Copyright © 2019 T Leitch & J Liew

Agenda

• Alternative Perfoemance Measures
• Beta in the Tails
• Assignment 1

mean return, std dev, & sharpe broken down over time

##  [1] "HFI"           "Converts"      "ShortBias"     "EMF"          
##  [5] "EquityNeutral" "EventDriven"   "Distressed"    "MultiSstrat"  
##  [9] "RiskArb"       "FIArb"         "Macro"         "LongShort"    
## [13] "MngdFuture"    "MultiHFI"      "AllHFI"        "ShortBias.1"  
## [17] "MktNeutral"    "GlobalMacro"   "spx"

## [1] "All Data"

## [1] "2008/Today"

## [1] "1993/2007"

Some stats broken down over time

## [1] "All Data"

## [1] "2008/Today"

## [1] "1993/2007"

Performance Measure - Sharpe Ratio

\[\frac{\overline{r} - r_f}{\sigma}\] For monthly return data

• Compound monthly returns to annualized return:
  
• Monthly standard deviation multiplied by square root of 12 equals annualized standard deviation:

Note the distinctions between raw price differences, simple returns, compounded returns, and continuously compounded returns. Must keep track of what time periods you are using

kable(SharpeRatio.annualized(hfrets[,1:6])) 

Performance Measure - Sortino Ratio

\[ \frac{\overline{r} - r_f}{\sigma^-}\]

Sortino ratio employs a specific measure for only down-side deviations. Note that standard deviation does not distinguish down-side and up-side deviations.

kable(SortinoRatio(hfrets[,1:6])) 

Performance Measure - Sterling/Calmar Ratio

\[ \frac{\overline{r} - r_f}{max(Drawdown)}\]

kable(CalmarRatio(hfrets[,1:6])) 

Sterling ratio differs from Calmar by adding an excess amount to the drawdown as a cushion

Performance Measure - Omega Ratio

Omega Ratio employs the entire distribution of returns. Defined by the probability weighted returns above “threshold” (r) over probability weighted returns below.

kable(Omega(hfrets[,1:6])) 

Are Betas for Hedge Funds Reliable?

• Beta is a good measure for risk under CAPM
• Beta is stable across different states-of-nature
• Do you think this is true for hedge funds?

• How would you test it?

Beta in the Tails

• Let’s look at beta in different parts of the return distribution
• We’ll use z scores for spx to decide whether a point is in the beta calc or not
• We’ll go from z= -2 to z=2

Beta in the Tails: Code

zz=seq(-2,2,by=.1)
beta=rep(0,length(zz))
sig=sd(hfrets[,"HFI"],na.rm=T)
i=0
for(z in zz){
  i=i+1
  if(z<0){
    idxZ=which(hfrets[,"spx"]<z*sig)
    fit=lm(hfrets[idxZ,"HFI"]~hfrets[idxZ,"spx"])
    beta[i]=fit$coefficients[2]
  }
    else if(z==0){
    fit=lm(hfrets[,"HFI"]~hfrets[,"spx"])
    beta[i]=fit$coefficients[2]
    }
    if(z>0){
    idxZ=which(hfrets[,"spx"]>z*sig)
    fit=lm(hfrets[idxZ,"HFI"]~hfrets[idxZ,"spx"])
    beta[i]=fit$coefficients[2]
  }
}
## plot(zz,y=beta,main="Beta for HFI based on tail cohorts (0=all data)",xlab="spx z value threshold")

Beta in the Tails: Code

Also look at CAPM.beta.bear & CAPM.beta.bull in PerformanceAnalytics package (how do they differ from this analysis?)

Case Study

How to Build an Institutional-Grade FOFs Investment Process

Case Study - Screening Process

Case Study - Bifurcated Fund Analysis Model

Case Study - Bifurcated Fund Analysis Model Results

Case Study - Incremental Portfolio Analysis Model

Case Study - Risk Exposures to Consider by Strategy

Mistakes/Limitations

Mistakes/Limitations

Mistakes/Limitations

• Fraud – Biggest Ponzi Scheme (losses unknown est. $10-65B), “split-strike-convergence-trade” by Bernie Madoff, March 2009.

• One-Trader Implosions – Amaranth (Nat Gas trade by Brian Hunter) , loss $6.4B, Sept ’06

• Sowood – Jeff Larson (ex-Harvard endowment) down 50%, sold portfolio to Citadel, in July ‘07

• Tykhe Capital LLC – Quant implosion, down 30% Aug.’07

• Many others…

Assignment 1

• Use data in edhec2
  • For all asset classes other than spx
  • FYI, asset HFI is the index across all asset classes
  • Use spx as the benchmark asset but you may instead use HFI against sector specific hedge funds
• For all data, then from 1997 to end of 2007, and 2007 to now, calulate
  • Sharpe ratio
  • Sortino Ratio
  • CAPM beta
  • Relative Skew & Kurtosis
  • Calmar ratio
  • Jensen’s alpha (use SPY in edhec2)
  • Omega ratio
  • CAPM bull & bear beta (use SPY in edhec2)
  • Information Ratio
  • Treynor Ratio
• Pick one index from edhec2 to graph beta in the tails versus SPY
• For the above, use any table or graph function available to
  • Analyze the different time perdiods
  • Compare different ratios across assets
  • Create a 3 page executive summary in pdf form