## Friday, June 17, 2011

### 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:

AssetsLiabilities
100Equity: 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).

AssetsLiabilities
101Equity: 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!)...