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: Still a Prince of an Investment

12/06/2013 11:36 AM

After the downgrade of Citigroup Inc. by Deutsche Bank on December 5, it is timely to do an update of our analysis of Citigroup Inc. bonds published on August 26, 2013. We did also 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 June 6, 2011. 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. With this history in mind, today’s study incorporates Citigroup bond price data as of December 5, 2013 to analyze the potential risk and return to bondholders of Citigroup Inc.

We remind readers that Citigroup Inc. announced a tender offer on August 14, 2013 for 7 different bond issues with total principal outstanding of $11.5 billion.

We conclude that Citigroup Inc. bonds have fairly typical spreads compared to peers, but default probabilities are much lower than peers.  Citigroup Inc.’s reward to risk ratio, measured by the credit spread to default probability ratio, continues to be 3, 4, or 5 times better than the typical investment grade bond issuer.  We explain our conclusions below.

Analytical Objective

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.” Part of our objective in this note is to derive this curve. We also answer whether or not Citigroup Inc. would be considered “investment grade” in light of the changed definition of investment grade mandated by Dodd-Frank and recently implemented by the Office of the Comptroller of the Currency.  For background on Dodd-Frank and related regulatory changes, see the note at the end of this analysis.

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 December 5, 54 Citigroup Inc. non-call fixed rate bonds were traded 508 times for $298.3 million in volume.  We used all of that data 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.

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, compared to the default probabilities for August 23, 2013, which we used in our prior study.  The default probabilities range from 0.02% at one month to 0.01% at 1 year and 0.08% at ten years. The default probabilities at these maturities are the same as they were in August after rounding to two decimal places.  The green line below shows the current annualized default probabilities.  The yellow line shows the same default probabilities on August 23, 2013.  For all maturities, the two lines are within 1 or 2 basis points of each other.

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 the 54 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 curve from the bottom (the orange dots) graphs the lowest yield reported by TRACE on that day on Citigroup Inc. bonds. The fourth line from the bottom (the green dots) displays the average yield reported by TRACE on the same day.  The highest yield (the red dots) is obviously the maximum yield in each Citigroup Inc. issue recorded by TRACE. For the reader’s convenience, we have added a trade volume-weighted credit spread, fitted to the average traded credit spread at each maturity.  This curve is shown in black.

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 84.2 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 traded 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 near 30 years.

We show the same data for August 23, 2013 in a slightly different format in the next graph.

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 maturities near 30 years.

The same data, again in a different format, is shown for August 23, 2013 in this graph.

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 20 to 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 15 and 25 times.  This reward to risk ratio is among the highest of any firm analyzed in this series of bond studies, although the reward to risk ratio has narrowed somewhat from our August analysis.

The August 23, 2013 reward to risk ratios are repeated here:

The credit spread to default probability ratios are shown in graphic form here. We have again added a traded-weighted polynomial relating the fitted credit spread-default probability ratio to the years to maturity on the underlying bonds.

The same graphic for August 23, 2013, in slightly different form, is shown here:

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name.  For the week ended November 29, 2013 (the most recent week for which data is available), the credit default swap trading volume on Citigroup Inc. was 63 trades with $382.2 million of notional principal, more than triple the volume in the August vacation doldrums. 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 0.81% at 10 years (up 0.04% from August), 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 2014 Comprehensive Capital Analysis and Review:

  • Change in nominal disposable income
  • Unemployment rate
  • BBB rated corporate bond yield
  • The VIX volatility index
  • Home price index

These macro factors explain 75.2% of the variation in the default probability of Citigroup Inc. The remainder of the risk is the idiosyncratic default risk 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 55th percentile, down 2 from August
1 year 34th percentile, unchanged
3 years 32th percentile, down 4 from August
5 years 12th percentile, down 1 from August
10 years 10th percentile, unchanged

Although the Citigroup Inc. default probabilities have increased slightly since August, their percentile rank relative to peers has improved or remained unchanged. Note, however, that 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 at 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. In that environment, 0.02% default risk is “high.” 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 exactly the same as the actual legacy 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.


Before reaching any conclusions about investment grade status, it is useful to look at some additional market views of Citigroup Inc. and its peers.  The following graph compares the traded credit spreads on Citigroup Inc. with the traded credit spreads on the “banks/finance” peer group on December 5, 2013:

The credit spreads for Citigroup Inc. were near the middle of the sector peer group. We now look at the matched-maturity default probabilities for Citigroup Inc. versus that same peer group. Citigroup Inc. default probabilities are well below average for the peer group even though its spreads were near the average.

We now compare the traded credit spreads for Citigroup Inc. with the traded spreads for every firm with a legacy credit rating in the old-style “investment grade” range.  Again, Citigroup Inc. spreads are near the average of this peer group in most cases.

By the matched maturity default probability criterion, comparing to investment grade firms with bond trades on December 5, Citigroup Inc.’s default probabilities are well below average.

Despite the U.S. government rescue of Citigroup Inc. during the credit crisis, 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.  Credit spreads, however, have not declined as much as the default probabilities for the firm on a proportional basis. This has resulted in a very high reward to risk ratio.

The bonds of Citigroup Inc. continue to provide a very attractive ratio of credit spread to default probability, with the short maturity reward for bearing credit risk totaling 20 to 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 on-going aggressive efforts of the new management team.

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.

Background on the Dodd-Frank Act and the Meaning of “Investment Grade”

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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