Banks, Equity, Liquidity, and Insolvency

It was my intention to write a number of posts on bank operations and tie them into a narrative of the 2008 financial crisis.  I got no further than explaining the role of capital in protecting banks against losses (Banks and the Importance of Equity) before the exigencies of finishing my classes in the fall semester delayed my plans.  A question by an anonymous reader has placed me back on path.

Brooks,
Thanks for taking a simple example to explain a complex issue such as this. Could you please explain the following for me:

- As loans given out by banks result in profits (e.g., through interest/fees less operating costs), these get added to the equity capital and thus, the equity capital account line grows. However, to me this does not feel like a "real thing" that is available to a bank to absorb losses. It feels like "Cash" is the thing that is ultimately available to the bank to absorb losses. If that is true, then why worry about equity capital at all?

In this post, I attempt to distinguish between insolvency and liquidity.  An institution is insolvent if its liabilities are greater than its assets.  It is illiquid if it does not have sufficient cash to meet its liabilities as they come due.  In the short run, an insolvent institution can be liquid if it has sufficient cash to pay its most immediate liabilities.  Obviously, it will eventually become illiquid as more liabilities become due.  I will also demonstrate that leverage, the number of dollars of liabilities per dollar of equity, magnifies both profits and losses.  
As a quick review, a bank's balance sheet is described by the equation, Assets=Liabilities+Equity.  The owners of a bank have a goal of maximizing profits for a given level of risk.  The risks are the probability that the bank will suffer losses from operations ( expenses exceed revenues) or a decline in asset value.  I will begin with the example provided by Juliusz Jabtecki and Mateusz Machaj, "The Regulated Meltdown of 2008," Critical Review, 21(2-3): 301-328, 2009.  At the beginning of operations (Year 0), the bank's leverage ratio is $20 of liabilities (deposits) for every $1 of equity. 

Figure 1. Year 0

Assets		Liabilities
Reserves (Cash)	$10	Equity	$5
Loans	$90	Deposits	$95
Total	$100	Total	$100

To keep the math simple, assume that in the first year of operations (Year 1), the bank earns a return of $5.00, or a 100% return on equity.  The bank must decide how to distribute the profit between dividends and retained earnings (I will show retained earnings as an increase in equity.), and if the profit is retained, how it will be invested.  In Figure 2, the bank did not pay dividends, increasing equity by $5.00, and it held all new equity as reserves (cash).  As it begins its second year of operations, it has $9.50 of liabilities for every $1.00 of equity; its leverage has decreased.  

Figure 2. Year 1: The Conservative Option with Profit

Assets		Liabilities
Reserves (Cash)	$15	Equity	$10
Loans	$90	Deposits	$95
Total	$105	Total	$105

If the bank earns a return of 5% ($90*.05=$4.50), the resulting return on equity is ($10/$4.50*100=) 45%.  

Figure 3. Year 1: The Aggressive Option with Profit

Assets		Liabilities
Reserves (Cash)	$2	Equity	$7
Loans	$100	Deposits	$95
Total	$102	Total	$102

Alternatively, if the bank had taken a more aggressive, riskier position as it began is second year of operations, paying $3.00 as dividends, increasing equity by $2.00, and investing the additional $2.00 of equity and $3 of returns in new loans, its balance sheet would be depicted by Figure 3.  Its leverage is $13.57 of liabilities for every $1.00 of equity.  In this case, a 5.0% return on loans ($100*.05=) $5.00, results in a return on equity of ($5/$7*100=) 71.4%.  The additional leverage magnified the return on equity. 

Figure 4: Year 2: The Conservative Option with Losses

Assets		Liabilities
Reserves (Cash)	$9.40	Equity	$4.60
Loans	$90.00	Deposits	$95.00
Total	$99.40	Total	$99.40

Now consider the bank's financial position if it had lost 6% on loans.  Figure 4 adjusts Figure 2 for losses in operations.  The bank's return on equity is (-$5.40/$4.60) -117.4%.  The bank's equity position is weaker, but it is both liquid and solvent.  Compare that outcome to that of the more aggressive investment strategy.  Figure 5 adjusts Figure 3 for a 6% or $6.00 loss on loans after one year of operations. 

Figure 5.  Year 2: The Aggressive Option with Losses from Operations

Assets		Liabilities
Reserves (Cash)	-$4	Equity	$1
Loans	$100	Deposits	$95
Total	$96	Total	$96

The bank is still solvent (Assets-Liabilities>0), but it is illiquid, it does not have cash to meet short term depositor demands.  Its return on equity is (-$6.00/$1.00) -600%.  The higher leverage magnified the losses.  The bank might be able to secure short-term loans to meet its cash demands.  If not, it will be forced to liquidate.

Figure 6.  Year 1: Operating losses

Assets		Liabilities
Reserves (Cash)	$4.60	Equity	-$.40
Loans	$90.00	Deposits	$95.00
Total	$94.60	Total	$94.60

Compare this outcome to a 6% loss on loans ($90*.06=$5.40) in the first year of operations (Figure 6).  If the same level of losses had occurred before implementing an aggressive investment strategy after a profitable year, the bank would have been liquid, but insolvent.  If the losses had occurred after a year of profitable operations, even with the aggressive strategy and illiquid cash position, the increase equity from the first year of operations protected it against insolvency.

My next post on banking will explain maturity mismatching (long-term assets and short-term liabilities), and how it impacts the regulation of banks.