Bank Risk/Return Tradeoff

By William C. Handorf, Ph.D., Professor of Finance, Banking and Real Estate, George Washington University’s School of Business

Every bank’s management team and board of directors balance risk and return when developing a business plan. The derived mission, goals and objectives attempt to establish value for stakeholders but limit risk to levels that promote viability under a range of adverse economic, competitive and regulatory scenarios. Banks can increase interest income by originating or purchasing high-yielding loans but subsequently face failure if net loan losses sharply exceed the allowances initially established. Institutions might elect to enhance net interest income (NII) by funding high-yield, long-term assets with low-cost, short-term funds and subsequently suffer losses during a period of rising interest rates. Banks can boost share value by leveraging their balance sheets but may later be subject to regulatory restrictions or receivership if losses precipitate a Prompt Corrective Action (PCA) finding of “critically undercapitalized” (by the Federal Deposit Insurance Corporation [FDIC]).

Perspective

Bank panics and failures are endemic in the United States.^{1A Monetary History of the United States, 1867-1960, Milton Friedman and Anna Jacobson Schwartz, 1963, Princeton University Press, Pages 1-860.} Distress is typically associated with a recession, high unemployment or elevated interest rates engineered by a restrictive monetary policy.^{2Manias, Panics, and Crashes: A History of Financial Crises, Charles P. Kindleberger and Robert Z. Aliber, October 4, 2005, Wiley Investment Classics, Fifth Edition, Pages 1-309.} Poor asset/liability management—including high-risk lending, excessively quick asset growth unaccompanied by capital, undue interest-rate repricing gaps and inadequate attention to maintaining sufficient liquidity are especially susceptible to turmoil.^{3Journal of Political Economy: “Bank Runs, Deposit Insurance, and Liquidity,” Douglas W. Diamond and Philip H. Dybvig, June 1983, Volume 91, Number 3, Pages 401-419.} Ultimately, failure can be traced to ineffective risk management and a lack of due care by the board and management.^{4American Banker/BankThink: “Banks Should Reject More Board Candidates,” Richard Parsons, October 19, 2012.}

In our study, we assess the financial performances of 20-plus large banks with operations in the United States over a recent business cycle.

In our study, we assess the financial performances of 20-plus large banks with operations in the United States over a recent business cycle. The institutions comprise approximately two-thirds of the assets of the nation’s 4,500 banks. The empirical analysis focuses on the valuation and perceived risk of each institution. The market rewards banks providing strong profits and above-average growth with a price-to-book (P/B) ratio above one. Moody’s Ratings assigns a baseline credit rating for large banks. The rating represents the likelihood that a bank will meet its financial obligations. The ratings range from “Aaa” (highest quality) to “C” (default with little prospect for recovery of interest or principal). Risk and return are not mutually exclusive. As bankers navigate artificial intelligence (AI), social media, cryptocurrency and shifting regulatory and economic landscapes, the business plan is summarized within pro forma financial statements.

Bank performance and condition

Banks are able to survive turbulent circumstances by generating consistent profits and retaining adequate capital and liquidity. A risk index integrates capital, earnings and risk. Tier 1 leverage capital, average profits over a given period of time and risk originating from poor asset quality, flawed risk management, inadequate liquidity or excessive sensitivity to interest rates form the basis of a risk index. Many internal and regulatory models are complex and opaque. A risk index is readily transparent and complements more advanced models containing numerous algorithms. A risk index, however, is not a substitute for comprehensive analysis.

Risk is captured by a sample standard deviation (ROA Sigma) of earnings over a period of time. A high-risk bank with erratic annual performance retains a high ROA Sigma. Return is measured as the average return on assets (Mean ROA) over the business cycle. A risk index derives the number of standard deviations a bank is from capital declining below a given threshold appliable to Tier 1 leverage capital (equity/assets not risk-weighted assets). Here, we focus on the performance and condition of the largest banks in the US between 2018 and 2024. This period includes the COVID-19 pandemic, a short but severe recession, massive federal fiscal spending, extremely accommodative monetary policy, forbearance and wrenching inflation. A large Swiss bank and three regional US banks failed during the tumult.

Risk Index = [(Tier 1 Capital + Mean ROA – Capital Threshold)/ROA Sigma]

To illustrate, a bank with a Tier 1 Leverage Capital Ratio of 7.00 percent, a Mean ROA of 1.00 percent, a Tier 1 capital threshold of 6.00 percent and a ROA Sigma of 0.50 percent has a risk index of 4.00 [(7.00%+1.00%-6.00%)/0.50%]. A bank can augment its existing equity capital if it is consistently able to generate net income, declares a modest dividend payout, resists aggressive stock-repurchase programs and grows at a rate commensurate with the income retained. Unprofitable banks with low Tier 1 leverage capital and erratic earnings exhibit a low risk index, which can be converted to a probability of incurring a regulatory finding by the application of Chebyshev’s inequality.^{5Probability, Random Variables and Stochastic Processes, Athanasios Papoulis, 1984, McGraw Hill, Second Edition, Pages 149-151.}

The probability of distress equals one-half times one divided by the risk index squared [.5(1/Risk Index²)]. The risk index of 4.00 implies a probability of 3.125 percent [.5(1/4²)] that the bank’s Tier 1 Leverage Capital Ratio will decline below the threshold designated within one year. Weak institutions are susceptible to unexpectedly large deposit runs and an inability to borrow funds. About 96 percent of the first 50 failing banks during the Great Recession and Financial Panic of 2008 retained a risk index of 3.00 or less one year prior to being liquidated or merged.^{6Real Estate Review: “The Panic of 2008: Bank Failure and Commercial Real Estate,” William C. Handorf, 2009, Volume 38, Number 4, Winter, Pages 27-37.}

Table 1 reviews the Tier 1 leverage capital, Mean ROA and ROA Sigma of the 20-plus large US banks evaluated between 2018 and 2024. The average bank has assets exceeding $700 billion and ranging between $150 billion and $3.6 trillion. The average Tier 1 leverage capital of the bank sample as of 2024 is 9.29 percent and ranges between 6.87 and 10.97 percent. The Mean ROA of the sample over the period is 1.10 percent and ranges between 0.33 and 1.85 percent. The average ROA Sigma is 0.33 percent and ranges between 0.18 and 0.51 percent. The average risk index is 13.82 standard deviations from having capital decline below an illustrative 6-percent threshold. There is a remote probability that any bank in the sample would witness a capital ratio declining below the threshold within one year. The risk index for the sample ranges between 8.27 and 22.36 standard deviations. A business plan must promote value.

The price/book ratio

Investors assess numerous factors when purchasing or selling a block of shares. Stock prices increase from accounting book value when management consistently generates profits and growth equal to or exceeding that required to compensate for risk. As shown in Table 1, the recent average price-to-book ratio of the 20-plus large banks sampled is 1.27 and ranges from a low of 0.70 to a high of 2.19. The price/book ratio is an inclusive measure of performance and growth computed by multiplying return on equity (ROE) by the price-to-earnings (P/E) ratio. Earnings per share may be represented by EPS, which cancels when ROE is multiplied by the P/E ratio.

Price/Book = Return on Equity x Price/Earnings Ratio
Price/Book = EPS/Book x Price/EPS

The market is willing to pay a high price per share for those banks that are creating high profits and generating expectations of continued strong growth. Return on equity equals a bank’s leverage multiplier times return on assets. Banks with low funding by equity capital possess a high leverage multiplier but are viewed by regulators as posing more risk, given their potential inability to cope with a subsequent period of stress. The leverage multiplier is simply the inverse of a bank’s Tier 1 Leverage Capital Ratio. A high leverage multiplier allows banks the opportunity to generate an above-average return on equity and achieve a high price/book ratio.

ROE = Leverage Multiplier x Return on Assets
Net Income/Equity = Assets/Equity x Net Income/Assets

Table 1 illustrates the correlation of each variable evaluated with the price/book ratio of the sample. Correlation provides a measure of the relative, not absolute, relationship between two variables and does not suggest causality or economic consequence. The correlation coefficient between two variables can range from +1.00, or perfect positive correlation, to –1.00, or perfect inverse correlation. The investigation allows bankers to assess factors important to creating shareholder value.

• Return on equity. With no surprise, the correlation between return on equity and the price/book ratio is a very high 79.6 percent, which exhibits statistical confidence at the one-percent level. There is a remote likelihood that the positive relationship between the two variables is by chance.
• Return on assets. The correlation between the Mean ROA and the price/book ratio is 36.5 percent, which is significant at the 5-percent confidence level. Profits are important to value. Business plans that seek higher net interest income, additional non-interest income and lower non-interest expense are rewarded. These elements are combined within the operating efficiency ratio (non-interest expense/{net interest income + non-interest income}). Economies of scale or scope achieved by merger or organic growth may lead to a lower operating efficiency ratio.
• Credit rating. The analysis converts each bank’s baseline credit rating into a numerical score. “Aaa” is equivalent to a rating of one, and each lower rating is assigned a higher number. The correlation between a bank’s baseline credit rating (lower value, better rating) and the price/book ratio is negative 33.5 percent, which is significant at the 10-percent level. Many credit-rating models, such as the classic Altman Z-score, comprise the market value of equity as an explanatory factor.^{7Journal of Credit Risk: “A fifty-year retrospective on credit risk models, the Altman Z-score family of models and their applications to financial markets and managerial strategies,” Edward I. Altman, December 2018, Volume 14, Pages 1-34.} Companies trading with higher capitalizations are viewed as going concerns. Net income provides the starting point for deriving operating cash flow. Credit ratings focus on the amount and stability of cash flow from operations as a source of liquidity.
• Tier 1 leverage capital. The correlation between Tier 1 leverage capital and the price/book is negative 21.9 percent. Banks with lower capital (higher leverage multiplier) are valued more highly, given their ability to magnify return on assets. Although the relationship is not statistically significant, the implication is that banks can have too much funding through equity if it leads to a low leverage multiplier and inadequate ROE.

Overall, banks generating a high return on equity, whether due to a better return on assets or an elevated leverage multiplier, and maintaining a passable credit rating create value for shareholders.

Overall, banks generating a high return on equity, whether due to a better return on assets or an elevated leverage multiplier, and maintaining a passable credit rating create value for shareholders.

Credit rating

Each nationally recognized credit-rating agency retains its own template and model for assessing risk—the letter grade, as modified by notches (1, 2, 3, or ±)—that principally reflect the answers to two questions. First, what is the probability of default (PD)? Second, what is the loss given default (LGD)? If the agency believes a bank has a higher PD and/or LGD, it will lead to a lower rating and higher funding costs for the institution when tapping the market for unsecured wholesale funds. Credit analysis recognizes both quantitative and qualitative factors.

The average baseline credit rating of each bank sampled is “A3” and ranges between “A1” and “Baa2.” An “A1” rating is assigned a numerical score of five, while a “Baa3” is represented by a score of nine. All of the ratings are medium-grade and considered investment quality. Several banks at the top are one notch below high-grade, and a number at the bottom are several notches above speculative.

• Earnings volatility. The correlation between the ROA Sigma and the credit rating is 51.5 percent, which is significant at the one-percent confidence level. Erratic earnings adversely impact credit quality. The stability of earnings and operating cash flow is central to a strong, viable enterprise.
• Return on equity. The correlation between return on equity and the credit rating is negative 48.4 percent, which is significant at the 5-percent level. Banks with a better credit rating generate a higher return on equity and market value. Institutions that create shareholder value are able to issue stock should economic conditions deteriorate and dissipate equity.
• Asset size. The Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 required banks deemed to be systemically important or “too big to fail” (TBTF) to increase funding through equity capital, direct more attention to maintaining adequate levels of liquidity, enhance risk-management processes and develop a “living will”. The concept of TBTF was supposedly ended by the passage of this law. However, the correlation between asset size, whether measured in billions of dollars or the logarithm of assets to normalize size, and the credit rating is negative 35.5 percent, which is significant at the 10-percent level. Larger banks retain a better credit rating as represented by a lower score.

Overall, banks retain a high credit rating by generating stable profits, posting a strong return on equity and pursuing manageable growth organically or via a merger. Other studies indicate that loan quality and asset size are important credit-rating explanatory factors.^{8Journal of Banking Regulation: “Regulatory Ratios, CDS Spreads and Credit Ratings in a Favorable Economic Environment,” William C. Handorf, July 2017, Volume 18, Issue 3, Pages 268-285.} Bankers must balance risk and return to satisfy credit-rating agencies, regulatory authorities and investors.

Summary

Business plans must emphasize strategies that promote consistent profits and growth. Bankers able to generate a solid return on equity create shareholder value and enhance credit ratings. Tier 1 capital needs to be sufficient to avoid regulatory restrictions and retain a medium-grade credit rating. Earnings generate cash flow, create value and promote liquidity.

 Table 1 Large Bank Valuation and Credit Risk (2018 to 2025)

Confidence Level: * @ 10%, ** @ 5%, *** @ 1%

Source: Uniform Bank Performance Reports (UBPRs) compiled by the Federal Financial Institutions Examination Council (FFIEC)

References

¹ A Monetary History of the United States, 1867-1960, Milton Friedman and Anna Jacobson Schwartz, 1963, Princeton University Press, Pages 1-860.

² Manias, Panics, and Crashes: A History of Financial Crises, Charles P. Kindleberger and Robert Z. Aliber, October 4, 2005, Wiley Investment Classics, Fifth Edition, Pages 1-309.

³ Journal of Political Economy: “Bank Runs, Deposit Insurance, and Liquidity,” Douglas W. Diamond and Philip H. Dybvig, June 1983, Volume 91, Number 3, Pages 401-419.

⁴ American Banker/BankThink: “Banks Should Reject More Board Candidates,” Richard Parsons, October 19, 2012.

⁵ Probability, Random Variables and Stochastic Processes, Athanasios Papoulis, 1984, McGraw Hill, Second Edition, Pages 149-151.

⁶ Real Estate Review: “The Panic of 2008: Bank Failure and Commercial Real Estate,” William C. Handorf, 2009, Volume 38, Number 4, Winter, Pages 27-37.

⁷ Journal of Credit Risk: “A fifty-year retrospective on credit risk models, the Altman Z-score family of models and their applications to financial markets and managerial strategies,” Edward I. Altman, December 2018, Volume 14, Pages 1-34.

⁸ Journal of Banking Regulation: “Regulatory Ratios, CDS Spreads and Credit Ratings in a Favorable Economic Environment,” William C. Handorf, July 2017, Volume 18, Issue 3, Pages 268-285.

ABOUT THE AUTHOR

William C. Handorf, Ph.D., is Professor of Finance, Banking and Real Estate at the George Washington University School of Business. In addition to more than 50 years as an academic, he has 60 years of experience in the banking sector as a banker, regulator, accountant, consultant and director.