## Leverage by the numbers

November 24, 2008

So what is the capital cushion underneath our largest financial institutions?  I spent today compiling this spreadsheet:

Those are some ugly numbers and I’ll explain why. Citigroup’s leverage ratio of 56 means that the bank has \$56 of assets for every \$1 of common equity. If the value of those assets falls 2%, then common stockholders are wiped out. Here’s why: Assets = Liabilities + EquityIf you understand this formula, you will understand the credit crisis. So read on…

That formula is known as “the accounting equation.”  Fundamentally, it shows how an asset (like a house) or collection of assets (like a company) is financed—either with borrowed money or your own, with debt or with equity.

One side of the equation has to equal the other.  If the assets fall in value, and not because cash was used to pay off a liability, then equity has to fall by an equal amount.  If assets fall far enough, then equity falls below zero.

Take a house for example.  A house is an asset, typically paid for with both a mortgage (liability) and a down payment (equity). If you pay \$100,000 for the house and put 20% down, you have an \$80,000 mortgage and \$20,000 of equity. The leverage ratio is 5.  (\$100,000 asset / \$20,000 equity = 5x assets/equity).  Notice that we’re taking two components of the accounting equation and putting one over the other: Assets / Equity = Leverage

A higher leverage ratio means greater potential for profit AND loss on your initial investment.  Let’s apply the accounting equation to a few scenarios.  For the first two, let’s take the above example where your leverage ratio is 5x:

• House value INCREASES \$10k to \$110k.  Remember: Assets = Liabilities + Equity.  \$110k house = \$80k mortgage + \$30k equity.  \$10k increase on original equity investment of \$20k = 50% return!
• House value DECREASES \$10k to \$90k.  \$90k house = \$80k mortgage + \$10k equity.  \$10k decrease on \$20k investment = -50% return.  Boo!

What if, just like so many home-borrowers did during the days of the housing bubble, you put 5% down instead of 20%?  First of all, your leverage ratio jumps to 20.  (\$100k house / \$5k equity investment = 20x assets/equity).  Let’s see how this impacts returns…

• House value INCREASES \$10k to \$110k.  \$110k house = \$95k mortgage + \$15k equity.  \$10k increase on original equity investment of \$5k = 200% return.  Yippee!
• House value DECREASES \$10k to \$90k.  \$90k house = \$95k mortgage – \$5k equity.  \$10k decrease on \$5k investment means not only have I lost my original investment, but now I owe \$5k more than I started with.  I’m upside-down on the mortgage.  F*ck me!

In this last scenario, I keep the house as long as I keep paying the mortgage.  If I default, however, the bank forecloses and sells the house.  If it can only get \$90k for it, it has to take a \$5k loss on ITS asset, which was the mortgage loan.

Here’s where the rubber meets the road, where a housing crisis becomes a banking crisis.

You see, that same equation (A = L + E) applies to banks.  Just like you save for a down payment and borrow money to buy a house, a bank will take deposits, sell debt and raise equity capital to make loans.  But if the value of its loans fall, then it has to write them down by that amount.  To keep the equation in balance, if it writes down assets, it must simultaneously write-down equity by the same amount.  Look at the last of the four scenarios above.  If the borrower stops making his payments, the bank has to foreclose and sell the house.  If it recovers less in the sale than the home-borrower owed on the mortgage, that’s the amount by which the bank has to write down its assets.

Since the equation (A = L + E) applies to the bank, it’s important to know the bank’s leverage ratio.  As it does with our imaginary home-borrower, the leverage ratio tells us how much cushion the bank has to lose money on the asset side of the balance sheet before equity goes negative.  The higher the leverage ratio, the less cushion.  Now go back to the top and look at the table.

All of those leverage ratios are high.  And they actually understate the truth.  For instance, besides the \$2.1 trillion of assets Citi has ON its balance sheet, it has another \$1.2 trillion OFF its balance sheet.  The only reason I didn’t include these in my calculation is I wasn’t sure how much off-balance sheet exposures the other banks have and I wanted the leverage calculations to be consistent.  (I tried to look it up in their SEC filings, but disclosure varies by company.  Citi is the only one of the bunch that spells it out clearly.)

With such stupendously high leverage ratios, is it any wonder that bank stocks are dropping like rocks?  Common stock is just another word for common “E”quity.  Market capitalization (share price * shares outstanding) is the Equity value of a company after Liabilities are deducted from the value of its Assets.  A = L + E.  If A/E is huge, then it takes only a small decline in A to wipe out all of E.

As more Americans fall behind on their mortgages, credit card bills, auto loans, student loans, etc., the financial companies that own these assets and have to write them down see the value of their equity get hammered, especially if they’ve employed excessive leverage.

Note today’s announcement by Citigroup and the government that the latter will “guarantee” (i.e. absorb losses) for some \$306 billion of Citigroup’s toxic assets.  If Citigroup had to take those losses, it would wipe them out.  The same will be true for the other big banks.  The Fed is already on the hook for \$29 billion of debts owed by JPM’s new subsidiary Bear Stearns.  And a few weeks ago the government agreed to guarantee \$139 billion of GE’s debt.  And then there’s the \$100 billion promised each to Fannie and Freddie, \$150 billion for AIG.

This is the story of the housing crisis, the banking crisis and the global financial meltdown. Everyone, everywhere was levered to the hilt, using piles of borrowed money to make leveraged bets on everything from real estate, to stocks, to currencies, to bonds, to companies themselves (LBOs), etc. With so many people maxing out leverage to drive returns, all it takes is a small decline in asset prices for all of them to go bust. Unfortunately, the decline in asset prices isn’t going to be small. Consequently, the value of equity capital will continue to get hammered.

All of these government bailouts, er, “guarantees” are simply a transfer of risk from the balance sheets of various financial companies to governments’.  To prevent “A” from falling too far, and thereby wiping out the “E” of the financial companies, the government absorbs the assets itself, immunizing the financial companies from loss.

The trouble is, the losses don’t just go away.  Someone will lose.  First it’s common shareholders. Next it will be the U.S. taxpayer.

(Don’t forget to read Part 2 and Part 3 of this series Leverage by the Numbers. The leverage numbers actually get scarier when you factor in “other assets”…)