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.

Read More



Apple Inc.: An Updated View from the Bond Market

01/21/2014 07:21 AM

This note focuses on an updated risk and return on the bonds of Apple Inc. (AAPL), a consumer product icon like Ford Motor Co. (F), which we analyzed on January 15, 2014. Today’s note incorporates Apple Inc. bond price data as of January 17, 2014.  We compare our results with our prior analysis of Apple Inc. bonds on September 24, 2013. On January 17, a total of 144 trades were reported on 4 fixed-rate non-call bond issues of Apple Inc. with trading volume of $57.9 million.

We find that Apple Inc. offers investors a very rare combination of virtues.  Apple Inc. is an iconic brand name that offers both low default risk and a very strong value proposition, as measured by the ratio of credit spread to matched-maturity default probability.  For example, Apple offers a credit spread to default probability ratio that is nearly 10 times more attractive than the same ratio on Sprint Communications Inc. (S), which we analyzed January 13, 2014.  We explain our conclusions in the rest of this note.

The Reward-to-Risk Ratio and “Investment Grade” Status

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 we explain below.

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 this reward-to-risk 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 (in green) for Apple Inc. ranging from one month to 10 years on an annualized basis. We compare them to the same default probabilities in our prior study on September 24, 2013, shown in yellow. Rounded to the nearest basis point, the default probabilities are only slightly changed. Current default probabilities have dropped slightly since September 24. 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 (0.00104% before rounding) to 0.00% at 1 year (0.00160% before rounding) and 0.10% at ten years.

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 of the 4 bond issues mentioned above in this analysis.

The graph below shows 6 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 dots graph the lowest yield reported by TRACE on that day on Apple Inc. bonds. The green dots display the traded-weighted average yield reported by TRACE on the same day.  The red dots are the maximum yield in each Apple Inc. issue recorded by TRACE. The black dots and connecting line reflect the trade-weighted yield curve constructed by fitting a cubic polynomial to credit spreads, discussed below.

The graph shows an increasing “liquidity premium” as maturity lengthens for the bonds of Apple Inc.  This premium is typical for companies with very strong credit risk.

The high, low, average and trade-weighted fitted 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 traded-weighted 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 5.15 times at 2.29 years to 11.52 times at 29.29 years. The ratios of spread to default probability for all traded bond issues is shown here:

Today’s reward-to-risk ratios are slightly narrower than we reported for September 24, 2013, reproduced in this chart:

The January 17, 2014 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 January 10, 2014 (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 181 weeks ended December 27, 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 current default probabilities for Apple Inc. (shown in green) range from 0.00% (after rounding) at 1 year to 0.96% at 10 years, down 0.02% from September 24, 2013 (shown in yellow).

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.

Prior to 2004, the five year default probabilities for Apple Inc. 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. Those who argue “an iconic company like Apple could never default” have only to look at the history of Apple itself and another icon, Sony, to see that a low default probability is a precious but often fleeting virtue.

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 one domestic risk factor and seven international risk factors (because of the firm’s world-wide product sourcing) among the 28 factors listed by the Federal Reserve in its 2014 Comprehensive Capital Analysis and Review. These macro factors explain 70.4% of the variation in the default probability of Apple Inc.:

    • Unemployment rate
    • 7 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 3rd percentile, down 1 point from September
1 year 3rd percentile, down 1 point from September
3 years 2nd percentile, down 1 point from September
5 years 0th percentile (lowest), unchanged
10 years 0th percentile (lowest), unchanged

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.


Before jumping to conclusions about the “investment grade” status of Apple (a strong temptation), prudence requires us to look at some more data.  We first compare the credit spreads of Apple Inc. with all peers in the “technology media and telecommunications” industry group whose bonds traded on January 17, 2014:

Apple credit spreads were near the bottom of the peer group.

We now examine the default probabilities of the sector peer group whose bonds traded on January 17, 2014.  Again, Apple Inc. shows much lower default risk than the peer group:

Next we turn to credit spreads on bonds traded January 17, 2014 and issued by firms who have a legacy credit rating with the older designation of “investment grade”:

Again, Apple Inc.’s performance versus peers is excellent.  Lastly, we compare the matched-maturity default probabilities for the investment grade peer group as well.

Again, Apple Inc. displays extremely low credit risk compared to the investment grade universe on January 17.

The default probabilities of Apple Inc. and the percentile ranking of those default probabilities are exceptionally good, as they were on September 24, 2013.  The credit spreads and ratio of credit spreads to default probabilities are also very good and offer exceptionally good value even compared to other iconic brand names like AT&T (T), which we reviewed December 17, 2013.  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 recently 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.

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.

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.

Background on the Dodd-Frank Act and the Meaning of “Investment Grade”

Section 939A of the Dodd-Frank Act states the following:


(a) AGENCY REVIEW.—Not later than 1 year after the date of the enactment of this subtitle, each Federal agency shall, to the extent applicable, review—
(1) any regulation issued by such agency that requires the use of an assessment of the credit-worthiness of a security or money market instrument; and
(2) any references to or requirements in such regulations regarding credit ratings.
(b) MODIFICATIONS REQUIRED.—Each such agency shall modify any such regulations identified by the review conducted under subsection (a) to remove any reference to or requirement of reliance on credit ratings and to substitute in such regulations such standard of credit-worthiness as each respective agency shall determine as appropriate for such regulations. In making such determination, such agencies shall seek to establish, to the extent feasible, uniform standards of credit-worthiness for use by each such agency, taking into account the entities regulated by each such agency and the purposes for which such entities would rely on such standards of credit-worthiness.
(c) REPORT.—Upon conclusion of the review required under subsection (a), each Federal agency shall transmit a report to Congress containing a description of any modification of any regulation such agency made pursuant to subsection (b).

The new rules issued by the Office of the Comptroller of the Currency in accordance with Dodd-Frank are described here. The summary provided by the OCC reads as follows:

“In this rulemaking, the OCC has amended the regulatory definition of ‘investment grade’ in 12 CFR 1 and 160 by removing references to credit ratings. Under the revised regulations, to determine whether a security is ‘investment grade,’ banks must determine that the probability of default by the obligor is low and the full and timely repayment of principal and interest is expected. To comply with the new standard, banks may not rely exclusively on external credit ratings, but they may continue to use such ratings as part of their determinations. Consistent with existing rules and guidance, an institution should supplement any consideration of external ratings with due diligence processes and additional analyses that are appropriate for the institution’s risk profile and for the size and complexity of the instrument. In other words, a security rated in the top four rating categories by a nationally recognized statistical rating organization is not automatically deemed to satisfy the revised ‘investment grade’ standard.”



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.

Read More