Demand slopes UP...Supply slopes DOWN!

This post is a continuation of a previous post on liquidity and leverage (both posts closely follow the analysis of Adrian and Shin (2008)).

First, a quick summary of previous post.  There is a negative relationship between growth in balance sheets (value of assets) and leverage for passive investors such as households.  All data is taken from the U.S. Flow of Funds accounts maintained by the Federal Reserve.

However there is a positive relationship between growth in balance sheets (asset values) and leverage for security brokers and dealers (i.e., investment banks).  For this group, at least, leverage is pro-cyclical.

Continuing with the implications of pro-cyclical leverage.  Back to basic balance sheet arguments.  Consider a firm that actively manages it's balance sheet in order to maintain a constant leverage ratio of 10:1.  Start with the following balance sheet:

Assets	Liabilities
100	Equity: 10
	Debt: 90

Again assume that the value of debt is constant in response to change in asset values (which seems reasonable for small changes in assets values).  Now suppose that the value of assets increase by 1% to 101.  The new balance sheet is as follows (note that equity has increased by 10% as a result of the 1% rise in asset prices).

Assets	Liabilities
101	Equity: 11
	Debt: 90

The leverage ratio is now 101 / 11 = 9.18.  If the firm wants to maintain a leverage ratio of 10, it must take on more debt and use the cash it borrows to buy more assets.  How much debt?  Firm requires that 101 + D / 11 = 10, which implies that D=9.  Thus an increase in the value of assets of 1 leads to an increase in the quantity demanded of assets by the firm worth 9.  Price of asset goes up, quantity demanded of the asset by firm goes up.  The demand curve for assets slopes up!  The firm's new balance sheet now has a leverage ratio of 10.

Assets	Liabilities
110	Equity: 11
	Debt: 90

Same type of mechanism is at play for negative shocks to asset prices.  Doing the math leads to the conclusion that for a firm actively managing its balance sheet to maintain a constant leverage ratio, the supply curve for assets slopes down.  Note that just as equity increases as asset prices increase, equity bears the burden of adjustment when asset prices are falling.

This mechanical adjustment process of leverage will be strengthened if either:

1. Leverage is pro-cyclical
2. Asset markets are not completely liquid

If asset markets are not completely liquid, then the asset price will be affected by the change in the firm's demand for assets following an, asset price shock.  Consider a negative asset price shock.  The negative shock to asset prices leads, through the mechanism above, to the firm to sell assets in order to maintain the desired leverage ratio.  If markets are not perfectly liquid, then the firm's decision to sell assets will further decrease the price of these assets, which then weakens the firm's balance sheet even more, which causes the firm to sell more assets, and so the cycle goes.

Adrian and Shin (2008) outline empirical evidence consistent with the above amplification story.  Specifically they demonstrate that firm's balance sheet components are able to forecast changes in asset price volatility.  I am working to replicate their results (as they are highly relevant to my own empirical work on leverage and asset price volatility) and will follow up with the R code of the replication as soon written (hopefully in the near future!)...

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).