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Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura.

# Bank of America Corporation: Default Probabilities and Relative Value Update

06/11/2014 01:43 AM

Bank of America Corporation (BAC) was the most heavily traded corporate name in the U.S. fixed rate bond market on June 10. Bank of America Corporation was the only non-sovereign reference name in the top 20 reference names by trading volume in the credit default swap market last week as well. We last analyzed default risk at Bank of America Corporation on March 7, 2014. In a July 8, 2013 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 June 10, 2014 to re-analyze the potential risk and return to bondholders of Bank of America Corporation. We use 613 trades on 91 Bank of America Corporation bond issues and a trading volume of$369 million in today’s analysis. The trading volume for today’s study was nearly double the volume used in our March 7, 2014 analysis.

Conclusion: Bank of America Corporation default probabilities have risen significantly since our March 7, 2014 report. 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. We believe most analysts feel the probability of rescue is embedded in the current legacy ratings for Bank of America Corporation. The same is true for credit spreads.

We believe a slim majority of analysts would judge the bank to be slightly above the border between investment grade and non-investment grade. Bond investors have been kind to Bank of America Corporation, bidding up bond prices to the point where the credit spread to default probability ratio is well below the median for large trades on June 10. We have seen this phenomenon often with iconic brand names. For investors who care only about risk and return, instead of the brand name, 358 of 431 heavily traded bond issues on June 10, 2014 offered a better reward to risk ratio than the most attractive Bank of America bond.

The Analysis
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 Bank of America Corporation to be “investment grade” under the June 13, 2012 rules mandated by the Dodd-Frank Act of 2010. The U.S. Office of the Comptroller of the Currency has announced its implementation of the Dodd-Frank rules in 2012. The default probabilities used are described in detail in the daily default probability analysis posted by Kamakura Corporation. The full text of the Dodd-Frank legislation as it concerns the definition of “investment grade” is summarized at the end of our analysis of Citigroup (C) bonds published December 9, 2013.

Assuming the recovery rate in the event of default would be the same on all bond issues of the same issuer, 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 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 for Bank of America Corporation 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 current default probabilities, in green, range from 0.33% at one month (up 0.20% from March 7) to 0.21% at 1 year (up 0.15% from March 7) and 0.56% at ten years (up 0.13%). The March 7, 2014 default probabilities used in our prior study are shown in yellow.

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. Bank of America Corporation was the most heavily traded corporate bond issuer in the U.S. fixed rate bond market on June 10, with 951 trades in 211 issues for a daily volume of $394 million. We eliminated all non-senior non-call bonds from this total to get the 91 bonds used for today’s study. 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 (TLT)(TBT), interpolated from the Federal Reserve H15 statistical release for that day, which exactly matches the maturity of the traded bonds of Bank of America Corporation. 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 dots graph the lowest yields reported by TRACE on that day on Bank of America Corporation bonds. The green dots display the trade-weighted average yield reported by TRACE on the same day. The red dots show the maximum yield in each Bank of America Corporation issue recorded by TRACE. The black dots and connecting black line show the yield consistent with the best fitting trade-weighted credit spread explained below. The graph shows a generally increasing “liquidity premium” as maturity lengthens for the bonds of Bank of America Corporation, with a peak in credit spread at about 20 years to maturity. We explore this premium in detail below. The high, low, average and fitted credit spreads at each maturity are graphed below for Bank of America Corporation. 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 (in black) that explains the trade-weighted average spread as a trade-weighted 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 Bank of America Corporation, the credit spread to default probability ratio generally ranges widely from 1.1 to 5.9 times, down significantly from our March 7, 2014 analysis. The credit spread to default probability ratios are shown in graphic form below for Bank of America Corporation. The graph shows the gentle decline in the credit spread to default probability ratio once the bond maturity exceeds about 3 years. Relative Value Analysis Are these reward to risk ratios “normal”? Are they above or below average? The best way to answer that question is to compare them to the credit spread to default probability ratios for all fixed rate non-call senior debt issues with trading volume of more than$5 million and a maturity of at least one year on June 10. The distribution of the credit spreads on the 431 traded bonds that met these criteria on June 10 is first plotted in this histogram:

The median credit spread for all 431 trades was 0.770%. The average credit spread was 1.042%. The next graph shows the wide dispersion of the credit spread to default probability ratios on those 431 June 10 trades:

The median credit spread to default probability ratio on those 431 trades was 7.952 and the average was 13.641. A total of 358 out of 431 large trades on June 10 had better credit spread to default probability ratios than the best ratio for any of the Bank of America Corporation bonds which traded at least $5 million in volume. This means that all of the heavily traded Bank of America Corporation bonds ranked in the bottom 17% by our “best value” criterion, the credit spread to default probability ratio. We list the credit spread to default probability ratios for bond trades over$5 million in volume for Bank of America Corporation. The Bank of America Corporation bonds ranked 359th through 391st of the 431 large trades on June 10.

Credit Default Swap Analysis
For the week ended June 6, 2014 (the most recent week for which data is available), the Depository Trust & Clearing Corporation reported 139 credit default swap trades with notional principal of $3.46 billion on Bank of America Corporation. This made Bank of America Corporation the only non-sovereign reference name ranked in the top 20 credit default swap reference names by notional principal traded during the week. The weekly history of notional principal traded on Bank of America Corporation in the credit default swap market is shown here: The weekly history of credit default swap trading on Bank of America Corporation, measured by the number of contracts traded, period is shown in this graph: Additional Counter-Party Credit Risk Analysis Kamakura Risk Information Services uses the bond prices described above to extract the trade-weighted zero coupon bond yields for Bank of America Corporation. The yields are derived in such a way that the forward credit spreads have maximum smoothness relative to the zero coupon bond yields for the U.S. Treasury curve on June 10, 2014. See van Deventer, Imai and Mesler, Advanced Financial Risk Management , 2nd edition, 2013 for additional details. These zero coupon credit spreads are critical to evaluating the counter-party credit risk of exposure to Bank of America Corporation and other counter-parties. On a cumulative basis, the default probabilities for Bank of America Corporation range from 0.21% at 1 year (up 0.15% from March 7, 2014) to 5.42% at 10 years (up 1.19% from March 7, 2014). The current cumulative default probabilities, shown in green, have risen considerably since our analysis using data from March 7 (shown in yellow). Over the last decade, the 1 year and 5 year annualized default probabilities for Bank of America Corporation show the huge shock posed by the credit crisis and the huge benefit of the$45 billion U.S. government capital injection. The 1 year default probability peaked at more than 20% in 2009. The annualized 5 year default probability peaked at slightly more than 5.00% in the same year.

As explained earlier in 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 Bank of America Corporation 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. With that caveat, the historical analysis shows that Bank of America Corporation default risk responds to changes in 6 risk factors among the 28 world-wide macro factors used by the Federal Reserve in its 2014 Comprehensive Capital Assessment and Review stress testing program. These macro factors explain 63.6% of the variation in the default probability of Bank of America Corporation. The remaining variation is the estimated idiosyncratic credit 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 U.S. “diversified financials” sector, Bank of America Corporation has the following percentile ranking for its default probabilities among its 226 peers at these maturities:

1 month         90th percentile, up 3 percentage points since March 7, 2014
1 year            86th percentile, up 8 percentage points
3 years          83rd percentile, up 10 percentage points
5 years          73nd percentile, up 11 percentage points
10 years        69th percentile, up 6 percentage points

For all time horizons, Bank of America default probabilities are in the riskier half of the peer group. Taking still another view, the actual and statistically predicted Bank of America Corporation credit ratings both show a rating in the lower half of “investment grade” territory. The statistically predicted rating is 2 notches below the legacy rating, those of Moody’s (MCO) and Standard & Poor’s (MHFI). The legacy credit ratings of Bank of America Corporation have changed six times in the last decade.

Conclusions
Before reaching a final conclusion about the “investment grade” status of Bank of America Corporation, we look at more market data. First, we look at Bank of America Corporation credit spreads versus credit spreads on every bond in the “Banks/Financials” sector that traded on June 10:

Bank of America Corporation credit spreads were near the average for the peer group. We now look at the matched maturity default probabilities on those traded bonds for both Bank of America Corporation and the peer group:

Consistent with the percentile rankings above, the default probabilities for Bank of America Corporation are well above the average of the industry peer group. We note that the bonds trading heavily are generally a much better group of credits than the industry in aggregate. We now turn to the legacy “investment grade” peers. First we compare traded credit spreads on June 10, 2014:

Again, Bank of America Corporation credit spreads are near the average of the investment grade peer group range. Investment grade default probabilities on a matched maturity basis for the bonds traded on June 10 are shown in this graph:

Again the default probabilities for Bank of America Corporation rank well above the median for the investment grade peer group.

Bank of America Corporation default probabilities have risen significantly since our March 7, 2014 report. 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 October 5, 2009 report by the Special Inspector General of the Troubled Asset Relief Program) 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 same is true for credit spreads. The statistically predicted rating does not include this probability, which is one reason why the statistically predicted rating is two notches lower than the actual rating.

We believe a slim majority of analysts would judge the bank to be slightly above the border between investment grade and non-investment grade. Bond investors have been kind to Bank of America Corporation, bidding up bond prices to the point where the credit spread to default probability ratio is well below the median for large trades on June 10. We have seen this phenomenon often with iconic brand names. For investors who care only about risk and return, instead of the brand name, 358 of 431 heavily traded bond issues on June 10, 2014 offered a better reward to risk ratio than the most attractive Bank of America bond.

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.