Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as Co-Chair, Center for Applied Quantitative Finance, Risk Research and Quantitative Solutions at SAS. Don’s focus at SAS is quantitative finance, credit risk, asset and liability management, and portfolio management for the most sophisticated financial services firms in the world.

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Apple Inc.: The View from the Bond Market

09/25/2013 10:34 AM

This note focuses on the risk and return on the bonds of Apple Inc. (AAPL), another icon of daily life around the world. Today’s note incorporates Apple Inc. bond price data as of September 24, 2013. A total of 240 trades were reported on 5 fixed-rate non-call bond issues of Apple Inc. with trading volume of $130.6 million. After eliminating erroneous data, we used 206 trades representing $127.1 million principal amount on 4 bond issues in this study.  We find a forward-looking risk and return pattern similar to that which we found for Wal-Mart Inc. (WMT), although the history of the two firms couldn’t be more different.

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 Apple 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 Apple 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 Apple 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 (0.00118% before rounding) to 0.00% at 1 year (0.00244% before rounding) and 0.10% at ten years.  These rounded default probabilities are identical to those of Wal-Mart Inc. as of yesterday.

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 but one of the 5 bond issues mentioned above in this analysis.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Apple 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 Apple 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 Apple 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 Apple Inc. issue recorded by TRACE.

The graph shows an increasing “liquidity premium” as maturity lengthens for the bonds of Apple Inc.  We explore this premium in detail below.

The high, low and average credit spreads at each maturity are graphed below.  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.  Because the number of bonds and the number of parameters in a cubic polynomial are the same, we get a perfect fit to Apple Inc. bond spreads:

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.  The credit spread to default probability ratio ranges from nearly 9 times at 2.61 years to almost 12 times at 29.61 years. The ratios of spread to default probability for all traded bond issues is shown here:

The credit spread to default probability ratios are shown in graphic form below. Again, we get a perfect fit of a cubic polynomial to the four bonds for which data is of good quality.

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 Apple Inc. was literally zero.  The number of credit default swap contracts traded on Apple Inc. in the 155 weeks ended June 28, 2013 is also zero.  This fact doesn’t indicate per se that a firm’s default probability is very low.  Instead, it indicates that there is so little difference of opinion on the credit quality of Apple Inc. that no one wants to trade.  For most firms (but not all) with no credit default swap trades during this period, this is a very positive factor.

On a cumulative basis, the default probabilities for Apple Inc. range from 0.00% (after rounding) at 1 year to 0.98% at 10 years, a very small cumulative probability of default just 0.02% higher than that of Wal-Mart Stores Inc. reported yesterday.

Over the last decade, the 1 year and 5 year default probabilities for Apple Inc. have never exceeded 0.25% at any time, even during the heart of the 2006-2011 credit crisis.

Wal-Mart Stores Inc. default probabilities, by contrast, never exceeded 0.14% over the same ten year period.  When default probabilities are plotted back to 1990, one can see clearly that Apple Inc. has gone through some very dangerous times in the past.

Five year default probabilities peaked near 4.50% and the 1 year default probability peaked at more than 3.50% in early 1998.  Why was Apple Inc. at such risk?  Founder Steve Jobs was not with the company, and a major technological shift shook the company to its roots.  The forward looking default probabilities for Apple Inc., which have stock prices as a key input, and the credit spreads for Apple Inc. clearly predict a future for Apple Inc. that is much better than its past, even without Steve Jobs.

In contrast to the daily movements in default probabilities graphed above, we turn to the legacy credit ratings for Apple Inc., those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor’s and Moody’s (MCO). In 2004, Apple Inc. was rated as a “junk” credit by Standard & Poor’s.  Standard & Poor’s affiliate Compustat reports no ratings for Apple Inc. from April, 2004 until April, 2013, when the company was rated just short of AAA. The lack of ratings for most of the decade contrasts with the daily updated default probabilities shown above.

The macro-economic factors driving the historical movements in the default probabilities of Apple 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 Apple Inc. default risk responds to changes in four domestic risk factors and five international risk factors (because of the firm’s world-wide product sourcing) among the 26 factors listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review. These macro factors explain 86.5% of the variation in the default probability of Apple Inc.:

  • Unemployment rate
  • Yield on BBB-rated corporate bonds
  • Dow Jones stock price index
  • Home price index
  • 5 international risk factors

Apple Inc. can be compared with its peers in the same industry sector, as defined by Morgan Stanley (MS) and reported by Compustat.  For the USA “information technology-technology and equipment” sector, Apple Inc. has the following percentile ranking for its default probabilities among its 318 peers at these maturities:

1 month 4th percentile
1 year 4th percentile
3 years 3rd percentile
5 years 0th percentile (lowest)
10 years 0th percentile (lowest)

This is the best collection of percentile ranks of any firm analyzed so far in this series of bond studies. Taking still another view, the actual and statistically predicted Apple Inc. credit ratings both show a rating strongly in “investment grade” territory.  The statistically predicted rating is four notches below the legacy rating.


The default probabilities of Apple Inc. and the percentile ranking of those default probabilities are exceptionally good.  The credit spreads and ratio of credit spreads to default probabilities are also very good and compared to the high value ratios found yesterday for Wal-Mart Inc.  That’s the good news.  Because of this good news, we believe that almost all analysts would rate Apple Inc. as “investment grade.” Is there bad news for Apple Inc.?  A look backwards shows that Apple Inc. had a near-death experience when Steve Jobs departed from the company and when dramatic shifts in technology did not move the company’s way.  Apple Inc. was rated as a junk credit as recently as 2004. Much of the huge recent success that Apple Inc. has experienced is attributable to the touch-screen technology (replacing the mouse and a keyboard with one’s fingers) and Apple’s rapid operating system response to this change in the hardware state of the art.  Will this success continue for the next 30 years as Apple Inc. bond pricing indicates?  That is the key question for investors in Apple Inc.
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.



Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as Co-Chair, Center for Applied Quantitative Finance, Risk Research and Quantitative Solutions at SAS. Don’s focus at SAS is quantitative finance, credit risk, asset and liability management, and portfolio management for the most sophisticated financial services firms in the world.

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