In this note we analyze the current levels and past history of default probabilities for Dell Inc. (NASDAQ:DELL) and we compare those default probabilities to credit spreads on 292 bond trades in 8 different bond issues on July 22, 2013. Trading volume in Dell Inc. bonds on that day totaled $37.3 million. 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 Dell Inc. We also consider whether or not a reasonable investor would judge the firm to be "investment grade" under the June 2012 rules mandated by the Dodd-Frank Act of 2010.

## Definition of Investment Grade

On June 13, 2012, the Office of the Comptroller of the Currency published the final rules defining whether a security is "investment grade," in accordance with Section 939A of the Dodd-Frank Act of 2010. The new rules delete reference to legacy credit ratings and replace them with default probabilities. The web page explaining the Office of the Comptroller of the Currency's new rules defining investment grade and related guidance can be found here.

## 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 Dell Inc. ranging from one month to 10 years on an annualized basis. The default probabilities range from 0.36% at one month to 0.17% at 1 year and 0.78% at ten years.

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. TRACE data for Dell Inc. included 301 trades in the bonds of the firm on July 22, 2013. After eliminating data errors, 292 trades were analyzed on 8 different bond issues.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Dell Inc. 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 Dell Inc. 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 Dell Inc. bonds. The fourth line from the bottom (in green) displays the average yield reported by TRACE on the same day. The highest yield is obviously the maximum yield in each Dell Inc. issue recorded by TRACE.

The data makes it very clear that there is a very large liquidity premium built into the yields of Dell Inc. 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 and average credit spread at each maturity are graphed below. While there is a fair amount of volatility in spread prevailing on the longer 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 Dell Inc. At all maturities, the reward from holding the bonds of Dell Inc., relative to the matched maturity default probability, is at least 4 basis points of credit spread reward for every basis point of default risk incurred. The ratio of spread to default probability generally declines as the maturity of the bonds lengthens.

The next graph plots the ratio of credit spread to default probability at each maturity.

For Dell Inc., the spread/default probability ratios are highest for maturities under three years. The reward for bearing a basis point of default risk declines from levels of 10-16 times to ratios generally in the 4 to 8 times default risk range.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name. For the week ended July 12, 2013 (the most recent week for which data is available), the credit default swap trading volume on Dell Inc. showed 68 contracts trading with a notional principal of $390.6 million. The next graph shows the weekly number of credit default swaps traded on Dell Inc. in the 155 weeks ended June 28, 2013.

The table below summarizes the volatile nature of credit default swap trading in Dell Inc. during this three year period.

On a cumulative basis, the default probabilities for Dell Inc. range from 0.17% at 1 year to 7.52% at 10 years, as shown in the following graph.

Over the last 10 years, the 1 year and 5 year default probabilities for Dell Inc. have varied as shown in the following graph. The one year default probability peaked at just under 1.40% and the 5 year default probability peaked just short of 0.60% in the first half of 2009 at the peak of the credit crisis.

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 (NYSE:MCO)) for Dell Inc. have changed once since the company was first rated in 2012.

The macro-economic factors driving the historical movements in the default probabilities of Dell Inc. over the period from 1990 to the present include the following factors of those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review:

- BBB-rated corporate bond yields
- 30 year fixed rate mortgage yields
- The Dow Jones Industrials stock price index
- Commercial real estate price index
- 5 international macro factors

These macro factors explain 74.9% of the variation in the default probability of Dell Inc. since 1990.

Dell Inc. can be compared with its peers in the same industry sector, as defined by Morgan Stanley and reported by Compustat. For the US technology, hardware and equipment sector, Dell Inc. has the following percentile ranking for its default probabilities among its peers at these maturities:

1 month 83rd percentile

1 year 65th percentile

3 years 47th percentile

5 years 35th percentile

10 years 31st percentile

Dell Inc. is in the bottom half of creditworthiness among its peers for maturities of one year or less. Dell Inc. ranks in the 2nd quartile by riskiness for maturities from 3 to 10 years. A comparison of the legacy credit rating for Dell Inc. with predicted ratings indicates that the company is rated equally by both statistical means and by legacy credit rating agencies.

## Conclusions

Dell Inc. has experienced fairly minimal variation in its default probabilities over the last decade, particularly in comparison with financial institutions. Current default probabilities are fairly high, however, and they reflect both an increased risk of a more aggressive capital structure and a substantial upheaval in Dell's core markets. At current default probability levels, we believe that a majority sophisticated analysts would rate Dell Inc. as investment grade by the Comptroller of the Currency definition, but it would be ranked near the bottom of the investment grade range.

## 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.