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)

9. Cumulative Trading

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

13. Portfolio optimization Using R

14. Efficient Frontier

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
}

24. Optimization with Truncated Straddle using R

25. Simulation Result for Portfolio 100