Applying Game Theory to Finance

“I can calculate the motions of heavenly bodies, but not the

madness of people”

- Isaac Newton, upon losing £20,000 in the South Sea Bubble in 1720

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Game Plan

Hostile Takeovers

Bubbles

Hostile Takeovers

“Robert Campeau is considered by many as the best example of a fool.”

- Dale Oesterle, Cato Review of Business & Government, 1996

“The biggest, looniest deal ever." - Fortune Magazine, July 1988, on Campeau’s acquisition of Federated Stores.

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Hostile Takeover Plan

Robert Campeau vs. Macy’s for Federated• Conditional vs. unconditional offers• Flat vs. tiered offers

Qwest Bond Swap• Coercive offers• Staggered offers

Poison Pills, Saturday Night Specials, etc.

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Macy’s vs. Campeau You are shareholders of Federated,

whose share price is $100.

Macy’s offers you $105 per share conditional on getting at least 50%

Campeau offers an unconditional tiered offer …

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Macy’s vs. Campeau If less than 50% tender to him, then each

gets $110 per share. If X% > 50% tender to him, then each

gets a “blended price” of

• Campeau pays $80 extra per share beyond 50%• If everyone tenders, Campeau pays $95 per share• If Campeau wins and you have not tendered, then

Campeau will be able to buy you out at $80

80$*)%50(110$*%50 X

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Macy’s vs. Campeau

Do you: Tender to Macy’s

ORTender to Campeau?

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Qwest Bond Swap

“Today a federal judge will decide whether Qwest can proceed with an exchange offer in which institutional investors (in a $1.5B issue) are being asked to exchange each $1,000 bond for a new one with face value $545. The offer is a coercive one that will leave bondholders who do not accept it in the back of line for repayment if Qwest goes broke…”

- “A Bond Swap Available Only to Big Players”, NY Times, December 18, 2002.

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Qwest Bond Swap

“If Judge Chin allows the offer to go ahead, institutional investors who own bonds will find themselves in a position with some resemblance to the classic ‘prisoners’ dilemma’... If no one tendered, then Qwest would be in the same position as before the offer, and any bondholder would be no worse off. But if a lot of holders tender, those who refuse will be worse off than they were.”

- “A Bond Swap Available Only to Big Players”, NY Times, December 18, 2002.

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Qwest Coercive Bond Swap

How is / is not the game played among bondholders similar to the Prisoners’ Dilemma?

Why exclude non-institutional investors from the offer?

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Qwest: Some Simple Cases

Qwest owes $1.5B w/ $600M assets.• Given success (everyone tenders) Qwest still goes

bankrupt • Is it a dominant strategy to tender?

Qwest owes $1.5B w/ $1B assets • Given success, Qwest avoids bankruptcy • Is it a dominant strategy to tender?

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Qwest: Less Simple Cases

Qwest owes $1.5B w/ assets that are worth either $600M or $1B.

• Given success, it avoids bankruptcy w/ Prob($1B)=45%

• Is tender a dominant strategy here?• … for higher or lower Prob($1B)?

Same as above but $300M worth of bondholders are excluded from the deal

• Tender becomes a dominant strategy for the $1.2B who remain

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Qwest Continued: When All Bonds aren’t Created Equal In reality, Qwest had many different bond

issues it wanted to retire through these swaps, with different repayment priority.

Qwest also didn’t issue its swap offers for all of its issues at once but rather staggered the offers

Does the order matter?

Should Qwest swap high-priority bonds first or low-priority ones?

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Zwest Game Fictional firm Zwest has three

bondholders A,B,C each owed $3M.

There is some uncertainty about Zwest’s future assets: Zwest will have $5 million with 66.7% and $8 million with 33.3%.

Absent any tendering, A gets repaid first followed by B, then C.

• Since assets are always less than $9 million, Zwest always goes bankrupt and has equity value of $0.

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Zwest Game Zwest will offer A,B,C each to exchange

their $3M bond for a priority $2M bond.

Those who tender will have higher priority than those who don’t, but priority rankings are preserved between those that tender and those that don’t.

• Example: if only B tenders, then B is paid $2M first then A is paid $3M then C is paid either $0M or $3M, depending on whether asset value is $5M or $8M.

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Zwest Game #1 (A first)

Zwest makes A decide first whether or not to tender, then B, then C

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Zwest Game #2 (C first)

Zwest makes C decide first whether or not to tender, then B, then A

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Play Zwest Games! Group into three pairs to play (you and a

partner will play together)• Roll a die to see who is A, B, C

With your partner decide which game you would rather be playing (in your role), and write this down with your names and a brief explanation

• Your choice will not affect which game you ultimately play

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Play Zwest Games!

I’ll inform you which game your group will be playing

Record the progress and the results on the sheet given to you

Commitment

“The Power to Constrain an Adversary Depends Upon the

Power to Bind Oneself.”- Thomas Schelling

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Commitment in the Examples We’ve Seen

Campeau committed to paying the high price $110 even if he failed to gain control

• This allowed him to avoid failure, since shareholders would all want to tender if he were going to fail

Qwest committed not to renegotiate later with the non-tenderers

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Game within a Game So far, we have examined hostile

takeovers as a voting game played among the target’s stockholders

But actually the shareholder vote is a “game within a game”

• Entrenched management, the raider, and other suitors strategize over influencing shareholders’ options and incentives in the forthcoming vote That in itself is a game …

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Bitter Pills

Numerous ways for entrenched management to increase the cost of a takeover (“Shark Repellant”)

• “Poison Pills”• “Macaroni Defense”

… and for raiders to fight back• “Lady MacBeth Strategy”• “Saturday Night Special”

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Saturday Night Specials“From the hostile bidder’s perspective, the most critical element – in contrast to substantive matters such as the price offered and the number of shares sought – is speed … If the hostile bidder can structure its offer so that target shareholders must decide to tender before a competitive bid can be arranged, a substantial advantage will be secured”

- Source, Gibson and Black (1995), “The Law and Finance of Corporate Acquisitions”

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Game within a Game within a Game (within a Game) Management needs shareholders to

approve a Poison Pill. Thus, shareholders and management play a game long before raider arrives.

Yet one layer deeper: Poison Pills remove management’s incentive to take more drastic, self-destructive behavior

• If management can commit to adopt such a “Scorched-Earth Policy”, then shareholders will be more willing to grant a Poison Pill

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Role of Regulation Players may strategically commit to

strategies that reduce overall gains from the game.

Beneficial regulation shapes the options available to players so that the options they will likely choose lead to better outcomes.

• Saturday Night Specials were made illegal by the Williams Act of 1968, which stipulated that any tender offer must be kept open for at least 20 days.

Bubbles

“We thought it was the 8th inning, and it was the 9th”

- Stanley Druckenmiller, former manager of Soros’ Quantum Fund, April 2000.

“Julian said, ‘This is irrational and I won’t play”, and they carried him out feet first. Druckenmiller said, ‘This is irrational and I’ll play’, and they carried him out feet first.”- NYTimes April 29, 2000: “Another Technology Victim; Soros Fund Manager Says He ‘Overplayed’

Hand”. (Julian Roberts managed Tiger Hedge Fund, dissolved in 1999.)

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Bubbles: Game Plan

1. Newspapers, academics, and crystal balls…

2. Should you sell when you know you are in a bubble?

3. Bubble Game

4. Lessons learned: Bubble Game

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Newspapers, academics, and crystal balls …

Spotting trends

The January Effect

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Spotting trends “__ is typically a strong month for stocks” “__ tends to be a good month for stocks” “__ has historically been a strong month” “__ is usually a great month for stocks”

“__ is often a negative month for stocks.” “__ tends to be a bad month for stocks” “__ is traditionally a poor month for stocks” “__ is a scary month for stocks”

Spotting Trends

Mark Twain, in Pudd’nhead Wilson:

“October. This is one of the peculiarly dangerous months to

speculate in stocks in… “The others are July, January,

September, April, November, May, March, June, December, August, and

February.”

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Spotting trendsSources: Motley Fool, CNN, USA Today, Dow Jones, Dean Inv. Ass.

Good: Jan, June, July, Dec Bad: Mar, Aug, Sep, Oct

If each month is equally likely to go up or down, there is an 80% chance that some month will be “bad” three years in a row!

80% of the time, a naïve analyst will identify (with 95% false confidence!) a day of the month on which the markets have historically performed better than average.

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January Effect

Tendency of the stock market to rise between December 31 and the end of the first week in January.

Well-documented by a spate of scholarly research in the 1980s

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Sampling of Research (USA data up to 80s)

In equally-weighted portfolio, average return 3.5% in January, only .5% in others

• Excess returns not seen in DJIA, so effect limited to and more pronounced in small stocks

• Over half of excess return on small stocks in Jan.

Excess returns greatest for small firms whose prices have declined previous year

• Excess returns in first five days not observed for “winners” of previous year

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Sampling of Research (non-USA data up to 80s)

January returns exceptional in 15/16 countries studied.

• In Belgium, Netherlands, Italy, January return exceeds the return for the whole year!

Taxes appear confirmed as part of story• Britain has April effect, Australia has July effect.

January itself seems significant• Effect in Japan (where no capital gains) as well as

Britain and Australia.

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What Should You Do?

Careful research has shown that there was a January effect from 1900-1980.

Should you go buy small-caps this December?

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January Defect?Source: The Independent Adviser for Vanguard Investors, December 10, 2002

“In the past few years, the January effect has been more of a January defect as investors, trying to get an edge on their competitors, have jumped earlier and earlier. In some cases the January effect takes place in November or even December.”

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Most Recent Research

The Declining January Effect: Evidences from the U.S. Equity Markets Source:Quarterly Review of Economics and Finance v43, n2 (Summer 2003): 395-404

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Bubbles

What is a bubble?

How do bubbles start?

How do bubbles persist?

How do bubbles burst?

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A Simple Model of Bubbles A structural change leads unsophisticated

investors to conclude there is a “new economy” with permanently higher growth (and permanently rising prices!).

• South Sea bubble in 1700s• Tech bubble in 1990s

BUT sophisticated investors know that the growth spurt is temporary and will return to normal levels

• Still, no one knows how long high growth will last

This model is based on Abreu and Brunnermeier, “Bubbles and Crashes”, Econometrica (2003)

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A Simple Model of Bubbles Sophisticated investors begin to realize

that the growth spurt has ended after the fact and not all at the same time.

As long as a majority of sophisticated investors stay invested, price continues to increase at a high rate. (This is an assumption.)

• For our purposes, “bubble” = majority of sophisticated investors know that growth has stopped, but still a majority stays invested.

BUT once a majority of sophisticated investors have sold, the naïve realize their error and the bubble bursts.

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How Do Bubbles Start? You are an investor in the early

1700s. The masses believe that the South

Seas Company’s price is sure to rise at high rates permanently.

To your surprise, you learn that South Seas trade is a dud!Should you sell immediately?!

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Bubble Game: Rules 5 players 10 periods. Decide Buy/Sell in each

• After period 10, Price will revert to Value

Price process• Price = Value = $1 at start• Price doubles each period until 3 or more

sophisticates have sold

Player payoffs• Once you Sell, you are done and get current price.• If you still own when 3 others have sold, you get

current Value

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Bubble Game: Rules Value process

• Value doubles each period during the growth period. • I will flip a coin each period to determine whether growth has

ended (beginning after round 1).• Example: If growth stops after round 3, then value = price

($1, $2, $4) in periods 1,2,3 but value = $4 in all periods T > 3 whereas price keeps on doubling. When bubble bursts, price falls back to $4.

Information process• Once growth ends, one randomly chosen player will

immediately learn that it has ended • The next period, a second player will learn that it has

ended, and so on • Note: Upon learning, you don’t know if you were the first

to learn, the second, … or the last!

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Sell Immediately Upon Learning: Nash Equilibrium?

Suppose that all others are following the strategy of selling immediately upon learning that growth has stopped (but not before)

Should you sell immediately upon learning yourself?

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How Do Bubbles Persist and Burst? Play the Bubble Game to find out!! Form groups of four or five so that there

are ten groups total• Select one from among you to represent your group.• Discuss among yourselves how to play – no discussion

will be allowed once game begins• Consult hand-out for more detailed info on game

We will play two iterations of the Bubble Game, then discuss for lessons learned

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News and “Overreaction” We have seen that bubbles can exist even

when there are numerous rational players BUT bubble can only persist when these

players are relatively uncertain about when others are going to sell

Even small news events can serve as coordinating devices that allow / force the rational investors all to escape the bubble

The response is not an “overreaction” to the news but the bubble bursting

• Note: This does not explain why the stock market moves a lot with every news story.