## Thursday, June 16, 2011

### Leverage and Balance Sheets...

Killing time at JFK International waiting to board my flight to Paris.  I recently came across a brilliant and simple discussion of the relationship between leverage and the size of balance sheets in Adrian and Shin (2008) and had to share...

Suppose that a household owns a house that is financed via a mortgage.  Suppose that the house has a value of 100, and that the value of the mortgage is 90 (thus household net-worth, or equity, is 100 - 90 = 10).  This household has the following balance sheet:

 Assets Liabilities 100 Equity: 10 Debt: 90

What is this household's leverage ratio? Leverage (L) is defined as the ratio of the value of total assets (A) and the value of equity (E).  In this case the household has a leverage ratio of 100:10 or 10:1.  What happens to the household's leverage ratio as the value of the house (its asset) fluctuates?  For simplicity assume that the value of debt stays fixed for small changes is asset prices.  Then leverage is roughly...

L ≈ A / (A - 90)

So as the value of the house (i.e., assets) rises, with the value of debt fixed, household net worth increases and the leverage goes down!  Leverage varies inversely with the value of total assets.  This inverse relationship is exactly what is born out in the data.  To calculate leverage, I use the ratio of household total assets and household net worth from the quarterly  U.S. Flow of Funds data for the years 1963 - 2011.

There is a clear negative relationship between changes in leverage and changes in household assets.

Now instead of household balance sheets, let's consider firm balance sheets.  Specifically, based on data availability, consider three classes of firms:
1. Non-financial (non-farm) firms
2. Commercial banks
3. Security brokers and dealers (includes investment banks)
If, like households, firms where fairly passive in their balance sheet management, then we should see a nice negative relationship between firms' asset values and leverage...however (not surprisingly) the data indicate that firms are a bit more active in managing their balance sheets than households.  As with households, all firm data is quarterly, and is taken from the U.S. Flow of Funds accounts maintained by the Federal Reserve.

Non-Financial (Non-Farm) Firms: I take the data from the U.S. flow of funds What is going on here? Certainly the clear negative relationship from the household scatter  is gone.  You can kind of begin to see clustering around zero growth in leverage (suggestive of firms actively managing balance sheets to maintain a fixed leverage ratio?)
Commercial Banks: The clustering phenomenon is now very apparent and consistent with the fact that commercial banks actively manage their balance sheets in order to maintain a fixed leverage ratio.
Security Brokers and Dealers: Now the relationship between leverage and assets is positive! This means that for security brokers and dealers (a group which includes all major Wall Street investment banks) leverage is pro-cyclical.

How can this be? What are the implications of pro-cyclical leverage?  I leave this as a topic for a future post...alternatively you can read Adrian and Shin (2008).