SIM Game Theory to Finance

8/14/2019 SIM Game Theory to Finance

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Applying Game Theory to Finance

I can calculate the motions ofheavenly bodies, but not the

madness of people

- Isaac Newton, upon losing 20,000 in theSouth Sea Bubble in 1720


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David McAdams 2

Game Plan

Hostile Takeovers

Bubbles


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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 Campeaus acquisition of Federated Stores.


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David McAdams 4

Hostile Takeover Plan

Robert Campeau vs. Macys 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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David McAdams 5

Macys vs. Campeau

You are shareholders of Federated,whose share price is $100.

Macys offers you $105 per shareconditional on getting at least 50%

Campeau offers an unconditionaltiered offer


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Macys vs. Campeau

If less than 50% tender to him, then eachgets $110 per share.

If X% > 50% tender to him, then eachgets 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, thenCampeau will be able to buy you out at $80

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


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Macys vs. Campeau

Do you:

Tender to Macys

OR

Tender to Campeau?


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Qwest Bond Swap

Today a federal judge will decide whether Qwestcan proceed with an exchange offer in whichinstitutional investors (in a $1.5B issue) are being

asked to exchange each $1,000 bond for a newone with face value $545. The offer is a coerciveone that will leave bondholders who do not acceptit in the back of line for repayment if Qwest goesbroke

- 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 willfind themselves in a position with some

resemblance to the classic prisonersdilemma... If no one tendered, then Qwestwould be in the same position as before theoffer, and any bondholder would be no worseoff. But if a lot of holders tender, those whorefuse 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 thePrisoners Dilemma?

Why exclude non-institutionalinvestors from the offer?



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?



Qwest: Less Simple Cases

Qwest owes $1.5B w/ assets that are wortheither $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 ofbondholders are excluded from the deal Tender becomes a dominant strategy for the $1.2B who

remain



Qwest Continued: When AllBonds arent Created Equal

In reality, Qwest had many different bondissues it wanted to retire through theseswaps, with different repayment priority.

Qwest also didnt issue its swap offers forall of its issues at once but ratherstaggered the offers

Does the order matter?

Should Qwest swap high-priority bondsfirst or low-priority ones?



Zwest Game

Fictional firm Zwest has threebondholders A,B,C each owed $3M.

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

Absent any tendering, A gets repaid firstfollowed by B, then C. Since assets are always less than $9 million, Zwest

always goes bankrupt and has equity value of $0.



Zwest Game

Zwest will offer A,B,C each to exchangetheir $3M bond for a priority $2M bond.

Those who tender will have higher prioritythan those who dont, but priorityrankings are preserved between thosethat tender and those that dont.

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



Zwest Game #1 (A first)

Zwest makes A decide first whether

or not to tender, then B, then C



Zwest Game #2 (C first)

Zwest makes C decide first whether

or not to tender, then B, then A



Play Zwest Games!

Group into three pairs to play (you and apartner will play together)

Roll a die to see who is A, B, C

With your partner decide which game youwould 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



Play Zwest Games!

Ill inform you which game your

group will be playing

Record the progress and the results

on the sheet given to you


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Commitment

The Power to Constrain anAdversary Depends Upon the

Power to Bind Oneself.- Thomas Schelling



Commitment in theExamples Weve Seen

Campeau committed to paying thehigh price $110 even ifhe failed to

gain control This allowed him to avoid failure, since

shareholders would all want to tender if hewere going to fail

Qwest committed not to renegotiatelater with the non-tenderers


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David McAdams 22

Game within a Game

So far, we have examined hostiletakeovers as a voting game playedamong the targets stockholders

But actually the shareholder vote is agame within a game

Entrenched management, the raider, and othersuitors strategize over influencing shareholdersoptions and incentives in the forthcoming vote That in itself is a game


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David McAdams 24

Saturday Night Specials

From the hostile bidders perspective, the mostcritical element in contrast to substantivematters such as the price offered and the number

of shares sought is speed If the hostile biddercan structure its offer so that target shareholdersmust decide to tender before a competitive bidcan be arranged, a substantial advantage will besecured

- Source, Gibson and Black (1995), The Law and Finance of CorporateAcquisitions


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David McAdams 25

Game within a Game withina Game (within a Game)

Management needs shareholders toapprove a Poison Pill. Thus, shareholdersand management play a game longbefore raider arrives.

Yet one layer deeper: Poison Pills removemanagements incentive to take more

drastic, self-destructive behavior If management can commit to adopt such aScorched-Earth Policy, then shareholders will bemore willing to grant a Poison Pill


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David McAdams 26

Role of Regulation

Players may strategically commit tostrategies that reduce overall gains fromthe game.

Beneficial regulation shapes the optionsavailable to players so that the optionsthey will likely choose lead to better

outcomes. Saturday Night Specials were made illegal by the

Williams Act of 1968, which stipulated that anytender offer must be kept open for at least 20 days.


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Bubbles

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

- Stanley Druckenmiller, former manager of Soros QuantumFund, April 2000.

Julian said, This is irrational and I wont play,

and they carried him out feet first.Druckenmiller said, This is irrational and Illplay, and they carried him out feet first.

- NYTimes April 29, 2000: Another Technology Victim; Soros Fund Manager Says HeOverplayed Hand. (Julian Roberts managed Tiger Hedge Fund, dissolved in 1999.)


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David McAdams 28

Bubbles: Game Plan

1. Newspapers, academics, andcrystal balls

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

3. Bubble Game

4. Lessons learned: Bubble Game


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David McAdams 29

Newspapers, academics, andcrystal balls

Spotting trends

The January Effect


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Spotting Trends

Mark Twain, in Puddnhead Wilson:

October. This is one of the

peculiarly dangerous months tospeculate in stocks in

The others are July, January,

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

and February.


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Spotting trends

Sources: 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 bebad three years in a row!

80% of the time, a nave analyst will identify(with 95% false confidence!) a day of the monthon which the markets have historicallyperformed better than average.


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David McAdams 33

January Effect

Tendency of the stock market to rise

between December 31 and the end of the

first week in January.

Well-documentedby a spate of scholarly

research in the 1980s


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David McAdams 34

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 limitedto 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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David McAdams 35

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

January returns exceptional in 15/16

countries studied.

In Belgium, Netherlands, Italy, January returnexceeds 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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David McAdams 36

What Should You Do?

Careful research has shown thatthere was a January effect from

1900-1980.

Should you go buy small-caps this

December?


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David McAdams 37

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 Januarydefect as investors, trying to get anedge on their competitors, have

jumped earlier and earlier. In somecases the January effect takes placein November or even December.


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Most Recent Research

The Declining January Effect:

Evidences from the U.S. EquityMarkets Source:Quarterly Review of

Economics and Finance v43, n2

(Summer 2003): 395-404


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David McAdams 39

Bubbles

What is a bubble?

How do bubbles start?

How do bubbles persist?

How do bubbles burst?


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David McAdams 41

A Simple Model of Bubbles

Sophisticated investors begin to realizethat the growth spurt has ended after thefactand not all at the same time.

As long as a majority of sophisticatedinvestors stay invested, price continues toincrease at a high rate. (This is an assumption.)

For our purposes, bubble = majority of

sophisticated investors know that growth hasstopped, but still a majority stays invested.

BUT once a majority of sophisticatedinvestors have sold, the nave realizetheir error and the bubble bursts.


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David McAdams 42

How Do Bubbles Start?

You are an investor in the early1700s.

The masses believe that the SouthSeas Companys price is sure to riseat 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 sophisticateshave sold

Player payoffs Once you Sell, you are done and get current price.

If you still own when 3 others have sold, you get currentValue


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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 hasended (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 > 3whereas price keeps on doubling. When bubble bursts, pricefalls 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 dont know if you were the first tolearn, the second, or the last!

S ll I di t l U


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Sell Immediately UponLearning: Nash Equilibrium?

Suppose that all others are followingthe strategy of selling immediately

upon learning that growth hasstopped (but not before)

Should you sell immediately uponlearning yourself?

H D B bbl P i t d


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How Do Bubbles Persist andBurst?

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 BubbleGame, then discuss for lessons learned


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News and Overreaction

We have seen that bubbles can exist even whenthere are numerous rational players

BUT bubble can only persist when these players

are relatively uncertain about when others aregoing to sell Even small news events can serve as

coordinating devices that allow / force therational investors all to escape the bubble

The response is not an overreaction to thenews but the bubble bursting

Note: This does not explain why the stock market moves a lotwith everynews story.

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