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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 wtConsumer
Discretionary 29.56Consumer Staples 11.26
Energy 7.01Financials 4.43
Health Care 11.61Industrials 9.63
Information Technology 10.57Materials 11.42
Telecommunications Services 0Utilities 4.51
Total 100
Weight Distribution
Industries Port ret Bench retConsumer
Discretionary 7.33 1.36Consumer Staples -1.13 4.98
Energy 31.2 30.52Financials 8.41 7.96
Health Care 27.33 7.8Industrials 17.3 22.47
Information Technology 14.26 19.65Materials 84.71 48.53
Telecommunications Services 0 0Utilities 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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