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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Citigroup Inc. Bonds: A Prince of an Investment After Many Pandit

08/26/2013 10:08 AM

The management changes at Citigroup Inc. since the events of the credit crisis have been very dramatic, perhaps more so than for any of the other firms we have analyzed in recent weeks. We did an extensive analysis of the credit crisis history of Citigroup borrowings from the Federal Reserve and the events leading up to those borrowings on . Citigroup Inc. consolidated borrowings during the credit crisis peaked at $24.2 billion on March 5, 2009, and the firm had borrowings outstanding on 211 days according to Federal Reserve reports. Today’s study incorporates Citigroup bond price data as of August 23, 2013 to analyze the potential risk and return to bondholders of Citigroup Inc., which announced a tender offer on August 14, 2013 for 7 different bond issues with total principal outstanding of $11.5 billion. The offer expires on September 11, 2013.

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.” Interest rate risk managers at major firms like Citigroup Inc. use the marginal cost of funds reflected in the bond market to centralize interest rate risk and to measure internal profitability based on this “transfer pricing yield curve.” For many investors, “investment grade” is an internal definition; for many banks and insurance companies “investment grade” is also defined by regulators. In this note we analyze the updated current levels and past history of default probabilities for Citigroup Inc. We also measure the reward, in terms of credit spread, for taking on the default risk of Citigroup Inc. bonds. On August 23, a slow summer Friday, Citigroup Inc. non-call fixed rate bonds were traded 505 times for $184.7 million in volume.  After eliminating outliers, we used 479 trades on 43 Citigroup Inc. bonds with a trade volume of $184.6 million in this study.

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. We analyze the maturities where the credit spread/default probability ratio is highest for Citigroup Inc. We also consider whether or not a reasonable U.S. bank investor would judge the firm 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.  The new rules delete references to legacy credit ratings and replace them with default probabilities as explained here.

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 Citigroup Inc. ranging from one month to 10 years on an annualized basis.  The default probabilities range from 0.02% at one month to 0.01% at 1 year and 0.08% at ten years.

We 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 bond data mentioned above for 43 Citigroup Inc. fixed rate non-call issues in this analysis.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Citigroup Inc. 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, interpolated from the Federal Reserve H15 statistical release for that day, which matches the maturity of the traded bonds of Citigroup Inc. The second lowest 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 third line from the bottom (in orange) graphs the lowest yield reported by TRACE on that day on Citigroup Inc. bonds. The fourth line from the bottom (in green) displays the average yield reported by TRACE on the same day.  The highest yield is obviously the maximum yield in each Citigroup Inc. issue recorded by TRACE.

Note that the longest maturity Citigroup Inc. bond has a maturity of 84.5 years. We used the 30 year U.S. Treasury yield as a proxy for a matched maturity U.S. Treasury rate and we assumed that the annualized 84.5 year default probability for Citigroup Inc. would be at the same level as the 10 year default probability. The data makes it clear that there is a sizable liquidity premium built into the yields of Citigroup Inc. above and beyond the “default-adjusted risk free curve” (the risk-free yield curve plus the matched maturity default probabilities for the firm).  The credit spreads are relatively erratic for maturities under 7 years. The credit spreads generally widen with maturity, the normal pattern for a high quality credit, with the exception of three bonds with maturities between 20 and 30 years.

The high, low and average credit spreads at each maturity are graphed below.  Credit spreads are gradually increasing with the maturity of the bonds, with the exception of the longest maturities. 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 cubic polynomial that explains the average spread as a function of years to maturity.  This polynomial explains 55% of the variation in the average credit spread over the maturity term structure:

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.  This ratio of spread to default probability is shown in the following table for Citigroup Inc. At almost all maturities under 2.5 years, the reward from holding the bonds of Citigroup Inc., relative to the matched maturity default probability, is more than 40 basis points of credit spread reward for every basis point of default risk. The ratio of spread to default probability decreases with maturity once the maturity of the bonds exceeds 2.5 years, falling to a spread to default ratio between 19 and 35 times.  This reward to risk ratio is among the highest of any firm analyzed in this series of bond studies.

The credit spread to default probability ratios are shown in graphic form here. We have again added a cubic polynomial relating the credit spread to default probability ratio to the years to maturity on the underlying bonds.  The smoothed line explains about 44% of the variation in the risk-reward ratio.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended August 16, 2013 (the most recent week for which data is available), the credit default swap trading volume on Citigroup Inc. was 10 trades with $114.5 million of notional principal, a small fraction of the daily bond trading volume on August 23. The number of credit default swap contracts traded on Citigroup Inc. in the 155 weeks ended June 28, 2013 is summarized in the following table:

Citigroup Inc. ranked 35th among all reference names in weekly credit default swap trading volume during this period, which is graphed below:

On a cumulative basis, the default probabilities for Citigroup Inc. range from 0.01% at 1 year to 0.77% at 10 years, as shown in the following graph.

Over the last decade, the 1 year and 5 year default probabilities for Citigroup Inc. have varied as shown in the following graph. The one year default probability peaked at just under 40% in the first half of 2009 during the worst part of the credit crisis. The 5 year default probability (annualized) peaked at just over 10%.

The legacy credit ratings [those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO)] for Citigroup Inc. have changed four times during the decade.

The macro-economic factors driving the historical movements in the default probabilities of Citigroup Inc. have 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. This assumption is certainly false in the case of Citigroup Inc., where the new management team has dramatically reduced the firm’s exposure to U.S. home price risk.  With that caveat, the historical analysis shows that Citigroup Inc. default risk responds to changes in the following factors among those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review:

  • Change in real gross domestic product
  • Change in nominal gross domestic product
  • Change in real disposable income
  • Change in nominal disposable income
  • Unemployment rate
  • 3 month U.S. Treasury bill rates
  • BBB rated corporate bond yield
  • The VIX volatility index
  • Home price index
  • Commercial real estate prices
  • 2 international macro factors

These macro factors explain 89.7% of the variation in the default probability of Citigroup Inc.

Citigroup Inc. can be compared with its peers in the same industry sector, as defined by Morgan Stanley (MS) and reported by Compustat.  For the USA “diversified financials” sector, Citigroup Inc. has the following percentile ranking for its default probabilities among its 218 peers at these maturities:

1 month 57th percentile
1 year 34th percentile
3 years 36th percentile
5 years 13th percentile
10 years 10th percentile

Even after the significant capital injections into Citigroup Inc. by the U.S. government and documented by the Inspector General of the Troubled Asset Relief Program on October 5, 2009, the percentile ranking of Citigroup Inc. default probabilities at one month is in the riskiest half of the diversified financial peer group. This fact has a simple and important explanation.  Even with a 1 month annualized default probability of 0.02%, Citigroup Inc. and the other diversified financials are enjoying a corporate credit risk environment which ranks at the 91st percentile (with 100 being best) over the period from 1990 to the present. The percentile ranking for Citigroup Inc. at 10 years is in the safest decile of credit risk among diversified financial firms. This is an impressive improvement from the Citigroup Inc. of 2009. A comparison of the legacy credit rating for Citigroup Inc. with predicted ratings indicates that the statistically predicted rating is one notch lower than the actual credit rating.  Both the actual and predicted ratings are “investment grade” by traditional credit rating standards of Moody’s Investors Service and the Standard & Poor’s affiliate of McGraw-Hill.


Citigroup Inc. is a dramatically transformed institution, compared to the Citigroup Inc. of 2007, when key director Robert Rubin confessed he was unaware of $50 billion of liquidity puts that bank traders had given clients who purchased risky tranches of collateralized debt obligations on mortgage-backed securities. The billions of capital injected into Citigroup Inc. by the U.S. government is concrete evidence of two things: the firm was considered “too big to fail” and the firm was very likely to fail (see the Inspector General’s report above) without such support. We believe that most analysts would predict that the U.S. government would again rescue the bank if necessary. The Kamakura default probabilities used above do NOT make this assumption.  The probability of rescue is ignored; the Kamakura default probabilities are the probability of failure. We believe most analysts feel the probability of rescue is embedded in the current legacy ratings for Citigroup Inc. That being said, the default risk of Citigroup Inc. has fallen to very low levels and market participants have responded with stock prices, bond spreads and credit derivative spreads that are consistent with a firm that has renewed strength.

The bonds of Citigroup Inc. provide a very attractive ratio of credit spread to default probability, with the short maturity reward for bearing credit risk totaling more than 40 basis points of credit spread for every basis point of default risk.  This is among the most attractive reward-to-risk ratios analyzed in this series of bond studies.  We believe a strong majority of analysts would judge the bank to be investment grade, thanks to the aggressive efforts of the new management team.

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.



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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