Copyright © 2018 T Leitch & J Liew

Agenda

• Converts
• Distressed
• Long/Short
  • “13-F for you”
    
  • Gross vs Net
    
  • “Uncovering HF Skill from the Portfolios Holdings They Hide” Agarwal et al. (2013)
    
  • Paulson & Co Example
    
• Merger Arb
  • Cash Only
    
  • Stock for Stock
    
  • Merger Arb Index
    
  • Merger Arb Products
    
• Case: ProShares
• Workshop: Factor Investing

Analysis of Convertible Bonds

Follows: Fabozzi 5th Edition (2004), “Bond Markets, Analysis, and Strategies”

Convertible Bond Terms

• Conversion Ratio – the # of shares of common stock that the bondholder will receive upon conversion (or exercising the call option)
• Upon conversion:
  • Physical Settle – bondholder receives from the issuer underlying shares
  • Cash Settle – bondholder receives cash value of the underlying shares
• Upon issuance of convert, issuer has granted the bondholder the right (but not the obligation) to purchase the common stock at the strike price: \[(par\,value\,of\,the\,convertible\,bond)\,/\,conversion\,ratio\]
• Conversion Value – the value of the bond if it is converted immediately \[Conversion\,Value\,=\,mkt\,price\,of\,common\,stock\,*\,conversion\,ratio\]

Exercise: Consider XYZ Convertible Bond

Maturity: 10 years
Coupon Rate: 10%
Conversion Ratio: 50
Par Value: $1,000
Curr. Mkt price convert: $950
Curr. Mkt price stocks: $17
Dividend per share: $1

The conversion price = ?

Answer

$1,000/50 = $20 (=Strike Price)

Background Info on Convert Industry

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Source: Mongan Stanley

Academic Evidence

• Arshanapalli, Fabozzi, Switzer, and Gosselin (2004), Lain (2006)
  • 70-75% of new issues are bought by hedge funds
• Agarwal, Fund, Loon, and Naik (2010)’s “Risk and Return in Convert Arbitrage: Evidence from the Convertible Bond Market”
  • Document key drivers of convertible arbitrage(CA), namely: (1) “buy-and-hold” strategy and (2) “buy-and-hedge” strategy. Explains about 30-60% R^2
  • Highlight importance of non-price variables such as market-wide events(e.g. LTCM) and the correlation of supply of CAs on performance
  • Larger funds are more active in (2) vs (1), and more vulnerable to supply shocks
  • Convertible arbitrageurs collectively are rewarded for playing the “intermediation” role

Convertible Arb

How to hedge?

What are the risks? Or how do you hedge each component? Interest Rate (bond) + Corporate Default Risk (health of issuer) + Call Option (delta)

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Convert Example

Security Description

Q: What is DHI or D.R. Horton?
Defn: Parity is the market value of stock shares if you converted now
Ex. (76.5697) * $10.49 = $803.216153, quoted as a percentage of par ($1000 or 100%), so you get “80.32” or 80.32% (= $803.216153/$1000)

Defn: Premium is the difference between convert price and parity as percent of parity Premium = (Bond Price – Parity) / Parity Ex. (107.678 – 80.3216153)/ 80.3216153 = 0.340586 or 34.06(%)

DHI 2 05/15/2014

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More convertible bonds…

Convertible Arb Cycle…

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Convert Classification Confusion, even among institutions-quality organizations…

Distressed Securities

Securities (typically bonds/bank loans) of companies that are in default or under bankruptcy protection, or headed for such a “distressed” condition

• Fixed income: LIBOR + 10% (LIBOR+1000bps)

• Ratings of CCC or below (from S&P, Moody’s Fitch)

• Do investors “recover” anything after bankruptcy?
  • Edward I. Altman (NYU Stern Professor)

What do “Distressed” managers hold?

Historical Universe of Defaulted Bonds from NYU Salomon Center Stern School of Business

Performance of Defaulted Bond Index

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Some notable Distressed Hedge Fund Managers

Avenue Capital, Mark Lasry, $12B AUM

Stephen Feinberg, Cerberus Capital
Size: $19.15 billion (1997); Style: Distressed investor; Location: Manhattan
Worked at Drexel Burnham Lambert in the Milken era. King of the vulture investors—currently sniffing around car-company wrecks in Detroit. Likes Republicans: Dan Quayle is on Cerberus team; former Treasury secretary John Snow is chairman.

David Tepper, Appaloosa Management Size: $5.3 billion (1997); Style: Distressed investor; Location: Chatham, N.J. Ran the junk-bond desk at Goldman. Joined ever-growing roster of ex-Goldmanites after founding Appaloosa in 1993. Like Cerberus, lurking around automotive industry. Worked with Cerberus on the Delphi automotive deal.
http://nymag.com/news/features/2007/hedgefunds/30342/
http://www.sec.gov/Archives/edgar/data/1006438/000100643810000003/0001006438-10-000003.txt

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Long/Short

• Long/Short generally refers to an investment strategy employed by hedge fund managers who typically trade stocks. Stocks that are expected to increase/decrease in value are purchased/sold short.
  
• Typically, managers will make investments based on fundamental analysis.This category may contains sector-specific managers as well as those that trade across global markets.
  
• Useful Terms: Gross and Net exposure
  
• Number of positions: ~20-60
  
• Long/Short returns are characterized as having “market” exposure but typically have less volatility than a long-only managers.
  
• Mutual funds have began to offer 130/30 products in direct competition to hedge fund long/short products.

“Gross” vs “Net” Exposure

In order to better understand the risks associated with long/short hedge funds, investors will ask about their “gross” and “net” exposures.
What is this?
Gross Exposure = Total $ Long + abs(Total $ Short)
Net Exposure = Total $ Long – Total $ Short

\[ Total \$ Long = \Sigma^{k}_{i=1}(SharesLong_{i}*Price_{i}) \]
\[ Total \$ Short = \Sigma^{m}_{j=1}(SharesShort_{j}*Price_{j}) \]

Pop Quiz on Gross/Net

Suppose manager A has $100m long, $50 m short. What is her gross and net exposures?

Answer

Gross = $100m + abs(-$50m) = $150m Net = $100m - $50m = $50m

Assuming she had $100m of assets, some refer to Gross as 150% ($150m/$100m) and Net of 50% ($50m/$100m)

How can you learn from the best Long/Short (value) managers?

Let’s make some assumptions… and learn!

• Let’s try to examine what they are holding? How?
  
• What are the benefits?
  
• Limitations?
  
• Will this be a useful exercise?

Who is?

“His trade made his hedge fund $15 billion in 2007 alone. It propelled him from relative obscurity to stardom and his hedge fund to become the third largest in the world.”

http://www.ibtimes.com/top-10-greatest-trades-all-time-253039

Case Study: Paulson & Co

“13-F for you”

Background: Institutional investment managers with more than $100m, must report their holdings in Form 13F with SEC. Positions are publically disclosed within 45 days after the end of each quarter.

Some say that: “13F information is released with such a long lag, this can’t be useful…”

http://www.sec.gov/answers/form13f.htm

Steps to construct “13-F for you”

Step 1: Visit www.sec.gov, search for hedge fund of interest, helpful if manager builds positions over time, i.e. value-trained better than high-frequency, why?
http://www.sec.gov/cgi-bin/browse-edgar?action=getcompany&CIK=0001035674&owner=exclude&count=40

Step 2: Ex. Look up “Paulson & Co” or CIK: 0001035674 (Central Index Key)

Step 3: Find 13-F information http://www.sec.gov/Archives/edgar/data/1035674/000114036113021112/0001140361-13-021112-index.htm

Step 4: Cut into excel, parse it, combine with price data,
Note: securities are assigned by CUSIP, need a map to tickers

Step 5: Examine historical performance

Paulson’s 13-F top positions over the past 3 quarters

Let’s examine the historical performance of the 5 largest positions from 9/30/2012: What portion of his portfolio does the 5 largest position represent? Did he beat the “market”?

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Let’s look at Paulson’s recent holdings…

“Uncovering Hedge Fund Skill from the Portfolios They Hide”

Background Info

• The 13F rule give the SEC discretion to delay disclosure if the information is deemed “necessary or appropriate in the public interest or for the protection of investors”
• Thus, filers may request confidential treatment for certain holdings on their 13F pending approval by the SEC
• If the request is denied, filers must reveal those holdings by filing an amendment to their original 13F/A
• HFs account for 56% of all confidential fillings, however only make up 30% of all institutions (eg. HFs, Investment Company/Advisor, Bank and Insurance)

Contributions

• Paper examines performance and informational content of institutional investor’s holdings by incorporating confidential holdings and comparing results to original holdings
• Sheds light on stock-picking abilities of hedge funds
• Documents affect of portfolio disclosure on money managers, especially hedge funds
• Examines mandatory ownership and holdings disclosures rules

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45.7% = (106/232), 30.2% = (942/3,134)

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“The triggering event for the 1998 rule tightening was the confusion over the 13F reporting of investor Warren Buffett, which caused a significant decline in the share price of Wells Fargo & Co. in August 1997. The 13F form did not show Berkshire Hathaway’s well-known 8% stake in the bank because it was reported in a confidential filing. But the misunderstanding in the market caused Wells Fargo’s stock price to drop 5.8% in 1 hour after Buffett’s 13F Filing.”

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Hedge Funds — Confidential vs Original Holdings

Statistically Significant Differences:

Stocks are smaller, more value, less analysts’ coverage, higher probability of default, more volatile both absolute and relative, and higher number of announced merger targets in prior year

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How can we combine, 13-F info and publically announced merger info?

First, learn how to implement

Merger Arb:

1. Cash and
   
2. Stock for Stock

Merger Arb

1. Cash Deal
   Ex. Cash deal, Intel acquires McAfee for $48 per share
   Deal terms below:
   
   The announcement date is 8/19/2010, what do you think happens to the price of McAfee around the announcement date?

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Announcement date 8/19/2010, price spikes upward toward $48, why not all the way?

Top Deals

Stock for Stock Deal

Ex. Stock for stock deal, FirstEnergy to acquire Allegheny for 0.667 (Aq sh/Tg sh)

Upon completion (0.667 * FE) will equal AYE,
So, trade is to (1) buy the target AYE and (2) sell 0.667 of acquirer FE

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Stock for stock deal: AYE vs 0.667 * FE

Upon completion for every 1,000 shares of AYE, holders will receive 667 shares of FE.

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Pulling it all together, 13-Fs and merger announced deals: Merger Arb Index

Easy Construction

• Step 1: Start with a sample list of hedge fund managers that employ merger arbitrage

• Step 2: Incorporate publicly available information to find positions

• Step 3: Count the number of overlapping positions each quarter, if over 3 positions include in portfolio

• Step 4: Hedge accordingly: cash, stock only, stock and cash, stock or cash, exclude exotic deals(collars).

• Step 5: Weigh each position by count divided by sum of all counts

• Step 6: Re-balance each quarter

Hedge Fund Manager List and Rebalance Date

Hedge Fund Manager List
1. Brencourt Advisors LLC
2. EAC (Soros) Management, LP
3. Eton Park Capital Management, L.P.
4. Glazer Capital, LLC
5. Gruss Asset Management LP
6. Halcyon Asset Management LLC
7. Paulson & Co Inc
8. Shorewater Advisors LLC
9. Taconic Capital Advisors LP
10. Westchester Capital Management, Inc.

Ex. Positions Over Time (Quarters)

Example for 9/30/2009

If deal consummates then leave final-value in index until next re-balancing period.

Historical Back-Test*

Merger Arb Benchmark Index
Annual Returns: 17.4%
Annualized Standard Dev.: 6.0%
Sharpe Ratio (2% Rf): 2.57
232 days from Feb 17, 2009 to Jan 15, 2009

HFRX Merger Arb Index

Annual Returns: 7.6%
Annualized Standard Dev.: 3.0%
Sharpe Ratio (2% Rf): 1.86
231 days from Feb 17, 2009 to Jan 14, 2009

Twice as volatile as HFRX Merger Arb but more than twice the historical returns results in higher Sharpe Ratio

• Please note that this back-test is only indicative and without transaction costs. Past performance is no indication of future performance.

Conclusion

• Introduce a simple investable Merger Arb Benchmark Index to benchmark hedge fund managers’ performance

• Index construction methodology - unique and theoretically sound combining 13F positions and announced merger transactions

• Back-test shows historically strong risk-adjusted returns, yielding a Sharpe Ratio of 2.57 gross of transaction and market impact costs over time-period examined

• Will this be useful benchmark for the institutional investors?

Current Merger Arb Products

Performance of MERFX

Over a longer time-span looking at monthly date, we find a slight edge to the index of risk-arb managers versus one position-level merger arb mutual fund (MERFX)

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Some Investment Models to Generate Alpha from CAPM Extensions

Sharpe-Lintner’s CAPM:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + \varepsilon_{i,t}\]

Fama-French’s 3 Factor Model:

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + \varepsilon_{i,t}\]
Carhart’s Model:

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + m_{i}WML_{t} + \varepsilon_{i,t}\]

Lagged Betas

Apply Scholes and Williams (1977) and Dimson (1979) simple techniques

\[R_{i,t} = \alpha_{i} + \beta_{0i}R_{m,t} + \beta_{1i}R_{m,t-1} + \beta_{2i}R_{m,t-2} + \beta_{3i}R_{m,t-3}+...+\varepsilon_{i,t}\]

Sharpe-Lintner’s CAPM: Sharpe Screening with PeerPerformance Package

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + \varepsilon_{i,t}\]

library("PeerPerformance", lib.loc="/opt/microsoft/ropen/3.4.3/lib64/R/library")
hfrets=readRDS("data/hfrets.rds")[,1:10]

## Sharpe screening 
knitr::kable(cbind(HFname=colnames(hfrets),outperform=sharpeScreening(hfrets, control = list(nCore = 1))$pipos))

## Modified Sharpe screening 
knitr::kable(cbind(HFname=colnames(hfrets),outperform=msharpeScreening(hfrets, control = list(nCore = 1))$pipos))

## Alpha screening
ctr = list(nCore = 1)
knitr::kable(cbind(HFname=colnames(hfrets),outperform=alphaScreening(hfrets, control = ctr)$pipos))

Fama-French’s 3 Factor Model:

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + \varepsilon_{i,t}\]

library(quantmod)
source("http://www.stat.cmu.edu/~cschafer/MSCF/getFamaFrench.txt")

#Get Fama French factors
ffhold = getFamaFrench(from="2012-1-1", to="2012-6-30")

#Get Apple stock's data
AAPL=getSymbols("AAPL", from="2012-1-1", to="2012-6-30", auto.assign=F)

#Find excess return
ffhold$AAPLexret = 100*dailyReturn(AAPL) - ffhold$RF

#Multiple Linear Regression
ff3modAAPL = lm(AAPLexret ~ Mkt.RF + SMB + HML, data=ffhold)

#Summary of regression
summary(ff3modAAPL)

## 
## Call:
## lm(formula = AAPLexret ~ Mkt.RF + SMB + HML, data = ffhold)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0164 -0.8426 -0.0340  0.7748  5.0299 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.1908     0.1225   1.558  0.12190    
## Mkt.RF        1.3617     0.1584   8.597 3.45e-14 ***
## SMB          -0.8402     0.3082  -2.726  0.00735 ** 
## HML          -1.9321     0.3091  -6.251 6.35e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.363 on 121 degrees of freedom
## Multiple R-squared:  0.4744, Adjusted R-squared:  0.4613 
## F-statistic:  36.4 on 3 and 121 DF,  p-value: < 2.2e-16

Sharpe-Lintner’s CAPM Rewritten for Execution

\[\alpha_{i} = R_{i,t} - \beta_{i}R_{m,t} - \varepsilon_{i,t}\]

• To go long \(\alpha_i\) buy asset i and sell \(\beta_i\) time the asset i position of the index short with a derivative - expected return is \(\alpha_i\)
• To go short \(\alpha_i\) sell asset i short and buy \(\beta_i\) times the asset i position of the index short with a derivative - expected return is \(-\alpha_i\)
• These are market neutral positions and can be excuted independtly for each asset

Fama-French’s 3 Factor Model Rewritten for Execution

\[\alpha_{i} = R_{i,t} - \beta_{i}R_{m,t} - s_{i}SMB_{t}- h_{i}HML_{t} -\varepsilon_{i,t}\]

• Can still take out market factor with long/short index position, but left with SMB and HML factors
  
• There are not futures/derivatives on SMB or HML
  
• Solution is portfolio construction:
  • Select weight for asset allocation to asset i, \(\omega_i\), such that \(\sum\omega_i s_i=0\) and \(\sum\omega_i h_i=0\)
    
  • This leave the portfolio neutral to SMB, HML, and, using future as last step, \(R_m\)
    
  • This portfolio is expected to earn \(\sum\omega_i \alpha_i\)
    
  • To optimize return, maximize \(\sum\omega_i \alpha_i\) subject to \(\sum\omega_i s_i=0\) and \(\sum\omega_i h_i=0\) and then hedge residual \(R_m\) with future
• This will be similar process for other multi factor models such as Carhart, Fama-French 5 factor
  
• Note we could look at individual securities above, but now we have to execute an ensemble to achieve market neutral \(\alpha\)

Last step for portfolio contruction

Optimise for Sharpe by minimizing \(sigma(P)\)

• Remember there is en \(epsilon_i\) for each security
• Find \(\sum\omega_i \alpha_i/\sum\omega_i\omega_j \rho_{i,j}\sigma_i\sigma_j\) such that \(\sum\omega_i s_i=0\) and \(\sum\omega_i h_i=0\)
• Similar for Sharpe Lintner, maximize Sharpe but w/o added contraints

Sharpe-Lintner’s CAPM: Sharpe Screening with PeerPerformance Package

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + \varepsilon_{i,t}\]

library("PeerPerformance", lib.loc="~/R/x86_64-pc-linux-gnu-library/3.4")
hfrets=readRDS("data/hfrets.rds")[,1:10]

## Sharpe screening 
knitr::kable(cbind(HFname=colnames(hfrets),outperform=sharpeScreening(hfrets, control = list(nCore = 1))$pipos))

## Modified Sharpe screening 
knitr::kable(cbind(HFname=colnames(hfrets),outperform=msharpeScreening(hfrets, control = list(nCore = 1))$pipos))

## Alpha screening
ctr = list(nCore = 1)
knitr::kable(cbind(HFname=colnames(hfrets),outperform=alphaScreening(hfrets, control = ctr)$pipos))

Fama-French’s 3 Factor Model:

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + \varepsilon_{i,t}\]

library(quantmod)
source("http://www.stat.cmu.edu/~cschafer/MSCF/getFamaFrench.txt")

#Get Fama French factors
ffhold = getFamaFrench(from="2012-1-1", to="2012-6-30")

#Get Apple stock's data
AAPL=getSymbols("AAPL", from="2012-1-1", to="2012-6-30", auto.assign=F)

#Find excess return
ffhold$AAPLexret = 100*dailyReturn(AAPL) - ffhold$RF

#Multiple Linear Regression
ff3modAAPL = lm(AAPLexret ~ Mkt.RF + SMB + HML, data=ffhold)

#Summary of regression
summary(ff3modAAPL)

## 
## Call:
## lm(formula = AAPLexret ~ Mkt.RF + SMB + HML, data = ffhold)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0164 -0.8426 -0.0340  0.7748  5.0299 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.1908     0.1225   1.558  0.12190    
## Mkt.RF        1.3617     0.1584   8.597 3.45e-14 ***
## SMB          -0.8402     0.3082  -2.726  0.00735 ** 
## HML          -1.9321     0.3091  -6.251 6.35e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.363 on 121 degrees of freedom
## Multiple R-squared:  0.4744, Adjusted R-squared:  0.4613 
## F-statistic:  36.4 on 3 and 121 DF,  p-value: < 2.2e-16

## Compare with Sharpe Lintner
#Multiple Linear Regression
ff3modAAPL = lm(AAPLexret ~ Mkt.RF, data=ffhold)

#Summary of regression
summary(ff3modAAPL)

## 
## Call:
## lm(formula = AAPLexret ~ Mkt.RF, data = ffhold)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2657 -0.9862 -0.1751  0.7242  7.0587 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.2184     0.1418   1.540    0.126    
## Mkt.RF        1.1091     0.1597   6.947 1.92e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.58 on 123 degrees of freedom
## Multiple R-squared:  0.2818, Adjusted R-squared:  0.2759 
## F-statistic: 48.26 on 1 and 123 DF,  p-value: 1.916e-10

Carhart’s Model:

\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + m_{i}WML_{t} + \varepsilon_{i,t}\]

Boring Old Factors…

Cumulative Returns

Spice it Up: Simple Trend Model

New Results

New Cumulative Returns

Comparing EW vs EW* (+36%!)