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Special disclosure by the author: The author spent two summers working under Wm. Mack Terry, head of the Financial Analysis and Planning Department, at Bank of America NT & SA in San Francisco nearly 40 years ago. The dispassionate partitioning of the risk and return of the Bank was one of the key roles of the Financial Analysis and Planning Department under Mr. Terry, and we continue in that tradition in what follows.

We first analyzed default risk at Bank of America Corporation (BAC) on July 8, 2013 and followed up with a second analysis as of August 20, 2013. On those two dates, the one year default probability for the firm was 0.18% and 0.08%, respectively. The ten year annualized default probability was 0.49% and 0.44% on July 8 and August 20. In the July post, we also reported on an extensive May 25, 2011 analysis of the credit crisis history of consolidated Bank of America borrowings (including borrowings of Countrywide Financial and Merrill Lynch) from the Federal Reserve and the events leading up to those borrowings. Bank of America consolidated borrowings during the credit crisis peaked at $48.1 billion, nearly double the amount of money that Lehman Brothers requested but did not get from the Federal Reserve prior to its bankruptcy filing on September 14, 2008.

Today's study incorporates Bank of America bond price data as of November 26, 2013 to re-analyze the potential risk and return to bondholders of Bank of America Corporation, which recently completed a tender for $6.2 billion in various notes due in 2014. We conclude that Bank of America Corporation would be judged to be an investment grade credit by a majority of analysts. That being said, there is not much margin from error in this assessment due to default probabilities that rank in the riskiest half of the "diversified financials" peer group in the United States.

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 Bank of America Corporation 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. For a summary of the impact of the 2010 Dodd-Frank Act on the definition of investment grade, please see the relevant section at the end of this post.

In this update, we analyze the current levels and past history of default probabilities for Bank of America Corporation. We also measure the reward, in terms of credit spread, for taking on the default risk of Bank of America Corporation bonds. On November 26, 100 Bank of America Corporation non-call fixed rate bonds were traded 639 times for $370.1 million in volume. We used all of that data in today's analysis. There were also a number of trades in the non-call fixed rate bonds of Bank of America NA, the bank subsidiary, on November 26 but we leave analysis of the bonds of the bank itself for another day and focus on the bonds of the holding company.

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 Bank of America Corporation.

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 (in green) for Bank of America Corporation ranging from one month to 10 years on an annualized basis, compared to their level on August 20 (in yellow). The default probabilities range from 0.12% at one month (down 0.04% since August 20) to 0.06% at 1 year (down 0.02% from our August report) and 0.48% at ten years (up 0.04% from August). For maturities longer than 10 years, we assume the default probability is constant at the 0 year level.

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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 TRACE data described above in this report.

The graph below shows 6 different yield curves that are relevant to a risk and return analysis of Bank of America Corporation 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 Bank of America Corporation. 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 Bank of America Corporation bonds. The fourth line from the bottom (in green) displays the trade-weighted average yield reported by TRACE on the same day.

The highest yield (in red) is obviously the maximum yield in each Bank of America Corporation issue recorded by TRACE. The sixth curve is plotted in black. This curve represents the yield on Bank of America Corporation non-call fixed rate debt that one obtains from the best fit of a cubic polynomial to average credit spreads on all 100 bonds on a trade-weighted basis. That is, an institutional trade of $10 million in principal amount gets 10,000 times more weight than a retail trade of $1,000 in principal amount. See the credit spread commentary below for more details.

The data makes it clear that there continues to be a sizable liquidity premium built into the yields of Bank of America Corporation 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 because all trades, no matter what their volume, are included in the graph. The credit spreads generally widen with maturity, the normal pattern for a high quality credit, with the exception of the three longest maturity bonds.

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The pattern on August 20 was fairly similar. That graph is shown here:

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The high, low, average and fitted 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. The black line is the fitted credit spread, using a cubic polynomial. The coefficients of the polynomial are chosen to minimize the sum of squared errors in average credit spread on a trade-weighted basis.

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We reproduce the same data from August 20 in the graph below, using a slightly different reporting format.

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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. This ratio of spread to default probability is shown in the following table for Bank of America Corporation. At almost all maturities under 4 years, the reward from holding the bonds of Bank of America Corporation, relative to the matched maturity default probability, is more than 7 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 4 years, falling to a spread to default ratio between 3 and 6 times. This narrowing reward to risk ratio, compared to August 20, is a function of market conditions, where we see a general narrowing of spreads across the board.

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The comparable ratios for August are reported here.

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The credit spread to default probability ratios are shown in graphic form here for November 26. For the reader's convenience, we show the ratio of fitted credit spread (trade-weighted) to default probability in black, as explained above.

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The same ratios are reported here for August 20 using a slightly different format.

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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 November 22, 2013 (the most recent week for which data is available), the credit default swap trading volume on Bank of America Corporation was 184 trades (up from 13 trades in August) with $1,731 million (up from $67.7 million in August) of notional principal, a very large change in volume above and beyond the impact of the summer holiday season on the August figures. This dramatic change in CDS volume is a matter of concern. The number of credit default swap contracts traded on Bank of America Corporation in the 155 weeks ended June 28, 2013 is summarized in the following table:

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Bank of America ranked 12th among all reference names in weekly credit default swap trading volume during this period, which is graphed below:

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In the next graph, we plot the 5 year credit default swap spreads that are predicted by Kamakura Corporation for Bank of America Corporation using 2.4 million observations of CDS bids, offered and quoted spreads over the period 2004 through 2012. The spreads are graphed from August 20, 2013 to the present. Predicted CDS spreads for Bank of America Corporation have narrowed since August 20 compared to 5 year default probabilities, which have remained relatively flat. This is consistent with the narrowing of the spread to default probability ratios reported above.

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On a cumulative basis, the default probabilities for Bank of America Corporation range from 0.06% at 1 year (down 0.02% from August) to 4.59% at 10 years (up 0.29% from August), as shown in the following graph. Bank of America Corporation is the 900th highest of 2,488 rated firms by this measure at a 10 year maturity.

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Over the last decade, the 1 year and 5 year default probabilities for Bank of America Corporation have varied as shown in the following graph. The one year default probability peaked at just under 20% in the first half of 2009 as Bank of America was absorbing Countrywide Financial and Merrill Lynch. The 5 year default probability (annualized) peaked at just over 5%.

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The legacy credit ratings, those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor's and Moody's (MCO), for Bank of America Corporation have changed six times during the decade.

The macro-economic factors driving the historical movements in the default probabilities of Bank of America Corporation include the following factors among those listed by the Federal Reserve in its Comprehensive Capital Analysis and Review:

  1. Unemployment rate
  2. 3 month U.S. Treasury bill rates
  3. 10 Year U.S. Treasury yield
  4. BBB rated corporate bond yield
  5. The VIX volatility index
  6. Home price index

These macro factors explain 67.2% of the variation in the default probability of Bank of America Corporation. The remaining variation in the default probability is due to the idiosyncratic risk of the firm.

Bank of America Corporation 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, Bank of America Corporation has the following percentile ranking for its default probabilities among its 217 peers at these maturities:

1 month 87th percentile, versus 84th in August

1 year 76th percentile, versus 78th in August

3 years 71st percentile, versus 74th in August

5 years 59th percentile, versus 62nd in August

10 years 62nd percentile, versus 63rd in August

Even after the significant capital injections into Bank of America Corporation by the U.S. government and documented by the Inspector General of the Troubled Asset Relief Program on October 5, 2009, the percentile rankings of its default probabilities continue to range from the 59th to the 87th percentile of U.S. diversified financial firms. A comparison of the legacy credit rating for Bank of America Corporation with predicted ratings indicates that the statistically predicted rating is two notches lower than the actual credit rating. Both the actual and predicted rating are "investment grade" by traditional credit rating standards of Moody's Investors Service and the Standard & Poor's affiliate of McGraw-Hill.

Conclusions

Before summarizing our conclusions, we look at the market view of Bank of America Corporation. The next graph compares the traded credit spreads for Bank of America Corporation (blue dots) versus those in the "Banks/Financials" peer group (light blue dots) reported by MarketAxess.

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Bank of America Corporation credit spreads are in the mid-to-upper range of the peer group. We next compare Bank of America Corporation matched-maturity default probabilities to those of the peer group for which bond trades were reported on November 26:

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Bank of America Corporation is near the top of the peer group by this measure.

Next, despite the Dodd-Frank Act, we use legacy ratings as a proxy for the consensus definition of "investment grade" and compare Bank of America Corporation traded credit spreads versus the traded credit spreads of all "legacy investment grade" firms on November 26. Bank of America Corporation credit spreads are roughly in the middle of the peer group.

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When we plot matched maturity default probabilities versus the "legacy investment grade" peer group, Bank of America Corporation is in the upper half of the peer group at the longer maturities.

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Our conclusions from August 20 are unchanged. Bank of America Corporation ranks in the riskier half of the diversified financial services sector from a credit risk perspective. The $45 billion of capital injected into Bank of America Corporation (initially a portion was invested via Merrill Lynch) is concrete evidence of two things: the firm was considered "too big to fail" and the firm was going to fail (see the title of 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 Bank of America Corporation. The statistically predicted rating does not include this probability, which is why the statistically predicted rating is two notches lower. The default probabilities for Bank of America are much improved in recent years, but they still are far above the median for the diversified financials sector. Because of this, we believe it is inappropriate for Bank of America Corporation to consider stock repurchases or dividend increases until default probabilities compare more favorably with peers.

The bonds of Bank of America Corporation provide a fairly typical ratio of credit spread to default probability, with the short maturity reward for bearing credit risk significantly higher than the long term reward (the spread to default probability ratio). We believe a majority of analysts would judge the bank to be slightly above the border between investment grade and non-investment grade. Bond investors who are optimistic that Bank of America Corporation's troubles are behind it will receive the most credit spread per basis point of default risk at maturities of 4 years or less.

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 Seeking Alpha, 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:

"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."

Source: Bank Of America Corporation Bonds: The Recovery Is Not Finished

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