Actual Leverage Ratios and Risk Premiums

The Dragon has previusly commented on misguided interpretations of leverage. Being exceptionally skilled at absent-minded meandering, some data presented itself exactly where we did not look. Specifically, in a paper examining another recent spectacular blow up entitled "Leveraged Municipal Bond Arbitrage, What Went Wrong?" (Deng et al., 2009). They offer the following calculations on a portfolio of long AAA municipal bonds with spreads to after-tax (@ a 35% rate) treasuries of the same maturity:

Our average estimated liquidity risk premium for January 2005 through April 30, 2007 is 74.7 basis points. From January 2005 to April 2007 option costs and average liquidity risk explain 138 basis points of the 147.6 basis points the brokerage firms marketed as an arbitrage opportunity.

That leaves 9.6 basis points to credit risk. So in relation to a financial institution (such as a bank) that is investing in these securities, a guarantor is baring 6.5% of the risk increment of the security above and beyond treasuries. Notably, that percentage gives no consideration to interest rate risk as priced in term premiums. Furthermore, the insurer receives a benefit from the optionality and possible early retirment of its risk rather than the opportunity cost risked by an investor.

All of this naively assumes that risk is accurately priced. Risk itself assures that we essentially always pay too much or too little for an exposure. However even with an exceptional marign of error, the magnitude shown in this example is striking.

Of course, spreads widen with lower grade bonds but that is due not only to increased credit risk but also to increased liquidity risk as those bonds tend to be issued by smaller, less frequent issuers. This is especially true in the municipal market. Lower credits are also less liquid because investors generally require more due diligence to cozy up to a credit. Wide bid-ask spreads and historical default rates suggest that attributing even 25% of AAA-A spread to credit risk is too much, but we will use that number in the example that follows.

For reference, here are the historical default rates published  in the Municipal Bond Fairness Act (HR 6308) (here) (which led to Moody's and Fitch recalibrating) and found on Wikipedia as of April 2011 here.

Cumulative historic default rates (in percent)
------------------------------------------------------------------------
                                        Moody's               S&P
        Rating categories        ---------------------------------------
                                    Muni      Corp      Muni      Corp
------------------------------------------------------------------------
Aaa/AAA.........................      0.00      0.52      0.00      0.60
Aa/AA...........................      0.06      0.52      0.00      1.50
A/A.............................      0.03      1.29      0.23      2.91
Baa/BBB.........................      0.13      4.64      0.32     10.29
Ba/BB...........................      2.65     19.12      1.74     29.93
B/B.............................     11.86     43.34      8.48     53.72
Caa-C/CCC-C.....................     16.58     69.18     44.81     69.19
Investment grade................      0.07      2.09      0.20      4.14
Non-invest grade................      4.29     31.37      7.37     42.35
All.............................      0.10      9.70      0.29     12.98
------------------------------------------------------------------------

Lets take the numbers from Deng et al and combine them with current environment spreads to account for interest rate risk and spreads between AAA and A rated munis. As of 4/19/11, the AAA 20-1 year term spread is about 400 basis points. To the benefit of our detractors, we will normalize that to 250. Also as of 4/19/11, the 20 year A - AAA muni spread is 93 basis points, which we will trust to approximate normal

Please visit this link to see the model:
https://spreadsheets.google.com/ccc?key=0AlFMaAd3v9o0dE9obFlmZWdwaTdlRFh1V1pncU8xaGc&hl=en_GB

The output indicates that 6.7% of the total risk is attributable to credit (note that the earlier 6.5% AAA number did not include term risk in the total risk denominator.) As such, the equivalent of a 10x bank leverage ratio would be a 149x FG leverage ratio. This indicates that threshold leverage ratios suggested by S&P and Fitch are too low for their intended uses.

While not nearly thorough, we contend this example has been balanced and conservative. The rating agencies ought to publish something that very much outdoes this summary investigation before instituting proposed leverage ratios.