The telecom sector world-wide has seen enormous disruption as new service providers challenge the former monopolies of land-line-based providers of telecommunications services. In recent notes, we have highlighted the bonds of Verizon Communications Inc. (NYSE:VZ) and Sprint Corporation (NYSE:S), which has seen a major investment from SoftBank (OTCPK:SFTBF)(OTCPK:SFTBY) of Japan and a significant drop in default probabilities upon announcement of a new distribution agreement with Costco (NASDAQ:COST). In this note, we focus on Telecom Italia S.p.A. (NYSE:TI.A), which has seen more volatility in its credit quality in recent years than the vast maturity of telecommunications firms. Telecom Italia issues bonds in the U.S. market via Telecom Italia Capital S.A. Bonds issued by Telecom Italia Capital S.A. have a guaranty from parent Telecom Italia. Telecom Italia, through its subsidiary TIM Brasil, also has a controlling interest in Brazilian public telecommunications firm TIM Participacoes S.A.

This note uses the default probabilities and bond spreads of Telecom Italia Capital S.A. to measure the relative reward-to-risk ratio on the bonds of the Telecom Italia group. Today's study incorporates Telecom Italia Capital S.A. bond price data as of September 18, 2013. A total of 158 trades were reported on 9 fixed-rate non-call bond issues of Telecom Italia Capital S.A. with trading volume of $63.5 million. All of this data was used in this study.

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 Telecom Italia Capital S.A. 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 Telecom Italia Capital S.A.

**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 Telecom Italia S.p.A., the guarantor, 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 10.24% at one month to 18.17% at 1 year and 30.70% at ten years. These default probabilities are dramatically higher than the default probabilities reported in any other bond analysis done in this series so far. Even Brazilian affiliate TIM Participacoes S.A. has much lower default probabilities. We explain why below.

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 the bond data mentioned above for the 9 Telecom Italia Capital S.A. fixed rate non-call bond issues mentioned above.

The graph below shows 5 different yield curves that are relevant to a risk and return analysis of Telecom Italia Capital S.A. 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 Telecom Italia Capital S.A. The highest 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 Telecom Italia Capital S.A. bonds. The green line displays the average yield reported by TRACE on the same day. The highest yield, the red line, is the maximum yield in each Telecom Italia Capital S.A. issue recorded by TRACE.

Telecom Italia is an extreme case of the phenomenon we first saw with Sprint: credit spreads are well below the best estimates of the annualized default probability of the issuer. This unusual negative liquidity premium built into the yields of Telecom Italia Capital S.A. generally widens as the maturity of the underlying bonds increases. We explain the reasons for this phenomenon below.

The high, low and average credit spreads at each maturity are graphed below. We see credit spreads are generally increasing with the maturity of the bonds. 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. This polynomial explains 96.84% of the variation in the average credit spread over the maturity term structure:

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. This ratio of spread to default probability is shown in the following table for Telecom Italia Capital S.A. It will astonish many readers to see that the credit spread is only 10-20% of the annualized default probabilities for the parent, Telecom Italia. In a rational world, there can be only two possible reasons for this phenomenon. The first and most obvious is potential model risk. We analyze the reasons for the very high default probabilities for Telecom Italia below and find it unlikely that the default probabilities contain a significant error. The second possibility, which we have seen in the credit crisis experience of Citigroup (C) and Fannie Mae (OTCQB:FNMA), is that the prices of senior bonds contain a premium due to the possibility of a government rescue if the company were to fail. This is exactly what happened in the cases of Citigroup and Fannie Mae. The Kamakura default probabilities are the probability of failure. The probability of a rescue is an exercise in politics that we ignore from an analytical perspective because only direct participants in such rescue discussions have the relevant information on the rescue probability. The ratio of credit spread to default probability for Telecom Italia Capital S.A. is given here:

The credit spread to default probability ratios are shown in graphic form here. We have again added a cubic polynomial relating the credit spread to default probability ratio to the years to maturity on the underlying bonds. The smoothed line explains 50.5% of the variation in the reward to risk ratio. Note again that the credit spread is just a fraction of the annualized default probability.

The Depository Trust & Clearing Corporation reports weekly on new credit default swap trading volume by reference name. For the week ended September 13, 2013 (the most recent week for which data is available), the credit default swap trading volume on Telecom Italia S.p.A., the parent, was 91 trades with $537 million of notional principal. Telecom Italia was one of the 40 most heavily traded names in the CDS marketplace. The number of credit default swap contracts traded on Telecom Italia Capital S.A. in the 155 weeks ended June 28, 2013 is summarized in the following table:

Telecom Italia S.p.A. ranked 28th among all reference names in weekly credit default swap trading volume during this period, which is graphed below:

On a cumulative basis, the default probabilities for Telecom Italia Capital S.A. range from 18.17% at 1 year to 97.45% at 10 years, a very high number, which highlights the need for a dramatic restructuring of Telecom Italia S.p.A.'s financial structure.

Why are the default probabilities for Telecom Italia S.p.A. so high? As explained in the last part of this note, the default probabilities are derived on a data base with more than 1.76 million observations and more than 2,000 defaulters since 1990. The chart below helps explain why Telecom Italia S.p.A. has much higher risk than Verizon:

Telecom Italia has a smaller size, in terms of market capitalization, than Verizon, which increases default risk. Telecom Italia has dramatically higher market leverage (as of June 30, before the recent Verizon bond issue) than Verizon, which is a big factor in the difference in default risk. By two measures, Telecom Italia is much less profitable than Verizon, which is another negative from a default probability perspective. The volatility of Telecom Italia common stock is much higher than the volatility for Verizon, another driver of higher credit risk. Finally, from an excess return and stock price level perspective, Telecom Italia is in much riskier territory than Verizon. Another comparison can be made with the listed Brazilian affiliate TIM Participacoes S.A., which has 1 year default probabilities of only 0.18% today. We show the same chart for the reader's convenience:

Looking at historical movements in Telecom Italia S.p.A. default probabilities, large losses have been a significant contributor to the spike in default probabilities. Note that "KDP" in the following charts means "Kamakura Default Probability":

Negative excess returns compared with the stock index for Italy have persisted for more than a year, with the best point of comparison at about -15% excess return and with much of the period showing excess returns of -40%.

Over the last decade, the 1 year and 5 year default probabilities for Telecom Italia Capital S.A. have been very volatile. The 1 year default probability peaked just short of 50% near the heart of the credit crisis. The five year default probability peaked recently at just over 30%.

TIM Participacoes S.A., the majority-owned Brazilian affiliate, by contrast, had a major spike in default probabilities in 2008-2009 but default probabilities have fallen steadily for the reasons that are apparent in the risk driver screens above.

In contrast to the daily movements in default probabilities graphed above, the legacy credit ratings [those reported by credit rating agencies like McGraw-Hill (MHFI) unit Standard & Poor's and Moody's (NYSE:MCO)] for Telecom Italia Capital S.A. have changed only twice during the decade, more slowly than the median 815 days since the last rating change for rated companies found in a recent study by Kamakura Corporation.

The macro-economic factors driving the historical movements in the default probabilities of Telecom Italia S.p.A. 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 Telecom Italia Capital S.A. default risk responds to changes in five European risk factors, one international factor, and the 10 year U.S. Treasury yield among those listed by the Federal Reserve in its 2013 Comprehensive Capital Analysis and Review. These macro factors explain 80.2% of the variation in the default probability of Telecom Italia Capital S.A.

Telecom Italia Capital S.A. can be compared with its peers in the same industry sector, as defined by Morgan Stanley (NYSE:MS) and reported by Compustat. For the euro area "telecom services" sector, Telecom Italia Capital S.A. has the following percentile ranking for its default probabilities among its 56 peers at these maturities:

1 month 98th percentile (the highest firm)

1 year 98th percentile (the highest firm)

3 years 96th percentile (the second highest firm)

5 years 98th percentile (the highest firm)

10 years 93rd percentile

The percentile ranking of Telecom Italia Capital S.A. default probabilities were higher than any other peer group company at 1 month, 1 year and 5 year maturities. For the 3 year maturity, the company was the second riskiest firm. Taking still another view, the actual and statistically predicted Telecom Italia Capital S.A. credit ratings show a split decision on "investment grade." The statistically predicted rating is two notches below the legacy rating. The statistically predicted rating is firmly in the non-investment grade category. The legacy credit rating is a borderline investment grade rating. Legacy credit ratings typically include a guess as to the probability of a rescue for firms for which a rescue is a non-zero possibility.

**Conclusions**

We believe the overwhelming majority of analysts would rate Telecom Italia Capital S.A. as non-investment grade. Telecom Italia Capital S.A. bond prices reflect a premium attributable to the probability of a rescue or a takeover just prior to default. From the perspective of a small institutional investor or a retail investor, knowledge of a takeover or rescue will be known to a few but not to you until such news becomes 100% public. The risk-return trade-off on Telecom Italia Capital S.A. bonds is highly unfavorable, and we don't see that changing without a return to dramatically better profitability, a tender offer, or a major restructuring like the sale of the stake in TIM Participacoes S.A.

**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.

**Additional disclosure:** Kamakura Corporation has business relationships with a number of firms mentioned in this article.