Lecture 2

Copyright © 2018 T Leitch & J Liew

Some Questions

• Q1: Are All Hedge Fund Strategies Created Equal?
• Q2: Should Investors Just Buy the “HF Index”?
• Q3: Is there a correlation factor that can help explain HF returns?
• Hedge Fund Managers’ Video Interviews

are hedge fundsfor suckers?

Choices, Chooices, Choices

Consider:

Hedge Fund Manager A with a Sharpe Ratio of 2.0 vs Hedge Fund Manager B with a Sharpe Ratio of 1.5

Which one should we invest in?

How to Measure?

• Are we measuring risk/return correctly?
• How liquid are the underlying investments? Does it matter?
• What are the hidden risks associated with less-liquid or illiquid securities/investing?
• Can we quantify it?
• Unstable relationships, how unstable?
• How do we even begin?

Hedge Funds Hedge?

“Do Hedge Funds Hedge?” by Asness et al

• Yes, hedge funds can provide significant diversification for traditional portfolios
  
• Examine, empirically, hedge fund indices CSFB/Tremont 1994-2000 (monthly data)
  

• Simple regression shows modest market exposure and positive value added
  
  But, this is very misleading…
  

• Since some HFs have illiquid securities and difficult to price OTC securities
• Positive serial correlation exists due to “stale” or “managed” prices

• Once lagged betas are employed, find that hedge funds do not add value over this period

Stale or Manipulated Asset Prices?

• Weisman (2000) argues that hedge funds manage their reported monthly returns – “marketing supportive accounting”
• Stale prices can lower estimates of volatility and correlation to traditional indices
• Likely, Scholes and Williams (1977) and Dimson(1979) have techniques to account for illiquid securities
• Show that employing monthly returns to estimate betas and correlations understate market exposure
• Note study only hedge fund indices not individual hedge funds

Survivorship, Backfill, and Self-selection

• Data CSFB/Tremont (now DJ CS HF indices, employed in HWK1)
  
• Data bias – Survivorship, Backfill, and Self-selection
  
  
  

Monthly vs Quarterly

Notice that monthly versus quarterly estimates of annualized standard deviation differ.

Hedge Fund Volatility

Notice that monthly versus quarterly estimates of annualized standard deviation differ.

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 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 
## -3.0070 -0.8316 -0.0304  0.7718  5.0524 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.1925     0.1225   1.571  0.11883    
## Mkt.RF        1.3574     0.1585   8.562 4.17e-14 ***
## SMB          -0.8318     0.3095  -2.687  0.00821 ** 
## HML          -1.9302     0.3097  -6.232 6.95e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.364 on 121 degrees of freedom
## Multiple R-squared:  0.4736, Adjusted R-squared:  0.4606 
## F-statistic: 36.29 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:

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

Lagged Betas

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

HF Performance

Differences do exist, and appear to be both statistically and economically significant.

Contributions

• “Do Hedge Funds Hedge” helped our industry better appreciate the differences in the return streams generated by the different hedge fund strategies
  
• Forced investors to think about the underlying liquidity of the positions that these hedge fund managers would generally hold
  
• Gave some insight to why a combination of hedge fund index strategies provided diversification benefits

Julian Roberston

HF Questions

• In the early days (circa 2000s), institutional investors’ interest in HFs were peaked
  
• Many questions were asked, such as can investors get “passive” exposure to HFs, similar to the two camps in the mutual fund industry:

1. “active” (e.g. Fidelity) vs (2) “passive” indexing (e.g. Vanguard’s S&P500)?

Given that HF data was suspect, solid conclusions were not possible

Suppose you were working at an “active” fund of funds and tasked with coming up with arguments that blasted the “passive” HF indices, how would you build your case against these indices?

Can we just invest in an index of Hedge Funds?

Q2: Should Investors Just Buy the “HF Index”?

Examination of Long/Short Hedge Fund Managers

Examination of Long/Short Hedge Fund Managers

“Skilled managers are in the minority”

Beta-in-the-Tails robust to different indices construction (at the time)

With greater than 70/30 discernment you can overcome extra fees charged by FOFs

Contributions

- “Hedge Fund Index Investing Examined” questioned the notion of index investing as a prudent means to gain HF exposure
- Helped justify the 1%/10% that FOFs were charging at that time, yippee!
- Results were consistent with actual investors’ experiences in hedge fund index platforms

Mike Novogoratz

oldest hedge fund videos

Q3: Is there a correlation factor that can help explain HF returns?

Reference:
The Effect of S&P500 Correlation on Hedge Fund Alpha, 2012, Jerome B. Baesel et al, The Journal of Wealth Management
Hedge Fund Benchmarking: Equity Correlation Regimes and Alpha, 2013, Jerome B. Baesel et al, Journal of Alternative Investments

S&P Correlation and Alpha

Realized Correlation

Employ the 500 stocks in the S&P500 and compute all possible pair-wise correlations. Plot over time.
Cut into three regimes: (1) Normal, (2) High, and (3) Low
Data from Jan-1990 to Dec-2010

Correlation Rules

Estimate the following model:

Model Specifications

Alphas

Results

Model Specifications

Contributions

• Combine traditional single-/multi-factor hedge fund models with a regime based correlation factor
• Have an intuitive story on why more alpha exists in low correlation environments
• Gives actionable policies in given states-of-nature
• Possible extensions to daily/intra-day analysis

Fama French Resource

Ken French Multi Factor model Website

Izzy Englander

How do you leverage returns?

How do you leverage up returns?

Assume that you want to put in $k > $1, into a risky investment that has a return of R.
Further assume the risk-free borrowing rate is Rf.

The levered returns is:

\[[\$1* R+(\$k-\$1)(R-Rf)]/\$1 = [\$* R-(\$k-\$1)* Rf]/\$1\]

since :

\[R+k* R-k* Rf-R+Rf = R(1+k-1)+Rf* (-k+1) = k* R-(k-1)* Rf\]

Homework Assignment #2