Warren Buffett, called by many "America's greatest investor," celebrated his 83rd birthday on August 30, 2013. Mr. Buffett's primary investment vehicle is, of course, Berkshire Hathaway Inc. [(NYSE:BRK.A) (NYSE:BRK.B)], which often issues debt through affiliate Berkshire Hathaway Finance Corporation. The latter firm is the beneficiary of a guarantee from Berkshire Hathaway Inc. This note focuses on the risk and return on the bonds of Berkshire Hathaway Inc. and Berkshire Hathaway Finance Corporation to derive the bond market's perspective on the future for Berkshire Hathaway Inc. and its iconic leader Mr. Buffett. We are pleased to report that the bond market has fully priced in another miraculous out-performance by Mr. Buffett. It is clear that the bond market is forecasting Mr. Buffett will out-live the longest maturity bond issued by both Berkshire Hathaway Inc. and Berkshire Hathaway Finance Corporation to celebrate his 112th birthday on August 30, 2042.

Today's note incorporates Berkshire Hathaway Inc. and Berkshire Hathaway Finance Corporation bond price data as of September 27, 2013. A total of 86 trades were reported on 9 fixed-rate non-call bond issues of Berkshire Hathaway Inc. with trading volume of $51.3 million. We used all of the data in this study, along with 95 trades on 13 bond issues worth $35.0 million of Berkshire Hathaway Finance Corporation. We report on both legally entities separately, avoiding the occasionally dangerous assumption that they are independent from a default risk perspective.

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 Berkshire Hathaway Inc. 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. The new rules delete references to legacy credit ratings and replace them with default probabilities as explained here.

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 Berkshire Hathaway Inc.

**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 Berkshire Hathaway Inc. 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 0.00% at one month (0.00063% before rounding) to 0.00% at 1 year (0.00054% before rounding) and 0.04% at ten years. The 10-year default probability is 22nd lowest among 2,458 rated firms world-wide.

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 all 22 of the bond issues mentioned above in this analysis, including bonds issued by Berkshire Hathaway Inc. and Berkshire Hathaway Finance Corporation.

The graph below shows 5 different yield "curves" that are relevant to a risk and return analysis of Berkshire Hathaway Inc. 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 Berkshire Hathaway Inc. 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 Berkshire Hathaway Inc. bonds. The green line displays the average yield reported by TRACE on the same day. The red line is the maximum yield in each Berkshire Hathaway Inc. issue recorded by TRACE.

The graph shows an increasing "liquidity premium" as maturity lengthens for the bonds of Berkshire Hathaway Inc. This is a pattern seen usually with firms of high credit quality. We explore this premium in detail below.

Berkshire Hathaway Finance Corporation bonds exhibit a similar pattern:

The weighted average yields of both Berkshire Hathaway Inc. and Berkshire Hathaway Finance Corporation can be plotted jointly. The graph below shows the bond yields of the two firms are nearly indistinguishable:

The high, low and average credit spreads at each maturity are graphed below for Berkshire Hathaway Inc. 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 96.96% of the variation in credit spreads over the maturity spectrum.

Berkshire Hathaway Finance Corporation credit spreads show the same pattern, with 92.85% of variation explained by the fitted polynomial:

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 Berkshire Hathaway Inc., the credit spread to default probability ratio ranges from 26 times to 467 times, an exceptionally high reward-to-risk ratio. The long-term reward-to-risk ratios are in the 26 to 34 range. The ratios of spread to default probability for all traded bond issues are shown here:

Berkshire Hathaway Finance Corporation credit spreads to default probability ratios are just as attractive:

The credit spread to default probability ratios are shown in graphic form below for Berkshire Hathaway Inc. The fitted polynomial explains 94.99% of the variation in the reward-to-risk ratios by maturity.

Berkshire Hathaway Finance Corporation reward-to-risk ratios are plotted in this graph:

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name. For the week ended September 20, 2013 (the most recent week for which data is available), the credit default swap trading volume on Berkshire Hathaway Inc. was 76 trades for $576 million. This volume, which is quite high for a high quality credit, ranks 102nd of 858 reference names traded. This is a much higher trading volume than in the U.S. bond market, and that differential is often a sign of a divergence of opinion on the outlook for that reference name. The number of credit default swap contracts traded on Berkshire Hathaway Inc. in the 155 weeks ended June 28, 2013 is summarized in the following chart. Berkshire Hathaway Inc. is one of the more heavily traded names in the world, with a rank of 135th.

The weekly volume of credit default swaps traded for Berkshire Hathaway Inc. is summarized in this graph:

On a cumulative basis, the default probabilities for Berkshire Hathaway Inc. range from 0.00% at 1 year (after rounding) to 0.36% at 10 years, a very low level of long-term default risk.

Over the last decade, the 1 year and 5 year default probabilities for Berkshire Hathaway Inc. both peaked in 2008-2009 at less than 0.05%, the lowest peak among the firms analyzed in this series of notes.

In contrast to the daily movements in default probabilities graphed above, we turn to the legacy credit ratings for Berkshire Hathaway Inc., those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor's and Moody's (NYSE:MCO). Over the last decade, the ratings of Berkshire Hathaway Inc. changed twice, the most recent of the two downgrades coming earlier this year. Readers may recall that Berkshire Hathaway was formerly rated AAA.

The macro-economic factors driving the historical movements in the default probabilities of Berkshire Hathaway Inc. 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 Berkshire Hathaway Inc. default risk responds to changes in 3 domestic risk factors and 3 international risk factors among the 26 world-wide macro factors used by the Federal Reserve in its 2013 Comprehensive Capital Assessment and Review stress testing program. These macro factors explain 60.2% of the variation in the default probability of Berkshire Hathaway Inc.

Berkshire Hathaway Inc. can be compared with its peers in the same industry sector, as defined by Morgan Stanley (NYSE:MS) and reported by Compustat. For the USA "insurance sector," Berkshire Hathaway Inc. has the following percentile ranking for its default probabilities among its 117 peers at these maturities:

1 month 9th percentile

1 year 8th percentile

3 years 1st percentile

5 years 1st percentile

10 years 1st percentile

This is one of the best collections of percentile ranks of any firm analyzed so far in this series of bond studies. Taking still another view, the actual and statistically predicted Berkshire Hathaway Inc. credit ratings both show a rating strongly in the "investment grade" territory. The statistically predicted rating is 4 notches below the legacy rating.

**Conclusions**

Sophisticated analysts would be almost unanimous in their assessment of Berkshire Hathaway Inc. as an investment grade company. That being said, the firm is remarkable because of the presence of Mr. Buffett, king of American investors. Without Mr. Buffett, some would argue that Berkshire Hathaway is just another conglomerate without a synergistic strategy. Perhaps a greater concern is the deal-flow that comes to Berkshire Hathaway because of Mr. Buffett's presence. The huge gains from the credit crisis investment in Goldman Sachs (NYSE:GS) are an example of this deal flow that would be hard to attract without Mr. Buffett.

One of the rating agencies was fairly direct in expressing its concern about the "event risk" surrounding Mr. Buffett's ongoing role at Berkshire Hathaway. The bond market's exceptionally optimistic forecast for the company is combined with extremely low default probabilities that again stem from the company's high stock price and returns. At current bond prices and default probabilities, Berkshire Hathaway group bonds offer some of the best value in the bond market in terms of the ratio of credit spread to default probability ratio. This ratio, however, reflects a very optimistic set of stock prices, bond prices, and default probabilities. They imply a very high probability that Mr. Buffett will out-live the 29 year bonds issued by both Berkshire Hathaway Inc. and Berkshire Hathaway Finance Corporation. We hope that this happy event comes about and that bond investors earn the projected rewards.

Hope is not a strategy, however, and we recommend that investors consider the odds that Mr. Buffett is actively involved on a dispassionate basis. One of the best sources of statistics in this regard is the study of King (Harvard University) and Soneji (Dartmouth), "The Future of Death in America," 2011. The graph below gives the probability of living to the next birthday for a male who initially is 83 years old. Again, we hope that Mr. Buffett continues to defy the odds.

**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.

**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. Kamakura Corporation has business relationships with a number of firms mentioned in the article.