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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. Read More

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Kamakura Blog

May 20

Written by: Donald van Deventer
5/20/2014 3:40 AM 

In this note we re-analyze the current levels and past history of default probabilities forWells Fargo & Company (WFC) updating the analysis previously reported on October 18, 2013. We compare Wells Fargo & Company default probabilities to credit spreads on 281 bond trades in 23 different bond issues on May 19, 2014 with a total trading volume of $87 million. We use this information to calculate the credit-adjusted dividend yield on Wells Fargo & Company common stock. We conclude with a relative value analysis and an assessment of Wells Fargo & Company’s investment grade status under the new Dodd-Frank Act definitions.

Conclusion: Wells Fargo & Company, other than the period immediately after the acquisition of Wachovia, has experienced very strong default probability levels for the last decade. At a 10 year horizon, the firm is in the top 4 percent of the USA banking sector in credit quality. At current default probability levels, we continue to believe that almost all sophisticated analysts would rate Wells Fargo & Company as investment grade by the new Comptroller of the Currency definition. On a credit-adjusted basis, Wells Fargo & Company’s dividend yield is 2.46%, 0.40% below the traditional yield calculation, 2.86%. Credit default swap trading volume has been heavy lately, but the firm’s bonds continue to trade in the top third, when ranked by “best value,” of all heavily traded bonds.

Analytical Objectives
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 Wells Fargo & Company to be “investment grade” under the June 13, 2012 rules mandated by the Dodd-Frank Act of 2010, as implemented by the U.S. Office of the Comptroller of the Currency.

Assuming the recovery rate in the event of default would be the same on all bond issues with the same seniority 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 Wells Fargo & Company.


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 Wells Fargo & Company ranging from one month to 10 years on an annualized basis. The default probabilities range from 0.02% at one month (down 0.02% from October 18) to 0.01% at 1 year (down 0.01%) and 0.08% at ten years (down 0.02%). The green line is the current default probabilities and the yellow line is the default probabilities as of our prior report, which used data for October 18, 2013. 


We explain the source and methodology for the default probabilities in each Instablog posted by Kamakura Corporation on

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 today’s analysis.

The graph below shows 6 different yield curves that are relevant to a risk and return analysis of Wells Fargo & Company bonds. The lowest curve, in dark blue, is the yield to maturity on the benchmark U.S. Treasury bonds most similar in maturity to the traded bonds of Wells Fargo & Company. 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 (the orange dots) graphs the lowest yield reported by TRACE on that day on Wells Fargo & Company 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 Wells Fargo & Company issue recorded by TRACE. The black dots and connecting black line represent the yield associated with a polynomial fitted on the trade-weighted basis to the trade-weighted average spread on each bond.

The data makes it very clear that there is a very large liquidity premium built into the yields of Wells Fargo & Company above and beyond the “default-adjusted risk free curve” (the risk-free yield curve plus the matched maturity default probabilities for the firm). 

The high, low, average and trade-weighted fitted credit spread at each maturity are graphed below. While there is a fair amount of volatility in spread prevailing on the shorter maturities, credit spreads are gradually increasing with the maturity of the bonds. 

Because we have 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 Wells Fargo & Company. At all maturities, the reward from holding the bonds of Wells Fargo & Company, relative to the matched maturity default probability, is high and roughly consistent with the levels found in our previous report. For maturities of 2 years and under, the ratio of credit spread to default probability ranges from 16 to 105. For longer maturities the range is from 5.8 to 17.7. The ratios are relatively unchanged from October 18, 2013.

The same figures as of October 18, 2013 are reproduced here:


The next graph plots the ratio of credit spread to default probability at each maturity. Again, we have added a smoothed line to the average spread to default probability ratio.

For Wells Fargo & Company, the spread to default probability ratios are high across the board. After some volatility at the shorter maturities, the reward for bearing a basis point of default risk declines from levels of over 30 times to ratios generally in the 10 to 20 times default risk range.

Relative Value Analysis
We now turn to relative value analysis using the bond data and default probabilities for all bond issues that were senior, fixed rate, with maturities over 1 year with trading volume of at least $5 million. For background, we recommend this introduction to the use of default probabilities in fixed income strategy by J.P. Morgan Asset Management. First, we look at the histogram of all 357 bond issues that met our criteria on May 19, 2014: 

The median credit spread on May 19 was 0.859% and the average was 1.254%. The next histogram graphs the ratio of credit spread to default probability for all 357 bond issues. The median ratio was 7.884 and the average was 11.200.

The relative rank of the Wells Fargo & Company bond issues is shown in this chart. Only 31 of the 357 bond issues had a better spread to default probability ratio than the best bond issued by Wells Fargo & Company. The longest maturity Wells Fargo & Company bonds that were heavily traded ranked from 64th to 107th, very solidly in the best one-third of all bond issues traded on May 19 when ranked by our “best value” formula.

Credit-Adjusted Dividend Yield Analysis
Today on, the key financial ratios for Wells Fargo & Company were summarized in this table: 

The real time update of the table is readily available to the curious reader. What is the “yield” on Wells Fargo & Company common stock? It is simply four times the quarterly dividend rate on the stock ($0.35) divided by the current stock price ($48.98), or 4x0.35/48.98 which is 2.86% (note the SeekingAlpha figure is different because of a time lag in updating the website). There is nothing wrong with this calculation, but it is a simple calculation that makes a number of implicit assumptions that we know are false:

  • That the dividend will not change in perpetuity, continuing as a quarterly payment of $0.35 forever. That is, the dividend will not be increased, decreased, or eliminated.
  • That Wells Fargo & Company will never go bankrupt.
  • That no adjustment for the risk of bankruptcy is useful in understanding the risk and return on the common stock.

The dividend yield calculation is mathematically identical to the yield on a consol or perpetual bond. For background on such calculations, see Chapter 4 of Advanced Financial Risk Management.
In the bond market, the idea that an investor should ignore the credit risk of a promise to pay would evoke laughter in trading rooms across the world’s financial capitals. We incorporate an evaluation of Wells Fargo & Company’s forecast (not promise) to pay a dividend using insights from today’s bond market analysis.

Credit Spreads and the Value of a Promise to Pay $1
What is the value of a promise by Wells Fargo & Company to pay $1 at a future date to a bond investor? We use the bond data above to derive the value today of a forecast (explicit, like an announced dividend, or implicit, like the assumption the dividend will be paid in perpetuity) by Wells Fargo & Company to pay $1 dollar (or $0.35, or some other amount) at a date in the future. We remind readers that dividends go up, and dividends go down. The Wells Fargo & Company website documents the company’s dividend history nicely. To keep today’s analysis simple, we assume that management intends to pay a dividend of $0.35 each quarter forever unless bankruptcy makes that impossible.

To calculate the present value of the forecast to pay $0.35 each quarter in the future, we need the present value of a $1 to be paid on any future date that reflects the credit risk of Wells Fargo & Company. The bond market provides a ready source of such data. We recognize that a dividend can be cut without triggering bankruptcy, so the dividend risk facing common shareholders is higher than the coupon risk facing bond holders. We ignore this difference in risk as a first approximation in calculating a credit-adjusted dividend yield.

We get the present value factors (“zero coupon bond prices”) by following these steps:

  • Smooth the U.S. Treasury curve as in the weekly Kamakura Corporation interest rate analysis to get the present value factors for a promise to pay by the U.S. Treasury
  • Calculate the risk premium in a promise to pay by Wells Fargo & Company that minimizes the errors in estimated bond prices using the 23 traded bonds above.

This chart shows the best fitting “zero coupon bond yields” for Wells Fargo & Company on May 19, 2014. The accuracy in fitting bond prices was 98.49% (adjusted r-squared of a non-linear regression).

We can calculate the present value factors from these continuously compounded yields using a spreadsheet-friendly formula in Chapter 4 of Advanced Financial Risk Management. This allows us to calculate the present value, over various time horizons, of the “constant dividend forecast” by Wells Fargo & Company. We show the first twelve months of that calculation in this table:

The present value of a forecasted payment by Wells Fargo & Company of $0.35 in 3 months (we ignore the June 1 dividend), 6 months, 9 months and 12 months is the sum of the 4 present values in the right hand column. We calculate the present value of such payments for 10 years ahead and for 30 years ahead. We then can ask this question: what constant quarterly amount, if promised by the U.S. Treasury, has the same present value as the one year present value of Wells Fargo & Company dividends? The answer is $0.34922. This figure is the credit-adjusted dividend payment by Wells Fargo & Company. If we multiply by 4 and divide by the $48.98 stock price, we get a 1 year credit-adjusted dividend yield of 2.85193%. This isn’t much different from the standard dividend yield, but the difference becomes very large as we extend the time horizon. The credit-adjusted dividend for a 10 year horizon is $0.33696 and for a 30 year horizon it is $0.30170. The 10 year credit-adjusted dividend yield is 2.75% and the 30 year credit-adjusted dividend yield is 2.46%, a full 0.40% below the nominal dividend yield. Why does the credit-adjusted dividend yield vary by maturity? For the same reason bond yields vary by maturity: the time value of money and the default risk over that horizon are very important.

The gaps between the nominal dividend yield and the long-term credit adjusted dividend yields can be very large for highly troubled companies. Imagine the gap for Lehman Brothers on September 12, 2008. Equity investors have been ignoring the data used by bond investors to evaluate a similar set of promises to pay, one promise called a dividend and one called interest or principal. The credit-adjusted dividend yield helps to close the information gap between bond investors and common stock investors, and we highly recommend the calculation to serious investors.

Credit Default Swap Analysis
The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name. For the week ended May 9, 2014 (the most recent week for which data is available), the credit default swap trading volume on Wells Fargo & Company showed 206 contracts trading with a notional principal of $1.9 billion. This is a heavy trading volume for a reference name of Wells Fargo & Company’s fine credit quality.

The notional principal traded weekly on Wells Fargo & Company credit default swaps since the DTCC began weekly reporting is shown here: 

The number of credit default swap contracts traded on Wells Fargo & Company over the same period is shown in this histogram:

Additional Analysis
On a cumulative basis, the default probabilities for Wells Fargo & Company have decreased slightly from our October report. The current cumulative default probabilities, shown in green, range from 0.01% at 1 year to 0.82% at 10 years, down 0.14% from our October 18 report. Cumulative default probabilities as of October are shown in yellow. 

Over the last 10 years, the 1 year and 5 year default probabilities for Wells Fargo & Company have varied as shown in the following graph. The one year default probability peaked at over 9.00% and the 5 year default probability peaked just short of 3.00% in the first half of 2009 after the Wells Fargo takeover of Wachovia. Wachovia’s peak borrowings from the Federal Reserve were $36.0 billion on October 6, 2008, four days before its acquisition by Wells Fargo became effective. A Kamakura Corporation report documents these borrowings on a daily basis and the time line leading up to the Wells Fargo acquisition.

The macro-economic factors driving the historical movements in the default probabilities of Wells Fargo & Company over the period from 1990 to the present include 4 factors of the 28 factors listed by the Federal Reserve in its 2014 Comprehensive Capital Analysis and Review. These macro factors explain 61.5% of the variation in the default probability of Wells Fargo & Company since 1990. The remaining variation in default probabilities represents the idiosyncratic risk of the firm.

Wells Fargo & Company can be compared with its peers in the same industry sector, as defined by Morgan Stanley and reported by Compustat. For the USA banking sector, Wells Fargo & Company has the following percentile ranking for its default probabilities among its 636 peers at these maturities: 

1 month      39th percentile, down 35 percentage points from October
1 year           7th percentile, down 24 percentage points
3 years         3rd percentile, down 5 percentage points
5 years         4th percentile, down 2
10 years       4th percentile, down 1

The relative ranking of Wells Fargo & Company has improved dramatically even though the change in default probabilities was relatively modest since October. The high 1 month ranking is due simply to the very good near-term prospects for the banking industry generally, with nearly all banking firms showing very low short term default risk. Kamakura Corporation reported today that corporate credit conditions are at an all-time record for “best” credit quality .

Over the same decade, the legacy credit ratings, those reported by credit rating agencies like McGraw-Hill (MHP) unit Standard & Poor’s and Moody’s (MCO), for Wells Fargo & Company have changed five times. A comparison of the legacy credit rating for Wells Fargo & Company with predicted ratings indicates that the company is overrated by two ratings grades. Both the actual legacy rating and the predicted legacy rating are solidly in the traditional ratings-based “investment grade” range.

Is Wells Fargo & Company an investment grade company by the modern Dodd Frank Act definition? We let the market speak on that issue. The first graph below compares the traded credit spreads with all credit spreads on bonds traded on May 19 by firms in the “banks/finance” peer group.

Wells Fargo & Company clearly trades in the safer half of the peer group. The next graph plots Wells Fargo & Company matched-maturity default probabilities versus the same default probabilities for the traded bonds of the peer group:

Again, the default probabilities for Wells Fargo & Company have a favorable comparison with the banking peer group. Next we compare the traded credit spreads of the company to those of firms with a legacy ratings-based “investment grade” rating.

Compared with this peer group as well, Wells Fargo & Company credit spreads are much tighter than average. Lastly, we compare the matched-maturity default probabilities for Wells Fargo & Company with the matched-maturity default probabilities for the investment grade peer group. 

Wells Fargo & Company, other than the period immediately after the acquisition of Wachovia, has experienced very strong default probability levels for the last decade. At a 10 year horizon, the firm is in the top 4 percent of the USA banking sector in credit quality. At current default probability levels, we continue to believe that almost all sophisticated analysts would rate Wells Fargo & Company as investment grade by the Comptroller of the Currency definition. On a credit-adjusted basis, Wells Fargo & Company’s credit-adjusted dividend yield is 2.46%, 0.40% below the traditional yield calculation, 2.86%. Credit default swap trading volume has been heavy lately, but the firm’s bonds continue to trade in the top third, by value, of all heavily traded bonds.

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.