Profitability and Characteristics of Risk Arbitrage : Evidences from Leveraged Buyouts in the U.S.

Professors: Sue-Fung Wang Keh-Luh Wan Student: Chiu-Nan Tsai Graduate Institute of Finance National Chiao Tung University Dec. 11, 2008

1 2008 NTU International Conference on Finance

Outline

1. Introduction2. Literature review3. Research design 3.1. The components of risk arbitrage returns 3.2. Variables definition 3.3. Research hypotheses4. Sample collection and description 4.1. Sample collection 4.2. Distribution of spread returns, risk arbitrage returns and durations 4.3. Descriptive statistics of variables 4.4. Dollar payoffs and realized arbitrage returns in the portfolios

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Outline

5. Model 5.1. Model selection 5.2. Regression analysis 5.3. The predicting of stock reversal6. Empirical results7. Conclusions

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Introduction There has been no research of leveraged buyouts (LBOs) on risk

arbitrage. --Recent empirical studies reported that arbitrageurs can earn

substantially excess returns of 10-20%.

LBOs are the thriving activities around the world in recent years.

There is still some criticism of LBOs. -- Lone Star Funds was guilty of stock manipulation (Feb, 2008)

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LBOs in the U.S. (1991~2006)

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What is risk arbitrage? Risk arbitrage is a trading strategy that attempts to profit from

spreads (the difference of offer price and the market price on the announcement day).

For leveraged buyouts, arbitrageurs usually take a long position of the target firms’ stocks, and hold to the completion day.

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2. Literature Review (1)

Time series analysis An annual abnormal return for the cash offers are 4% (Mitchell & Pulvino

, 2001)

Cross sectional analysis (1) Risk arbitrage for cash tender offers can earn annual abnormal returns

of 24.01% (Jindra & Walkling, 2001). (2) Risk arbitrage for cash offers generates 11.35% of annual excess returns in limited arbitrage (Baker & Savasoglu, 2002) .

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2. Literature Review (2)

Arbitrage spreads returns have positive relation with durations on cash tender offers. (Jindra & Walkling , 2004).

The shorter deals seemed to significantly outperform the longer deals in the North America (Zollo, 2004).

The beta of private equity funds is not a significant driver of performances. (Zollo & Ludo, 2006; Ljunqvist & Richardson, 2003).

Risk arbitrage returns tend to be positively related to the target firm’s size (Jindra & Walkling, 2004; Baker & Savasoglu, 2002)

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2. Literature Review (3)

Most researchers reported that risk arbitrage returns tend to increase with the magnitude of bid premiums (Jindra & Walkling, 2001; Mitchell & Pulvino, 2002; Baker & Savasoglu, 2002).

Liquidity (1) Arbitrage return is negatively related to the stock liquidity (Cornelli &

Li ,2000). (2) There is no reliable relation between excess arbitrage returns and bid- ask spreads (Chen & Kan, 1995) (3) The higher bid-ask spread will be, the greater the proportion of informed investors (Agrawal et al., 2004).

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3. Research design

Where i is per deal PO is the offered price of target firms PF is the final price sold to the acquirers P is the closing stock price on the announcement day is the spread returns is the revision returns is the accumulated dividend is the percentage of transaction cost

i

i

iO

iF

iiO

ii

i

iiF

ii c

PDPPPP

cP

DPPR

iiii cRRSRR

iO

iF

ii PPPRR /

iiO

ii PPPSR /

3.1 The components of risk arbitrage returns

ic

;

iD

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(Jindra &Walkling, 2004)

Offer price

Announcement date Completion date

(effective date)

Unrevised

Downward

Upward

Closing price

Duration

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Table 1 The statistics for spread returns across direction of revision and duration

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Duration

Returns (%)Short

(<93 days)Medium(93-183 )

Lon(>183 days)

Total

Upward Mean1(SR)Mean2 (TR)

4.7714.05

6.3813.98

14.2033.72

8.4520.58

Numbers 16 25 29 70

Unchanged Mean1 (SR)Mean2 (TR)

9.609.60

11.4011.40

57.4057.40

26.1326.13

Numbers 9 11 6 26

Downward Mean1 (SR)Mean2 (TR)

10.54 2.03

13.132.39

13.68-1.22

12.450.97

Numbers 59 107 37 203

Total Mean1 (SR)Mean2(TR)

8.308.56

10.309.26

28.4329.97

16.0115.93

Numbers 84 143 72 299

3.2.Variables definition (1)

Spread returns (SR)

(Po is the offer price; P is the market price on the

announcement day).

Duration (Dur)

The period of the announcement date and the completion or withdrawal date.

Beta (Beta)

A loading factor in the market model.(Target firms stock returns and market

returns, S&P 500 NYSE/AMEX/NASDAQ value-weighted market index).

iiO

ii PPPSR /

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3.2. Variables definition (2) Price-to-book ratio (P/B)

Book value is target equity value at the end of the most recent fiscal year prior to the announcement, and market value is the target market value on the announcement date .

Bid premiums (BP)

, Po is the offer price, and Pb is the closing price one day prior to the announcement day. bb

Oi PPP /

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3.2. Variables definition (3)

Bid-ask spread ratio (Spread)

Abnormal spread divided by normal spread ( bid-ask spread is

where are the asking price and the bid price on transaction day).

(1)Abnormal spread for this measurement is the average ratio in the

interval of t = -42 to t = +2.

(2) Normal spread is the average ratio in the interval of t = –50 to t = –25;

t is the announcement date.

)(2

1bidask

bidask

PPPP

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bidask PP ,

3.3. Research hypothesesH1: Given offer price and durations, spread returns will be negatively

relative with revision returns and positive with durations.

H2: Target firms with both higher bid premium and liquidity have to yield

higher spread returns.

H3: Target firms with less liquidity could easily reverse their price on the

completion date.

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4.1. Sample collection

Period:1991~2006. Region: U.S.A All LBOs are friendly and cash offering. Total samples are 331 (249 successful and 82 failed deal) .

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4.1. Sample collection (2)

We deleted the samples by following principle:

(1) Observations without merger announcement dates,

completion dates, deal size, offer price and bid premiums.

(2) The transaction values are smaller than 10 millions.

(3) The deal type is stock offer and other type.

(4) Rumor deal and secondary LBOs

(5) All target firms are listed companies whose stock price can

not be acquired from the CRSP.

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Table 2 The transaction value and numbers of LBOs (1991~2006)

Completed SDC data Sample (cash offer)  Year Cash offer Success Failure  

Numbers Values(mm$) Numbers Values (mm$) Numbers Values(mm$)

1991 85 6119 4 53 1 391992 98 10,098 3 208 1 81993 93 8,592 5 367 1 481994 85 7,816 4 440 4 2561995 105 13,179 3 2,514 7 11581996 95 18,770 7 1,967 4 1361997 105 21,802 21 8,773 4 5911998 105 20,234 22 6,572 14 3,1601999 131 32,381 37 13,253 11 2,5082000 187 35,020 37 11,804 12 7,5372001 86 10,786 15 3,530 5 2592002 78 23,655 11 1,084 4 4482003 76 22,004 10 2,442 2 3,3132004 138 64,584 15 17,741 5 1,5212005 163 113,679 28 52,012 4 11,4072006 186 295,582 27 85,471 4 5,466Total 1816 704,303 249 666,458 82 37,845

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Table 3 Distribution of the spread returns, revision returns and duration (1)

(%) Mean Min Q1 Median Q3 Max Standard Dev.

Spread returns 11.46 -18.28 2.6143 6.03 14,11 275.00 20.51

Spread returns (Annualize)

41.71 -109.5 8.14 17.40 35.17 946.93 96.23

Revision returns -4.34 -137.50 -2.58 -0.37 0.00 61.85 21.59

Revision returns(Annualize)

-21.87 -1373 -8.88 -1.01 0.00 371.85 109.28

Total returns 7.12 -65.26 0.65 4.24 12.32 261.36 25.55

Total returns(Annualize)

19.84 -683.7 1.91 13.51 33.47 899.98 93.52

Duration 141 14 87.5 127 181 425 75.43

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Table 4 Distribution of the spread returns, revision returns and duration (2)

(%) Mean Min Q1 Median Q3 Max Standard Dev.

Panel A: successful dealSpread returns 9.22 -18.28 2.48 5.05 12.50 80.00 12.24Spread returns (Annualize)

28.14 -104.3 7.10 15.76 31.47 300.21 42.33

Revision returns 1.05 -29.27 -1.08 -0.21 0.00 53.27 8.75Revision returns(Annualize)

0.85 -111.3 -3.93 -0.61 0.00 191.56 22.96

Total returns 10.27 -40.08 2.05 5.08 14.05 86.67 15.27Total returns(Annualize)

28.99 -146.3 6.53 16.31 33.46 300.21 46.22

Duration 141 22 91 126 173 425 71.51Panel B: Failed dealSpread returns 19.34 -6.88 6.19 11.34 20.76 275.00 36.23Spread returns (Annualize)

89.60 -109.5 12.97 28.77 99.69 946.93 181.85

Revision returns -23.35 -137.50 -38.44 -21.62 -0.26 61.85 37.32Revision returns(Annualize)

-102.08 -137.50 -136 -77.76 -0.33 371.85 210.91

Total returns -4.01 -65.26 -26.17 -9.39 7.61 261.36 44.69Total returns(Annualize)

-12.48 683.71 81.52 -19.16 37.70 899.98 176.38

Duration 135 14 63 128 185 405 88.521

Table 5 Distribution of durations

Range(days)

Numbersof obs

Proportion(%)

CumulativeProportion

(%)Downward Unrevised Upward

<30 6 2.00 2.0 4 0 2[30,60) 30 10.03 12 24 3 3[60,90) 40 13.38 25 26 4 10[90,120) 58 19.40 49 41 9 8

[120,150) 51 17.06 62 40 2 9

[150,180) 36 12.04 74 26 2 8

[180,210) 23 7.69 82 13 4 6

>210 55 18.39 100 28 3 24Total 299 203 26 70

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4.2. Descriptive statistics of the characteristic of firms and deals

(1) Most target firms are small cap firms

(2) Manufacturing, Service and Trade sectors.

(3) 75% of firms yield less than 20 % sales growth.

(4) Private equity funds prefer target firms with stable cash flows and lower debts.

(5) Most target firms (about 75%) enjoy high liquidity.

(6) Bid premiums in our final observations are 29% on average.

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4.3. Dollar payoffs and realized returns in two portfolios

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5.1. Regression analysis

where i : ith deal offer SR : spread returns RR : revision returns BP : bid-premium s Dur : durations P/B: price-to-book ratio Beta : market model loading factors Spread : bid-ask spread ratio

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)3()2,0(~65/43210 Niid

iiiSpreadiBetaiBPiDuriBPiRRiSR

5.2. The predicting of stock reversal

)exp(1)exp()(

0

0

ii

iii X

XY

downrevisenonYdownreviseYif

uSpreadBPRmBetaBPDurY

YXg iiiiiiii

i

ii

,0;,1

)4(/)1(1

)1(ln)( 6543210

 

Xi : all independent variables

Dur : duration for every deal.

P/B : price-to-book ratio

Beta : market model loading factor

Rm : market return

BP : bid-premium

Spread : bid-ask spread ratio

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6.1. Results of regression analysis (1)

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OLS GLS 2SLSIntercept -0.0683*

(0.0223)-0.0005(0.9756)

-0.1208**(0.0000)

RR -0.2195**(0.0000)

-0.1994**(0.0000)

-0.1776**(0.0000)

BP 0.4685**(0.0000)

0.2178**(0.0000)

0.7624**(0.0000)

Duration 0.0002(0.0649)

0.0003**(0.0000)

0.0002(0.0733)

P/B 0.0017(0.5829)

-0.0054(0.7640)

-0.0269(0.2327)

Beta -0.0301*(0.0172)

-0.0022(0.9197)

-0.0104(0.4126)

Spread(t=-42,+2)

0.0104(0.4966)

-0.0064(0.6391)

-0.0034(0.7102)

p-value of F <0.0001** <0.0001** 0.0001**Adj-R2 0.4588 0.5463 0.4566Durbin-Watson 1.98 1.91 1.97White heteroscedasticity

<0.001** 0.1036 <0.001**

Normality test <0.001** <0.001** <0.001**

6.1. Results of regression analysis (2)

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Success FailureOLS GLS 2SLS OLS GLS 2SLS

Intercept 0.0090(0.7134)

-0.0001(0.9723)

0.0074(0.8195)

0.4163(0.0172)

-0.0836(0.3633)

-0.5757**(0.0069)

RR -0.2683**(0.0000)

-0.2457**(0.0000)

-0.2681**(0.0000)

0.0246(0.8949)

-0.0138(0.8981)

0.4169*(0.0126)

BP 0.1264**(0.0000)

0.1782**(0.0000)

0.1377**(0.0049)

0.1386*(0.0123)

0.0429**(0.0031)

1.0473**(0.0000)

Dur 0.0003**(0.0027)

0.0004**(0.0000)

0.0004**(0.0029)

-0.0003(0.5094)

-0.0003(0.1998)

-0.0011**(0.0030)

P/B 0.0001(0.8051)

-0.0028**(0.0088)

-0.0006(0.8141)

-0.2720(0.0798)

0.0991(0.2060)

0.4984**(0.0064)

Beta -0.0010(0.9456)

-0.0018(0.9431)

-0.0029(0.8372)

-0.1185**(0.0014)

0.0806(0.4199)

-0.0063(0.8551)

Spread (t=-42,+2) -0.0041(0.5780)

-0.0081(0.5799)

-0.0039(0.8061)

-0.0397(0.5361)

0.0184(0.6797)

0.0168(0.6435)

p-value of F <0.001** <0.001** <0.001** 0.0004** 0.3333 <0.001**

Adj-R2 0.2963 0.5975 0.2610 0.2807 0.3847 0.5225Durbin-Watson 1.94 2.11 2.02 2.04 0.88 1.84White heteroscedasticity

<0.001** 0.1482 0.0003** <0.0001** 0.9603 <0.0001**

Normality test <0.0001** <0.0001** <0.0001** <0.0001** 0.0002** <0.0001**

6.1. Results of regression analysis (3)

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Small bid premium Large bid premiumOLS GLS OLS GLS

Intercept 0.0641**(0.0006)

0.0675**(0.0031)

0.0255(0.8445)

-0.0018(0.5790)

RR -0.1500**(0.0003)

-0.1573**(0.0034)

-0.3228**(0.0004)

-0.2152**(0.0003)

Dur <0.0001(0.8979)

<0.0001(0.9616)

0.0005(0.0888)

<0.0001(0.6259)

P/B -0.0016(0.4713)

-0.0064(0.2031)

-0.1245*(0.0299)

-0.0163**(0.0065)

Beta 0.0096(0.3597)

0.0153(0.4308)

-0.1144**(0.0001)

0.0927(0.1457)

spread (t=-42,+2) -0.0051(0.5582)

-0.0070(0.4773)

0.0912(0.4503)

0.1737**(0.0001)

p-value of F 0.0076** 0.0304* 0.0001** <0.0001**Adj-R2 0.0914 0.0988 0.1878 0.8316Durbin-Watson 1.90 1.76 1.47 2.01White heteroscedasticity 0.0476* 0.4726 <0.001** 0.2078Normality test <0.0001** <0.0001** <0.0001** <0.0001**

6.2 Results of predicting of stock reversal

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Model 1 Model 2(Robustness)

Intercept 0.2439(0.07010)

0.8338*(0.0297)

Dur -0.0049**(0.0032)

-0.0048**(0.0043)

P/B 0.1324*(0.0503)

0.1258*(0.0433)

Beta -0.2074(0.2746)

-0.1763(0.3427)

BP 0.4182(0.2919)

0.4470(0.2760)

Spread (t=-42,+2) 0.8494(0.1210)

Spread (t=-1,+1) 0.2795(0.1497)

P-value of LR statistic 0.0013** 0.0024**McFadden R2 0.0540 0.0524Correlogram-Q test(lag=2)

0.3860.292

0.3480.402

7. Conclusions

Spread returns have negative relation with revision returns. Spread returns are significantly related to durations and bid

premiums. Deals with shorter duration and higher P/B tend to reversal

during the deal. Our result reveals that a portfolio of risk arbitrage positions in

leveraged buyouts produces annual arbitrage returns of 20%.

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