Deutsche Bank AG (NYSE:DB) is the prototypical "too big to fail" bank from a European perspective. For that reason, the bank is getting a very high level of scrutiny even from U.S. bank regulators. We last analyzed bond risk and return at Deutsche Bank AG using data from May 30, 2014. Today's study incorporates Deutsche Bank AG's (London Branch) bond price data as of April 22, 2015, to re-analyze the potential risk and return to bondholders of Deutsche Bank AG (London Branch), and, by implication, the parent Deutsche Bank AG. We use 42 trades on 7 Deutsche Bank AG (London Branch) bond issues and a trading volume of $28 million in today's analysis. There were also trades in 2 bond issues by parent Deutsche Bank AG and in 1 bond issue by Deutsche Bank Trust Company Americas, but we only mention that data as a supplemental source of information.

*Conclusion: Deutsche Bank AG default probabilities are essentially unchanged since our May 30, 2014, report. Deutsche Bank still ranks in the riskier half of the diversified financials peer group for maturities of five years and under. Its marginal (not average) cost of funds is 0.365% higher than its peers who make up the reference names behind U.S. Dollar Cost of Funds Index.*

*We believe a majority of analysts would judge the bank to be slightly above the border between investment grade and non-investment grade. The reward-to-risk ratio, the ratio of credit spread to default probability, on Deutsche Bank AG and Deutsche Bank AG (London Branch) ranges from the 38**th* *to the 72**nd* *percentile of the 412 heavily-traded corporate bonds on April 22. There were 156 out of 412 heavily-traded bonds, which offered a better reward-to-risk ratio than Deutsche Bank AG on April 22, 2015.*

**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 Deutsche Bank AG (London Branch) 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 (NYSE: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 to default probability ratio is highest for Deutsche Bank AG (London Branch).

**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 Deutsche Bank AG ranging from one month to 10 years on an annualized basis. As a first approximation, we assume that the parent firm and Deutsche Bank AG (London Branch) have identical default probabilities. 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 blue, range from 0.56% at one month (unchanged from May 30, 2014) to 0.24% at 1 year and 0.20% at ten years (unchanged). The May 30, 2014, default probabilities used in our prior study are shown in yellow.

Next, we display the default probabilities for Deutsche Bank Trust Company Americas, the principal U.S. bank subsidiary of Deutsche Bank AG, relative to the term structure of default probabilities of the parent. The bank default probabilities are provided by the Kamakura Risk Information Services U.S. Bank Default Probability Model announced on May 30, 2014, by Kamakura Corporation. The default probabilities can vary from the parent default probabilities for a number of reasons:

- The bank default probabilities use very high-quality, industry-specific accounting figures from the FDIC call reports. The bank model also uses macro factors as key inputs.
- The parent default probabilities use more generic financial statement information along with macro factors and stock prices.
- The parent has a real option, which has been used by a number of financial institutions, to allow the bank subsidiary to default.
- Regulators have a real option to block dividend payments from the bank to the parent.
- Both models are subject to normal estimation uncertainty.

The first graph shows the evolution of the 1-year default probabilities of Deutsche Bank AG (in yellow) and Deutsche Bank Trust Company Americas (in blue) over the last decade. The impact of the credit crisis on both entities is dramatic, but it was less extreme than it was for many of Deutsche Bank AG's large peer banks.

The second graph compares the two measures of the term structure of default risk. Deutsche Bank Trust Company America's 1-year default probability is 0.28% as of April 22, 2015.

**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. Deutsche Bank AG (London Branch) was the 77th most heavily-traded corporate bond issuer in the U.S. fixed rate bond market on April 22, with 121 trades in 33 issues for a daily volume of $28 million. We eliminated all non-senior, non-call bonds and all trades of $250,000 or less from this total to get the 7 bonds used for today's study. There were also 19 trades in two bond issues of Deutsche Bank AG traded on the day.

The graph below shows 6 different yield "curves" that are relevant to a risk and return analysis of Deutsche Bank AG (London Branch) 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 exactly matches the maturity of the traded bonds of Deutsche Bank AG (London Branch). 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 Deutsche Bank AG (London Branch) 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 Deutsche Bank AG (London Branch) 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 Deutsche Bank AG (London Branch). We explore this premium in detail below.

The high, low, average and fitted credit spreads at each maturity are graphed below for Deutsche Bank AG (London Branch). We have done nothing to smooth the data reported by TRACE, which includes both large lot and small lot bond trades. For the readers' 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. We ignore the floating rate note due May 30, 2017. For Deutsche Bank AG (London Branch), the credit spread to default probability ratio generally ranges widely from 2.1 to 7.9 times.

The credit spread to default probability ratios are shown in graphic form below for Deutsche Bank AG (London Branch). The graph shows a steady rise in the credit spread to default probability ratio as the maturity lengthens toward 10 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 April 22. The distribution of the credit spreads on the 412 traded bonds that met these criteria on April 22 is first plotted in this histogram:

The median credit spread for all 412 trades was 1.108%. The average credit spread was 1.636%. The next graph shows the wide dispersion of the credit spread to default probability ratios on those 412 April 22 trades:

The median credit spread to default probability ratio on those 412 trades was 9.995 and the average was 13.690. A total of 156 out of 412 large trades on April 22 had better credit spread to default probability ratios than the best ratio for any of the Deutsche Bank AG-related bonds, which traded at least $5 million in volume. The Deutsche Bank AG (London Branch) issue due in 2018 was ranked 299th. This means that the heavily-traded Deutsche Bank AG-related bonds ranked at the 38th and 72nd percentile 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 Deutsche Bank AG and Deutsche Bank AG (London Branch) here:

**Credit Default Swap Analysis**

For the week ended April 17, 2015 (the most recent week for which data is available), the Depository Trust & Clearing Corporation reported 41 credit default swap trades with notional principal of $227 million on Deutsche Bank AG. This made Deutsche Bank AG the 52nd ranked reference name among the reference names traded during the week.

The weekly history of notional principal traded on Deutsche Bank AG in the credit default swap market is shown here:

The weekly history of credit default swap trading on Deutsche Bank AG, measured by the number of contracts traded, period is shown in this graph:

**Comparison with the U.S. Dollar Cost of Funds Index**

This graph compares Deutsche Bank AG (London Branch)'s trade-weighted average credit spreads with the U.S. Dollar Cost of Funds Index^{TM} on the same day. The U.S. Dollar Cost of Funds Index^{TM} measures the trade-weighted cost of funds for the largest deposit-taking U.S. bank holding companies. The index is a credit spread, measured in percent and updated daily, over the matched maturity U.S. Treasury yield on the same day. The current bank holding companies used in determining the index are Deutsche Bank AG (London Branch) (NYSE:BAC) itself, Citigroup Inc. (C), JPMorgan Chase & Co. (NYSE:JPM), and Wells Fargo & Company (NYSE:WFC). The index is an independent market-based alternative to the Libor-swap curve that has traditionally been used by many banks as an estimate of their marginal cost of funds. Kamakura Corporation is the calculation agent, and the underlying bond price data is provided by TRACE and the U.S. Department of the Treasury.

The graph data is summarized quantitatively in this table. Deutsche Bank AG's (London Branch) average spread to the U.S. Dollar Cost of Funds Index is 0.365%, a considerable funding disadvantage versus peer banks.

**Other Analysis**

On a cumulative basis, the default probabilities for Deutsche Bank AG range from 0.24% at 1 year to 1.95% at 10 years. The current cumulative default probabilities, shown in blue, are nearly identical to the cumulative default probabilities from May 30, 2014 (shown in yellow).

Over the last decade, the 1-year default probabilities for Deutsche Bank AG show the impact of the credit crisis clearly. The 1-year default probability peaked near 3.50%. The annualized 5-year default probability peaked near 1.00%.

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 macroeconomic factors. Over a long period of time, macroeconomic 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 macroeconomic factors driving the historical movements in the default probabilities of Deutsche Bank AG 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 Deutsche Bank AG default risk responds to changes in 13 risk factors among the 28 world-wide macro factors used by the Federal Reserve in its 2015 Comprehensive Capital Assessment and Review stress testing program. These macro factors explain 67% of the variation in the default probability of Deutsche Bank AG. The remaining variation is the estimated idiosyncratic credit risk of the firm.

Deutsche Bank AG 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 "diversified financials" sector, Deutsche Bank AG has the following percentile ranking for its default probabilities among its 1,851 peers at these maturities:

1 month 95th percentile

1 year 84th percentile

3 years 76th percentile

5 years 51st percentile

10 years 36th percentile

For all time horizons up to 5 years, Deutsche Bank AG default probabilities are in the riskier half of the peer group. Taking still another view, the actual and statistically predicted Deutsche Bank AG 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 (NYSE:MCO) and Standard & Poor's (MHFI). The legacy credit ratings of Deutsche Bank AG have changed 4 times in the last decade.

**Conclusions**

Before reaching a final conclusion about the "investment grade" status of Deutsche Bank AG, we look at more market data. First, we look at Deutsche Bank AG (London Branch) credit spreads versus credit spreads on every bond in the "Banks/Financials" sector that traded on April 22:

Deutsche Bank AG (London Branch) 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 Deutsche Bank AG and the peer group:

Consistent with the percentile rankings above, the default probabilities for Deutsche Bank AG are at or 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 April 22, 2015:

Again, Deutsche Bank AG (London Branch) 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 April 22 are shown in this graph:

The scale of the graph makes an assessment difficult, but we know from the percentile rankings above that the default probabilities for Deutsche Bank AG rank somewhat above the median for the investment grade peer group.

Deutsche Bank AG default probabilities are essentially unchanged since our May 30, 2014, report. Deutsche Bank still ranks in the riskier half of the diversified financials peer group for maturities of five years and under. Its marginal (not average) cost of funds is 0.365% higher than its peers who make up the reference names behind U.S. Dollar Cost of Funds Index.

We believe a majority of analysts would judge the bank to be slightly above the border between investment grade and non-investment grade. The reward-to-risk ratio, the ratio of credit spread to default probability, on Deutsche Bank AG and Deutsche Bank AG (London Branch) ranges from the 38th to the 72nd percentile of the 412 heavily-traded corporate bonds on April 22. There were 156 out of 412 heavily-traded bonds that offered a better reward-to-risk ratio than Deutsche Bank AG on April 22, 2015.

**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, 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.

**Disclosure:** The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.