Tuesday, June 23, 2009

Put Options and Capital Adequacy, Evidence from the Options Market

Posted on RiskCenter by Donald R. van Deventer:

How much capital do four major bank holding companies need to be sure that their current market capitalization can be maintained through January 2011? This simple question was addressed by bank regulators in the U.S. using “stress tests” on the 19 largest bank holding companies in an intensive process between February and April 2009. Here we use public information from the options market for bank holding company common stock to get the same information in the view of market participants. We compare the results to the ranking of 4 of the 19 largest bank holding companies by ratings, by Kamakura default probabilities, and by the financing indicated by government stress tests as a percent of total assets.

In our blog post of May 7, 2009 (“Comparing Fed-Mandated Capital Needs with Default Probabilities and Ratings“), we showed that Kamakura Risk Information Services default probabilities had a much higher degree of consistency with stress-test-related capital needs than agency ratings. That small studied covered all 19 bank holding companies subject to the stress tests. Here, on a subset of that group, we add the insights on the subject of capital adequacy implied by put prices traded the bank holding companies’ common stock. We selected four companies from the group of 19 firms stress tested: American Express, Suntrust, Bank of America, and Wells Fargo. For each of the four firms, we compare stress test capital needs as a percent of assets, Standard & Poor’s rating, and default probabilities (“KDP” for Kamakura default probabilities) for 1 and 2 year maturities from the Kamakura Risk Information Services version 4.1 reduced form model.

Bank Holding Company Name

Ticker Symbol

Indicated Stress Test Capital Needs ($ billions)

Stress Test as Percent of Assets

1 year KDP, JC4, June 18, 2009

2 year KDP, jc4, June 18, 2009

Rating, June 18, 2009

Ratings Numerical Value

American Express Co.

axp

0.0

0.00%

0.05%

0.34%

BBB+

8

Wells Fargo & Co.

wfc

13.7

1.05%

0.11%

0.59%

AA-

4

Bank of America Corporation

bac

33.9

1.86%

0.58%

1.61%

A

6

SunTrust Banks Inc.

sti

2.2

1.16%

0.36%

1.22%

BBB+

8

To this information, we add information from the market for common stock and put options on common stock. As we discussed in our blog post on May 13, 2009 (“Brother, Can You Spare a Dime or a Dollar? VAR versus the Put Option for Capital Allocation”), both Robert Jarrow and Robert C. Merton have argued that put prices are the best single indicator of total risk that a company possesses. The measure we seek to employ is the longest maturity put option price at a strike price equal to current common stock price, displayed as a percentage of the current stock price. This measure ensures that capital at the longest available put maturity will always be at the current market capitalization or greater. Barring any moral hazard prohibitions, this strategy could conceptually be implemented in the following way. First, calculate the cost of put options on all common shares outstanding at current market price, representing a total current market capitalization of $Y. We label the cost of the put options as amount $X. The bank holding company then issues enough additional common shares to buy put options on the original shares (which would have cost $X) and the new shares issued. The new shares represent additional market capitalization of $X and put options on them will cost $X times ($X/$Y). We compare the risk levels of these four bank holding companies by measuring the ratio of the cost of the put to the underlying common stock price at current market levels.

On June 19, the longest maturity put prices observable in the market place mature in January 2011, by coincidence spanning exactly the 2009-2010 period covered by government stress tests. Put prices are traded at “even” strike prices so we look at the nearest strike price above and below current common stock prices for all four firms. The common stock prices, put bid and offered prices, and calculated mid-market prices for the strike price immediately below the stock price is as follows:

Bank Holding Company Name

Stock Price, June 19, 2009

Lower Bound Put Strike Price

Lower Bound Bid Price

Lower Bound Offered Price

Lower Bound Mid-Market Price

American Express Co.

24.18

22.50

5.20

5.50

5.35

Wells Fargo & Co.

23.56

22.50

6.30

6.50

6.40

Bank of America Corporation

12.83

12.50

3.65

3.70

3.68

SunTrust Banks Inc.

15.61

15.00

4.50

5.00

4.75

The nearest strike price immediately above the current stock price, along with bid, offered, and mid-market prices, are given below:

Bank Holding Company Name

Stock Price, June 19, 2009

Upper Bond Put Strike Price

Upper Bound Bid Price

Upper Bound Offered Price

Upper Bound Mid-Market Price

American Express Co.

24.18

25.00

6.50

6.80

6.65

Wells Fargo & Co.

23.56

25.00

7.70

7.90

7.80

Bank of America Corporation

12.83

15.00

5.20

5.30

5.25

SunTrust Banks Inc.

15.61

17.50

5.90

6.60

6.25

Instead of invoking a “volatility smile” for estimating the price of a put option with a strike price exactly at market (an implicit admission that the Black-Scholes put model is mis-specified), we do a simple linear interpolation of the put prices from the “even” strike prices above and below the current market price. The interpolated put prices and their ratios to current stock price are given in this table:

Bank Holding Company Name

Stock Price, June 19, 2009

Interpolated Put Cost with Strike at Market Price

Interpolated Put Price as Percent of Market Price

American Express Co.

24.18

6.22

25.74%

Wells Fargo & Co.

23.56

6.99

29.68%

Bank of America Corporation

12.83

3.88

30.26%

SunTrust Banks Inc.

15.61

5.12

32.77%

The table shows that American Express has less total risk than the other three firms, because the cost of insuring that market capitalization (in terms of today’s stock price) stays at or above current market levels is a smaller percentage of current market capitalization (25.74%, calculated as the put price/common stock price) than it is for the other three firms. SunTrust, by the Merton-Jarrow risk index, is the riskiest with a ratio of put price to stock price of 32.77% for a January 2011 maturity.

How does this result, which takes about 5 minutes to calculate for each bank, compare with ratings, KRIS default probabilities, and government mandated stress tests? The table below shows the correlations between each of these risk indices for our small sample of banks: In calculating correlation, we converted ratings to an ordinal number with AAA as 1, AA+ as 2, and so on.


Put as Percent of Market

1 Year KDP

2 Year KDP

Stress Test as Percent of Assets

Ratings

Put as Percent of Market

100.0%

62.4%

71.5%

73.8%

-9.4%

1 Year KDP

62.4%

100.0%

99.2%

88.0%

3.6%

2 Year KDP

71.5%

99.2%

100.0%

90.3%

1.8%

Stress Test as Percent of Assets

73.8%

88.0%

90.3%

100.0%

-40.8%

Ratings

-9.4%

3.6%

1.8%

-40.8%

100.0%

The put price ratio had a 73.8% correlation with government-mandated stress tests, compared with an 88% and 90% correlation with stress test results for the 1 year and 2 year Kamakura default probabilities (“KDP”). Ratings, by contrast, on this small sample had a negative correlation of 40.8% with government stress test results when one would have expected a strongly positive correlation.

The purpose of this post is to show that the put option approach to risk assessment is practical, fast, and highly accurate when compared either to government mandated stress test results or Kamakura default probabilities. On this small sample, the same could not be said for agency ratings.

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