Optimal Debt Financing andthe Pricing of Illiquid Assets

Antonio Bernardo and Ivo WelchDiscussion

Model

• In tradition of Shleifer and Vishny, Geanakoplos, Stein, others

• Arbitrageurs make two period investments in period 0 using leverage.

• We focus on the case where bad news comes out in period 1, reducing arbitrageur wealth and ability to borrow

Liquidity Constraints Cause AssetPrices to Fall More than Fundamental

• Geanakoplos: “Optimists are wiped out; fundamental value down, volatility increases

• Stein: New investors have limited money; returns go up

• Concern by investors that arbitrageur model of expected returns is wrong (S-V)

• Without leverage: CRRA (constant elasticity/Cobb-Douglas) implies returns fluctuate with real growth

This Model

• After first period, a realization of whether in good or bad state

• Second period returns are normally distributed (not sure how negative are paid)

• Exogenously given debt ratio for arbitrageurs in second period

• Otherwise, split would be that arbitrageurs would take the upper tail of the distribution in second period

Equilibrium

• Arbitrageurs realize that in bad states they will be forced to sell some assets.

• The more that will be sold by risk-neutral arbitrageurs to risk averse investors the lower the price

• This leads to an equilibrium first period (and then, more simply, second period debt ratio)

Some Notes

• “Fire sales” in these models are very different from e.g. Diamond Dybvig --- it’s just that expected market returns fluctuate over time

• Exogenous debt constraint prevents us from having Arrow-Debreu securities and so complete markets

• Because of collateral constraints expected returns on assets may be correlated as in Geanakoplos-Fostel

How Does this Relate to Eventsin the Financial Crisis?

• For commercial banks, the regulatory capital system combined with government insurance encouraged firms to avoid asset sales and capital increases– FDIC top 7 years of equity/assets in 1941-2010– 300 bank failures in 2009-10 at an average shortfall

of 23% of assets– Bankia most recently in Europe– What could have been a smaller problem became a

much bigger one

My view

• Yes, limits to leverage do increase volatility in asset prices, create correlations

• However, no policy suggestions are made in the paper --- appropriately

• Government is a poor bearer of financial market risk (as opposed to some other risks)

• Losses will happen. Policy should be focused on a “Coasian” solution where “property rights” in financial losses are well defined --- and fully allocated to private investors