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. All other things being equal, maximizing the ratio of credit spread to the matched maturity default probability will achieve this objective. In this note, we analyze the current levels and past history of default probabilities for Bank of America (NYSE:BAC). As part of this analysis, we 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. On its web page the OCC states, "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." 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 first graph shows the current default probabilities for Bank of America ranging from one month to 10 years on an annualized basis.

We explain the source and methodology for the default probabilities below. On a cumulative basis, the default probabilities for Bank of America range from 0.18% at 1 year to 4.75% at 10 years.

Over the last 10 years, the 1 year and 5 year default probabilities for Bank of America have varied as shown in the following graph.

Over the same period, the legacy credit ratings for Bank of America have changed six times.

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

- U.S. Treasury 3 month bill rate
- U.S. Treasury 10 year yield
- BBB-rated corporate bond yields
- Level of the Dow Jones Index
- VIX volatility index
- Level of home prices
- 6 international risk factors

Jointly, these factors explained 89.4% of the variation in the firm's 1 year default probability. Bank of America can be compared with its peers in the same industry sector. For the US diversified financials sector, Bank of America has the following percentile ranking (100 indicates highest default probability) for its default probabilities among its peers at these maturities:

1 month 89th percentile

1 year 82nd percentile

3 years 77th percentile

5 years 70th percentile

10 years 66th percentile

A comparison of the legacy credit rating for Bank of America indicates that the company is overrated by 2 ratings grades, based on the best statistical predictors of legacy credit ratings based on 263,000 observations of ratings, default probabilities and other company attributes from 1990 to the present.

**Conclusion**

Bank of America ranks in the riskiest half of US diversified financials at all maturities from one month to ten years. Bank of America's default probabilities have declined very substantially from the levels at the worst part of the financial crisis, however. Most investment professionals, using the current default probability levels and macro-factor sensitivity for Bank of America, would indicate that the company is "investment grade" by the definition of the Comptroller of the Currency given above.

**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 probabilities 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.