Review Session Part 4

Danny Shoag

Outline

• Corporate Control – Debt, Equity– Sample Essay Question

• Bubbles – Simple Math– Sample Problem

• Leverage– Sample Problem and Short Essay

• Big Think– New Assets, Policy Responses, etc.

Debt, Equity and Corporate Control

• Convexity and Concavity of Payoff Diagrams for Equity and Debt

• Quick demonstration attitudes towards risk:– Imagine a firm with $100 in assets, which owes $90 to

its debt holders and is presented with a fair gamble to gain or lose $50 with 50% probability.• Expected value for the debt holders w/o the gamble = $90.

With the gamble they have an expected value of .5*$90 +.5*$50 = $70. They do not want the gamble.

• Expected value for the equity holders w/o the gamble is $10. With the gamble they get .5*$60+.5*0 =$30. They want the gamble.

Extensions• Think about other stakeholders in the company

and how they are affected by risk• An example essay question:– In class we discussed a number of bank failures and

the role of the FDIC and the government generally. (1) Why do we allow the FDIC to seize banks before formal bankruptcy? Last September, Lehman Brothers filed for Chapter 11 bankruptcy. (2) Why wasn’t it put into receivership by the FDIC? (3) What occurred after Lehman’s bankruptcy filing? In your answer, cite the papers you’ve read. (4) Relate your Lehman answer to the concepts of risk shifting and agency seen in lecture.

Prices and Bubbles• We’ve repeatedly seen the Euler equation:

U’(ct) =βE[(1+R)U’(ct+1)]

• Risk neutral pricing- u’=1, and let β=(1/1+rf) • (1)

• (2)

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Bubbles Cont• We generally assume that the last term equals

zero. Intuitively, does doing so make sense? What does this imply about bubbles?

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Bubbles Cont

• Why is this setup a problem for bubbles? Bubbles have no dividends!

• Prices must grow as fast as the interest rate (IN EXPECTATION). So the limit wouldn’t go to zero.

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Bubbles

• Sample Question:– “Joe Poor-Student tells you that the rational

expectations model rules out bubbles because bubble asset prices must grow at the interest rate, and hence can never pop. (1) Show why he is wrong. (2) Explain a legitimate reason for ruling bubbles out in a rational expectations model (hint: remember your homework!). (3) Under what conditions does this reason hold. (4) Give an example of a situation in which this does not hold.”

Question Answered

• (1). Let the price of the bubble grow with rate (1+r)/α with probability α, and be worth zero with probability (1- α).

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Question Answered Cont• (2) At least on some paths, the bubble’s price

becomes extremely large. The bubble is a part of someone’s wealth. This person is going to want to consume a portion of this wealth. So if the interest rate r is larger than the growth rate of the economy g, then someone might eventually have wealth greater than the total goods in the economy, and try to consume more than the total goods in the economy, violating his budget constraint. So we cant have a bubble that can explode faster than economic growth. So we can rule out bubbles if gr

Last bit

• One example where r<g is Social Security.• Social Security is like a bubble in that it never

invests in dividend yielding projects, but rather pays benefits by collecting revenue from another generation –’selling the asset’.

• As long as the money going in is greater than the money coming out (r<g) it’s a rational bubble!

Leverage

• Definition = Assets/(Assets-Liabilities) = Assets/Equity

• Example:

• What’s the leverage ratio?• What happens to Leverage when prices rise to

$110?

Assets Liabilities

House $100 Equity $10

Mortgage $90

Leverage Cont

• Passive Agents: Debt doesn’t change, so equity must rise. So leverage falls.

• L=110/20 is less than L=100/10

This is not the case for banks and broker-dealers

Graphs from Adrian and Shin (08)

Leverage with adjustmentSample problem: • Suppose Housing prices rise to $110.

– How much do you need to borrow and invest to maintain a constant leverage?

* Suppose prices rise to $110 and then fall back to $100. What happens to your equity if you are a passive investor (let your leverage ratio vary)? What would happen to your equity if you were trying to maintain a constant leverage ratio? What would be your leverage at the end? If you needed to maintain your leverage of $10, how much of your assets would you need to sell?

ANSWER

• Assets/ 20 = 10• Assets = 200. So you need to borrow $90 and

buy $90 extra units of housing. Your balance sheet would look like

with leverage once again =10.

Assets Liabilities

House $200 Equity $20

Mortgage $180

Answer Cont

• Without any adjustment, if the price rises and falls, your equity at the end is unchanged.

• If you took on extra debt, you now own $200/$110~1.82 houses. At the end that’s worth $182. Since you owe $180, your equity is now $2.

Assets Liabilities

House $182 Equity $2

Mortgage $180

Answer Cont

• Your leverage ratio at the end is $182/$2 = 91!• Yikes!• You need to get back to 10 = $20/$2. So you

need to sell $182-$20 = $162 worth of housing in a market where prices have just fallen. You use this money to pay your debt, and end with a balance sheet of

Assets Liabilities

House $20 Equity $2

Mortgage $18

Leverage Short Essay

• Why might this strategy have adverse effects, even if you think prices are more likely to go up? In other words, leverage targeting was a way of doubling down on your bet. Why might this be bad?– CONGESTION, FIRE SALES: If many people are

targeting leverage and betting on the same assets, there might be externalities in the pricing mechanism. Even if you liked the prior bet, you may not be able to sell such massive quantities in a downturn without moving prices.

New Assets and Policy

• New AssetsCDOs (Collateralized Debt Obligations)– Buzz words: Tranches, Correlation, Securitization,

Ratings, NINJA loans– Concepts: Adverse Selection, Regulatory

Arbitrage, Catastrophe Bonds, Diversification (not just geography!)

CDSs (Credit Default Swaps)– Buzz words: Counter-party, Hedging, AIG– Concepts: Incentives, Hurricane Insurance

Big Think cont• Sample Essay: – Bankruptcy negotiations often turn debt holders into

equity holders in the restructured company. This gives claimants in the bankruptcy proceeding incentives to work towards the success of the new company. How does the presence of CDS contracts and hedged bond holders effect these behaviors?

[ANSWER]Hedged bond holders obviously have less incentive to

work for the creation of a new company. CDS sellers do not have a seat in the negotiations, and even if they were given one, they might not have the same stake in the new company.

Policy

• Monetary Policy and the Zero-Lower Bound– Alternate MP – Buying up different assets (Term

Structure and Risk Premium)– Democratic oversight and Future Inflation

• Keynesian Stimulus– Does it work? Can we afford it?

• New Regulation– Can the regulators regulate? Madoff– Political feasibility: Could regulators have clamped

down, even if they saw the bubble?

GOOD LUCK!

COME TO OFFICE HOURS!

Danny’s OH: Thurs 11:30-12:30 in Littauer