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Royal Bank of Scotland Group PLC (NYSE:RBS) (OTC:RLSPY) is both one of the world's largest financial institutions and one of the world's biggest victims of the financial crisis, as documented in this analysis of daily credit crisis borrowings by Kamakura Corporation. The Royal Bank of Scotland Group PLC's annual report explains the firm's worldwide operations in detail. Rescue efforts by the government of the United Kingdom have left the citizens of the United Kingdom with a large majority stake that the Royal Bank of Scotland PLC describes this way on its website (see previous link):

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In this note, we turn to the U.S. dollar bonds issued both by the parent itself and by its subsidiary Royal Bank of Scotland PLC with the guarantee of the parent. We seek to bring a bond market perspective to the outlook for Royal Bank of Scotland Group PLC as a complement to analysis based on a common stock holder's perspective. We note that the government of the United Kingdom is actively considering a break-up of the Royal Bank of Scotland Group PLC, a major event risk facing the company. Today's note incorporates Royal Bank of Scotland Group PLC bond price data as of October 8, 2013. A total of 62 trades were reported on 7 fixed-rate non-call bond issues of Royal Bank of Scotland Group PLC with trading volume of $24.4 million. We used all of this data in this note. Trade data for other legal entities affiliated with the parent company (Royal Bank of Scotland PLC and Royal Bank of Scotland NV) totaled 116 trades on 19 bonds with trading volume of $16.1 million. We used 96 trades on 16 bonds with trading volume of $6.4 million after eliminating data errors. One of the bonds used was issued by Royal Bank of Scotland NV and the rest were issued by Royal Bank of Scotland PLC.

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 Royal Bank of Scotland Group PLC 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. Section 939A states the following:

"SEC. 939A. REVIEW OF RELIANCE ON RATINGS.

(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 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 , each Federal agency shall transmit a report to Congress containing a description of any modification of any regulation such agency made pursuant to subsection."

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."

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 Royal Bank of Scotland Group PLC.

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 Royal Bank of Scotland Group PLC 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 0.39% at one month to 0.17% at 1 year and 0.19% at ten years.

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The term structure of default risk for the United Kingdom, the majority owner of the Royal Bank of Scotland Group PLC, is shown here:

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Sovereign default probabilities are higher than many observers expect because, as Prof. Jens Hilscher of Kamakura Corporation and Brandeis University explains, "Corporates default because they have to. Sovereigns default because they want to." The current debt ceiling impasse in the United States is a case in point. For documentation of the fact that the average sovereign is four times more risky than the average public firm, see this introduction to sovereign default risk.

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 23 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 Royal Bank of Scotland Group PLC 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 (NYSEARCA:TLT)(NYSEARCA:TBT), interpolated from the Federal Reserve H15 statistical release for that day, which matches the maturity of the traded bonds of the Royal Bank of Scotland Group PLC. The 1 month U.S. Treasury rate is up about 0.16% from last week due to the impasse over the U.S. government debt ceiling that is on-going as this note was written. 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 Royal Bank of Scotland Group PLC 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 Royal Bank of Scotland Group PLC bond issue recorded by TRACE.

The graph shows an increasing "liquidity premium" as maturity lengthens for the bonds of Royal Bank of Scotland Group PLC. This is a pattern seen usually with firms of good credit quality. We explore this premium in detail below.

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Royal Bank of Scotland PLC and NV bonds show a much higher degree of volatility in the yields reported by TRACE, in part because the dollar volume of trades is quite small. We report the yields from TRACE without modification in this graph:

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In the following graph, the average yields are plotted versus U.S. Treasury yields for both Royal Bank of Scotland Group PLC and its subsidiaries Royal Bank of Scotland PLC and NV. The yields are closely intertwined as one would expect, apart from the legal risk that the bank subsidiaries are supported more heavily by the government of the United Kingdom than the parent company.

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The high, low and average credit spreads at each maturity are graphed below for Royal Bank of Scotland Group PLC. 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. The polynomial explains 79.96% of the variation in credit spreads over the maturity spectrum.

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Royal Bank of Scotland PLC and NV credit spreads are shown in this graph. The fitted polynomial explains 71.6% of the variation in credit spreads by maturity.

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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 Royal Bank of Scotland Group PLC and Royal Bank of Scotland PLC and NV, the credit spread to default probability ratio ranges from 1.5 to 8 times at maturities under 2 years to a range from 12 to 20 times at longer maturities. The ratios of spread to default probability for all traded bond issues are shown here:

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Royal Bank of Scotland PLC and NV reward to risk ratios are reported in this chart:

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The credit spread to default probability ratios are shown in graphic form below for Royal Bank of Scotland Group PLC and Royal Bank of Scotland PLC and NV in the next two charts. The fitted polynomial explains 79.1% of the variation in the reward to risk ratios by maturity for the parent Royal Bank of Scotland Group PLC.

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A similar polynomial explains 82.61% of the variation of the reward to risk ratio for subsidiaries Royal Bank of Scotland PLC and NV.

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The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name. For the week ended October 4, 2013 (the most recent week for which data is available), the credit default swap trading volume on subsidiary Royal Bank of Scotland PLC was 125 trades for $882.6 million. The number of credit default swap contracts traded on Royal Bank of Scotland PLC in the 155 weeks ended June 28, 2013 is summarized in the following chart. Royal Bank of Scotland PLC CDS volume ranked 55th among all reference names traded world-wide during this period.

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

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On a cumulative basis, the default probabilities for Royal Bank of Scotland Group PLC range from 0.17% at 1 year to 1.85% at 10 years.

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Over the last decade, the 1 year and 5-year annualized default probabilities for Royal Bank of Scotland Group PLC spiked to an astonishing degree in the credit crisis until the government of the United Kingdom stepped in to rescue the firm. The 1-year default probability peaked at slightly over 60% in early 2009. The 5-year default probability peaked at slightly over 20% on an annualized basis at the same time.

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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 Royal Bank of Scotland Group PLC 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 Royal Bank of Scotland Group PLC default risk responds to changes in 3 domestic U.S. risk factors and 10 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 94.8% of the variation in the default probability of Royal Bank of Scotland Group PLC. The remaining variation is the estimated idiosyncratic credit risk of the firm.

Royal Bank of Scotland Group PLC can be compared with its peers in the same industry sector, as defined by Morgan Stanley (NYSE:MS) and reported by Compustat. For the world-wide "financials" sector, Royal Bank of Scotland Group PLC has the following percentile ranking for its default probabilities among its 5,518 peers at these maturities:

1 month 93rd percentile

1 year 79th percentile

3 years 71st percentile

5 years 48th percentile

10 years 33rd percentile

The short-term ranking of Royal Bank of Scotland Group PLC relative to its peers is higher because business conditions are so good currently that they rank at the 83rd 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, Royal Bank of Scotland Group PLC ranks in the safest half of its peer group from a credit risk perspective. Taking still another view, the actual and statistically predicted Royal Bank of Scotland Group PLC credit ratings both show a rating in the "investment grade" territory. The statistically predicted rating is 1 notch below the legacy rating from firms like the Standard & Poor's affiliate of McGraw-Hill (NYSE:MHFI) and Moody's Investors Service (NYSE:MCO). The legacy ratings of the company have changed only 3 times in the last decade, in spite of the need for the government to rescue the bank.

Conclusions

We believe that a majority of sophisticated analysts would rank Royal Bank of Scotland Group PLC 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 long run default probability outlook of Royal Bank of Scotland Group PLC ranks in the best half of its peer group. That being said, there is considerable event risk from the potential break-up of the organization and change in its "semi-government" status. The history of the firm shows that "business as usual" led to failure, and a big question going forward for investors is "what is 'business as usual' for RBS in 2013?" We remind readers that a below average default probability is not sufficient reason to buy a bond. The bond must offer "good value," which we define in terms of the ratio of credit spread to the matching maturity default probability. By this measure, Royal Bank of Scotland Group PLC bonds offer a reward to risk ratio that is triple the level normally seen from iconic "brand name" corporates in the U.S. market, but this reward to risk ratio has to be considered in the light of the very large event risk the firm faces. We conclude that the bonds of Royal Bank of Scotland Group PLC and its subsidiaries would work best in the portfolio of an investor who can diversify away the event risk in the context of one's full portfolio holdings.

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 database. 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.

Disclosure: I 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. I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: Kamakura Corporation has business relationships with a number of firms mentioned in this article.

Source: Royal Bank Of Scotland Group PLC Bonds: None But The Brave