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Lujiazui Hedge Fund Inc.
Ryota Arafuka
Kuang-Po Lee
Krunal Naik
Jiaqi Wang
Jianhua Yen
Investment Portfolio Diversification
• Asset allocation diversification
 Horizontal diversification
 Vertical diversification
• Geographic diversification
Hedge Fund Investment Portfolio
Source: “Global Survey Hedge Fund and Investor Survey 2012” by Ernst & Young
Our Investment Style
• Relative value
 Fixed income arbitrage
 Convertible arbitrage
 Equity market neutral
 Event driven
• Directional
 Equity long/short
 Macro
 CTA
Our Objectives
Equal Contribution to
•Weight
- Gives the portfolio diversification
•Variance
- Allocates portfolio variance equally across the
portfolio components
•Risk
- Directly diversify downside risk among
components by using ETL contribution
Random Portfolio
• Random permutations of weights
• Selected criteria
• High frequency long/short
• Multi-strategy
• Model should be self sustained with decisions confined
by set of constraints
• Assign probabilities to strategies corresponding to
calculated risks in given scenario
R Language for Random Portfolio
Application Example
• Total value : $10m
• No. of selected assets for RP=50
• Constraints
 Long-only
 50 to 60 names
 No asset may have more than 4% weight
 Industry spread : 10
 S&P 500, random portfolio, and previous portfolio will be
benchmark
 Duration considered 12 months
 Frequency 10
(Relatively low for us, but this is for testing model)
Cumulative Trading
Comparison of Value with S&P 500
Industries Port wt
Consumer
Discretionary 29.56
Consumer Staples 11.26
Energy 7.01
Financials 4.43
Health Care 11.61
Industrials 9.63
Information
Technology 10.57
Materials 11.42
Telecommunications
Services 0
Utilities 4.51
Total 100
Weight Distribution
Industries Port ret Bench ret
Consumer
Discretionary 7.33 1.36
Consumer Staples -1.13 4.98
Energy 31.2 30.52
Financials 8.41 7.96
Health Care 27.33 7.8
Industrials 17.3 22.47
Information
Technology 14.26 19.65
Materials 84.71 48.53
Telecommunications
Services 0 0
Utilities 3.92 5.96
Total 20.79 13.64
Cumulative Returns
Portfolio optimization Using R
Efficient Frontier
Efficient Frontier with Short-selling
Measure of Portfolio Performance:
•Annualized return
•Annualized standard deviation
•VAR and ES (Expected shortfall)
•Sharp ratio, Omega Ratio, Sortino Ratio
Implementation of R –
Using package PerformanceAnalytics
Code to Create Artificial Stocks
• # create the antithetic pair of stocks and publish it into the environment
• # generate sequence of dates
• times <- seq(as.POSIXct(strptime('2011-01-1 16:00:00', '%Y-%m-%d %H:%M:%S')),
• as.POSIXct(strptime('2011-12-1 16:00:00', '%Y-%m-%d %H:%M:%S')),
• by="1 months")
•
• # generate and store dummy price series = 200,100,200,100,200 ...
• prices.xts <- xts(rep(c(200,100),length(times)/2), order.by=as.POSIXct(times))
• stk <- 'STK1'
• colnames(prices.xts) <- paste(stk,'.Adjusted',sep="")
• assign(x=stk, value=prices.xts, envir=global.env )
•
• # generate and store dummy price series = 100,200,100,200,100 ...
• prices.xts <- xts(rep(c(100,200),length(times)/2), order.by=as.POSIXct(times))
• stk <- 'STK2'
• colnames(prices.xts) <- paste(stk,'.Adjusted',sep="")
• assign(x=stk, value=prices.xts, envir=global.env )
•
• # run the strategy and create a plot
• strategy(portfolio= c("STK1","STK2"),threshold=.9,doplot=TRUE,title="Artificial Portfolio Example")
Download Option Data from Yahoo Finance
• # Goal: download adjusted price data for selected security, convert to returns, and write to output file
•
• library(tseries)
•
• # Load security data from Yahoo! Finance
• prices1 <- get.hist.quote("SPY", quote="Adj", start="2005-12-25", retclass="zoo")
•
• prices1 <- na.locf(prices1) # Copy last traded price when NA
•
• # To make week end prices:
• nextfri.Date <- function(x) 7 * ceiling(as.numeric(x - 1)/7) + as.Date(1)
• weekly.prices <- aggregate(prices, nextfri.Date,tail,1)
•
• # To convert month end prices:
• monthly.prices <- aggregate(prices1, as.yearmon, tail, 1)
•
• # Convert weekly prices into weekly returns
• r.weekly <- diff(log(weekly.prices)) # convert prices to log returns
• r1.weekly <- exp(r.weekly)-1 # back to simple returns
•
• # Convert monthly prices into monthly returns
• r.monthly <- diff(log(monthly.prices)) # convert prices to log returns
• r1.monthly <- exp(r.monthly)-1 # back to simple returns
•
• # Write output data to csv file
• write.zoo(r1.weekly, file="weekly.csv",sep=",",col.names=c("Dates","Percent Return"))
• write.zoo(r1.monthly, file="monthly.csv",sep=",",col.names=c("Dates","Percent Return"))
Code to Generate Random Portfolio
require(PortfolioProbe)
rp100w05 <- random.portfolio(1e4, prices=sp5.close[1,],
gross=1e6, long.only=TRUE, port.size=100,
max.weight=.05)
Then the returns are computed:
sret.rp100w05 <- valuation(rp100w05, prices=sp5.close[c language="(1,1511),"][/c],
returns="simple") lret.rp100w05 <- valuation(rp100w05, prices=sp5.close[c
language="(1,1511),"][/c], returns="log")
R code for Adjusting Weight
> pp.bootsim
function (retmat, weight, times=252)
{ dlar <- retmat[sample(nrow(retmat), times,
replace=TRUE),]
pp.porteval(dlar, weight) }
R Code for Portfolio Optimization
R Code for Portfolio Evaluation
> pp.porteval
function (dlar, weight)
{
(exp(colSums(dlar[, names(weight)])) - 1) %*%
weight
}
Optimization with Truncated Straddle using R
Simulation Result for Portfolio 100

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Random Portfolio using R to create investment strategy for Hedge Fund

  • 1. Lujiazui Hedge Fund Inc. Ryota Arafuka Kuang-Po Lee Krunal Naik Jiaqi Wang Jianhua Yen
  • 2. Investment Portfolio Diversification • Asset allocation diversification  Horizontal diversification  Vertical diversification • Geographic diversification
  • 3. Hedge Fund Investment Portfolio Source: “Global Survey Hedge Fund and Investor Survey 2012” by Ernst & Young
  • 4. Our Investment Style • Relative value  Fixed income arbitrage  Convertible arbitrage  Equity market neutral  Event driven • Directional  Equity long/short  Macro  CTA
  • 5. Our Objectives Equal Contribution to •Weight - Gives the portfolio diversification •Variance - Allocates portfolio variance equally across the portfolio components •Risk - Directly diversify downside risk among components by using ETL contribution
  • 6. Random Portfolio • Random permutations of weights • Selected criteria • High frequency long/short • Multi-strategy • Model should be self sustained with decisions confined by set of constraints • Assign probabilities to strategies corresponding to calculated risks in given scenario
  • 7. R Language for Random Portfolio
  • 8. Application Example • Total value : $10m • No. of selected assets for RP=50 • Constraints  Long-only  50 to 60 names  No asset may have more than 4% weight  Industry spread : 10  S&P 500, random portfolio, and previous portfolio will be benchmark  Duration considered 12 months  Frequency 10 (Relatively low for us, but this is for testing model)
  • 10. Comparison of Value with S&P 500
  • 11. Industries Port wt Consumer Discretionary 29.56 Consumer Staples 11.26 Energy 7.01 Financials 4.43 Health Care 11.61 Industrials 9.63 Information Technology 10.57 Materials 11.42 Telecommunications Services 0 Utilities 4.51 Total 100 Weight Distribution
  • 12. Industries Port ret Bench ret Consumer Discretionary 7.33 1.36 Consumer Staples -1.13 4.98 Energy 31.2 30.52 Financials 8.41 7.96 Health Care 27.33 7.8 Industrials 17.3 22.47 Information Technology 14.26 19.65 Materials 84.71 48.53 Telecommunications Services 0 0 Utilities 3.92 5.96 Total 20.79 13.64 Cumulative Returns
  • 15. Efficient Frontier with Short-selling
  • 16. Measure of Portfolio Performance: •Annualized return •Annualized standard deviation •VAR and ES (Expected shortfall) •Sharp ratio, Omega Ratio, Sortino Ratio Implementation of R – Using package PerformanceAnalytics
  • 17. Code to Create Artificial Stocks • # create the antithetic pair of stocks and publish it into the environment • # generate sequence of dates • times <- seq(as.POSIXct(strptime('2011-01-1 16:00:00', '%Y-%m-%d %H:%M:%S')), • as.POSIXct(strptime('2011-12-1 16:00:00', '%Y-%m-%d %H:%M:%S')), • by="1 months") • • # generate and store dummy price series = 200,100,200,100,200 ... • prices.xts <- xts(rep(c(200,100),length(times)/2), order.by=as.POSIXct(times)) • stk <- 'STK1' • colnames(prices.xts) <- paste(stk,'.Adjusted',sep="") • assign(x=stk, value=prices.xts, envir=global.env ) • • # generate and store dummy price series = 100,200,100,200,100 ... • prices.xts <- xts(rep(c(100,200),length(times)/2), order.by=as.POSIXct(times)) • stk <- 'STK2' • colnames(prices.xts) <- paste(stk,'.Adjusted',sep="") • assign(x=stk, value=prices.xts, envir=global.env ) • • # run the strategy and create a plot • strategy(portfolio= c("STK1","STK2"),threshold=.9,doplot=TRUE,title="Artificial Portfolio Example")
  • 18. Download Option Data from Yahoo Finance • # Goal: download adjusted price data for selected security, convert to returns, and write to output file • • library(tseries) • • # Load security data from Yahoo! Finance • prices1 <- get.hist.quote("SPY", quote="Adj", start="2005-12-25", retclass="zoo") • • prices1 <- na.locf(prices1) # Copy last traded price when NA • • # To make week end prices: • nextfri.Date <- function(x) 7 * ceiling(as.numeric(x - 1)/7) + as.Date(1) • weekly.prices <- aggregate(prices, nextfri.Date,tail,1) • • # To convert month end prices: • monthly.prices <- aggregate(prices1, as.yearmon, tail, 1) • • # Convert weekly prices into weekly returns • r.weekly <- diff(log(weekly.prices)) # convert prices to log returns • r1.weekly <- exp(r.weekly)-1 # back to simple returns • • # Convert monthly prices into monthly returns • r.monthly <- diff(log(monthly.prices)) # convert prices to log returns • r1.monthly <- exp(r.monthly)-1 # back to simple returns • • # Write output data to csv file • write.zoo(r1.weekly, file="weekly.csv",sep=",",col.names=c("Dates","Percent Return")) • write.zoo(r1.monthly, file="monthly.csv",sep=",",col.names=c("Dates","Percent Return"))
  • 19. Code to Generate Random Portfolio require(PortfolioProbe) rp100w05 <- random.portfolio(1e4, prices=sp5.close[1,], gross=1e6, long.only=TRUE, port.size=100, max.weight=.05) Then the returns are computed: sret.rp100w05 <- valuation(rp100w05, prices=sp5.close[c language="(1,1511),"][/c], returns="simple") lret.rp100w05 <- valuation(rp100w05, prices=sp5.close[c language="(1,1511),"][/c], returns="log")
  • 20. R code for Adjusting Weight > pp.bootsim function (retmat, weight, times=252) { dlar <- retmat[sample(nrow(retmat), times, replace=TRUE),] pp.porteval(dlar, weight) }
  • 21. R Code for Portfolio Optimization
  • 22. R Code for Portfolio Evaluation > pp.porteval function (dlar, weight) { (exp(colSums(dlar[, names(weight)])) - 1) %*% weight }
  • 23.
  • 24. Optimization with Truncated Straddle using R
  • 25. Simulation Result for Portfolio 100

Notes de l'éditeur

  1. There are two methods of performance measurement in common use: benchmarks and peer groups. Using a benchmark requires a long time (as in decades) to get reasonable statistical power. Using peer groups looks superficially a lot like using random portfolios. Both use a single time period, both compare our fund of interest to a group of alternative portfolios. CVAR: Unlike Value-at-Risk (VaR), CVaR has all the properties a risk measure should have to be coherent and is a convex function of the portfolio weights