-wide macro factors used by Kamakura Corporation in its standard risk analysis, a broader set than the Federal Reserve used in its 2013 Comprehensive Capital Assessment and Review stress testing program. These macro factors explain 64.3% of the variation in the default probability of Petroleo Brasileiro S.A. The remaining variation is the estimated idiosyncratic credit risk of the firm.

Petroleo Brasileiro S.A. can be compared with its peers in the same industry sector, as defined by Morgan Stanley (MS) and reported by Compustat.  For the world-wide “energy” sector, Petroleo Brasileiro S.A. has the following percentile ranking for its default probabilities among its 1,780 peers at these maturities:

1 month 86th percentile
1 year 73rd percentile
3 years 65th percentile
5 years 51st percentile
10 years 42nd percentile

The short term ranking of Petroleo Brasileiro S.A. relative to its peers is higher because business conditions are so good currently that they rank at the 86th percentile for the period from 1990 to the present. The strong corporate business conditions drive the default probabilities of all firms to low levels.  Over a longer time horizon, Petroleo Brasileiro S.A. ranks in the riskier half of its peer group from a credit risk perspective through a 5 year horizon and slightly better than that at 10 years. Taking still another view, the actual and statistically predicted Petroleo Brasileiro S.A. credit ratings both show a rating in the low end of the “investment grade” territory.  The statistically predicted rating is 1 notch higher than the legacy rating from firms like the Standard & Poor’s affiliate of McGraw-Hill (MHFI) and Moody’s Investors Service (MCO).  The legacy ratings of the company have changed only 3 times since 2007.

Using a slightly different classification of the peer group, we can compare the credit spreads of Petroleo Brasileiro S.A. with the credit spreads of all firms in the energy sector whose bonds traded on October 29.  The results are shown in this graph.

We find Petroleo Brasileiro S.A. credit spreads at the very high end of the energy peer group.  We can make the same comparison with the matched maturity default probabilities for every bond of the energy peer group that traded on October 29.  The results are shown here.

The company’s default probabilities are on the high end of the energy firms whose bonds traded October 29, 2013.


Before reaching conclusions about whether Petroleo Brasileiro S.A. is investment grade, we review the market’s assessment.  The first graph in this section compares the firm’s credit spreads with the traded credit spreads on October 29 of all firms with a legacy rating in the “investment grade” range.

It is clear from the graph that Petroleo Brasileiro S.A. credit spreads are on the high end of the investment grade group.  In the next graph, we compare Petroleo Brasileiro S.A. default probabilities with the matched maturity default probabilities for all investment grade-rated firms whose bonds traded on October 29.

Again, we find that the default probabilities for Petroleo Brasileiro S.A. are on the high end of the investment grade range.

We believe that sophisticated analysts would be split nearly equally about whether it is appropriate to rank Petroleo Brasileiro S.A. as an investment grade company. We note that no candidate for President of the United States has ever won 100% of the popular vote, which is one reason why our informal assessment of the opinions of a large number of analysts never states that there is a unanimous opinion. Such a statement would be unprovable and extremely unlikely to be true in any event. The 10 year default probability outlook of Petroleo Brasileiro S.A. barely ranks in the best half of its peer group.  The default probabilities for maturities of 5 years and under are in the wrong half of the riskiest half of the peer group.  The bonds of Petrobras Brasileiro S.A. trade at an above average credit spread to default probability ratio of about 8 times.  This premium is in part determined by the fact that the legacy credit rating agencies still rank the firm as “investment grade.”  While the link between ratings and credit spreads is very weak (ratings explain only 28% of credit spread movements), a downgrade of the firm’s bonds would have a significant negative impact on bond prices. We believe that the market-based peer group comparisons correctly show that Petroleo Brasileiro S. A. is risky compared to its peers and that only investors with a large risk appetite are likely to feel comfortable with this name in their portfolio.

Author’s Note

Regular readers of these notes are aware that we generally do not list the major news headlines relevant to the firm in question. We believe that other authors on SeekingAlpha, Yahoo, at The New York Times, The Financial Times, and the Wall Street Journal do a fine job of this.  Our omission of those headlines is intentional.  Similarly, to argue that a specific news event is more important than all other news events in the outlook for the firm is something we again believe is inappropriate for this author.  Our focus is on current bond prices, credit spreads, and default probabilities, key statistics that we feel are critical for both fixed income and equity investors.

Background on Default Probabilities Used

The Kamakura Risk Information Services version 5.0 Jarrow-Chava reduced form default probability model makes default predictions using a sophisticated combination of financial ratios, stock price history, and macro-economic factors. The version 5.0 model was estimated over the period from 1990 to 2008, and includes the insights of the worst part of the recent credit crisis. Kamakura default probabilities are based on 1.76 million observations and more than 2000 defaults. The term structure of default is constructed by using a related series of econometric relationships estimated on this data base. An overview of the full suite of related default probability models is available here.

General Background on Reduced Form Models

For a general introduction to reduced form credit models, Hilscher, Jarrow and van Deventer (2008) is a good place to begin. Hilscher and Wilson (2013) have shown that reduced form default probabilities are more accurate than legacy credit ratings by a substantial amount. Van Deventer (2012) explains the benefits and the process for replacing legacy credit ratings with reduced form default probabilities in the credit risk management process. The theoretical basis for reduced form credit models was established by Jarrow and Turnbull (1995) and extended by Jarrow (2001). Shumway (2001) was one of the first researchers to employ logistic regression to estimate reduced form default probabilities. Chava and Jarrow (2004) applied logistic regression to a monthly database of public firms. Campbell, Hilscher and Szilagyi (2008) demonstrated that the reduced form approach to default modeling was substantially more accurate than the Merton model of risky debt. Bharath and Shumway (2008), working completely independently, reached the same conclusions. A follow-on paper by Campbell, Hilscher and Szilagyi (2011) confirmed their earlier conclusions in a paper that was awarded the Markowitz Prize for best paper in the Journal of Investment Management by a judging panel that included Prof. Robert Merton.

The Dodd-Frank Act and Related Regulations

Section 939A of the Dodd-Frank Act states the following:


(a) AGENCY REVIEW.—Not later than 1 year after the date of the enactment of this subtitle, each Federal agency shall, to the extent applicable, review—
(1) any regulation issued by such agency that requires the use of an assessment of the credit-worthiness of a security or money market instrument; and
(2) any references to or requirements in such regulations regarding credit ratings.
(b) MODIFICATIONS REQUIRED.—Each such agency shall modify any such regulations identified by the review conducted under subsection (a) to remove any reference to or requirement of reliance on credit ratings and to substitute in such regulations such standard of credit-worthiness as each respective agency shall determine as appropriate for such regulations. In making such determination, such agencies shall seek to establish, to the extent feasible, uniform standards of credit-worthiness for use by each such agency, taking into account the entities regulated by each such agency and the purposes for which such entities would rely on such standards of credit-worthiness.
(c) REPORT.—Upon conclusion of the review required under subsection (a), each Federal agency shall transmit a report to Congress containing a description of any modification of any regulation such agency made pursuant to subsection (b).

The new rules issued by the Office of the Comptroller of the Currency in accordance with Dodd-Frank are described here. The summary provided by the OCC reads as follows:

“In this rulemaking, the OCC has amended the regulatory definition of ‘investment grade’ in 12 CFR 1 and 160 by removing references to credit ratings. Under the revised regulations, to determine whether a security is ‘investment grade,’ banks must determine that the probability of default by the obligor is low and the full and timely repayment of principal and interest is expected. To comply with the new standard, banks may not rely exclusively on external credit ratings, but they may continue to use such ratings as part of their determinations. Consistent with existing rules and guidance, an institution should supplement any consideration of external ratings with due diligence processes and additional analyses that are appropriate for the institution’s risk profile and for the size and complexity of the instrument. In other words, a security rated in the top four rating categories by a nationally recognized statistical rating organization is not automatically deemed to satisfy the revised ‘investment grade’ standard.”


Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as Co-Chair, Center for Applied Quantitative Finance, Risk Research and Quantitative Solutions at SAS. Don’s focus at SAS is quantitative finance, credit risk, asset and liability management, and portfolio management for the most sophisticated financial services firms in the world.

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