ECO9723: Econometrics T&A
Sebastiano Manzan
Fall 2015
Assignment 5: Forecasting VaR
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Submit the problem in Blackboard by 6pm of MONDAY December 14th, 2015
the weight of this problem set is 3% of the overall grade
The problem set is done individually, but you can discuss it with other students
Upload in Blackboard the Word file and the Rmd file
The aim of this assignment is to calculate and compare several risk measures for a portfolio of
two assets. You are assigned two ETFs that represent traded “mutual funds” that give investors
exposure to a wide set of asset classes. Download the adjusted closing price for the two ETFs
assigned to you (see the last two pages of the assignment) at the daily frequency starting from the
oldest date such that both ETFs have historical prices. Create the percentage log-returns using the
usual formula Rt = 100 ∗ ln(Pt /Pt−1 ), where Pt represents the adjusted closing price in day t. Two
possible problems that you might encounter:
• I obtained the tickers from Yahoo Finance and I have not tested whether there is an ETF
(and prices) associated with each ticker; in case your ticker does not exist, pick a substitute
from the following list: DEE, CUT, SIVR, UUP, DBC, TMV, ITB, IWX, NDQ, VCLT
• All ETFs should have at least 5 years of historical prices; in case your ETF has significantly
less (two years of less) replace it with one of the following: IWX, CUT, NDQ, UUP, RFG,
DBC, VCLT, TMV, DEE, ENY
VaR assuming normality
1. Create the portfolio return of holding 40% in ETF 1 and 60% in ETF 2 which is given by
Rp,t = w1 ∗ R1,t + w2 ∗ R2,t , where R1,t and R2,t are the daily returns of ETF 1 and 2 and w1
and w2 are the portfolio weights. Calculate the correlation between the ETF returns and their
descriptive statistics and compare them with the statistics for the portfolio return. Discuss.
2. Calculate 99% VaR for the ETF returns and the portfolio return using EMA with λ = 0.06
and provide a time series plot of the risk measure. Discuss.
3. Calculate the violations of the 99% portfolio VaR starting from the 251st available day until
the end of the sample. Discuss the results in relation to the value that is expected if the risk
model is the true model.
Historical Simulation (HS)
4. Calculate portfolio VaR at 99% based on the HS approach with M = 250 and provide a time
series plot of portfolio risk for EMA and HS. Discuss the differences (if any) between the two
measures.
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5. Calculate the violations of HS VaR and compare the results to those for EMA. Which method
is closer to the expected percentage of violations? [NB: the violation rate for the two methods
refers to to the same set of days since we calculated the violations starting from the 251st day
in point 3]
Portfolio VaR
Let’s consider now the disaggregate approach to risk calculation which requires to forecast the
volatility of each ETF, in addition to also forecast the covariance/correlation between the two assets.
6. Forecast the variance of the daily returns for the two ETFs using EMA(0.06) and provide a
time series plot of their standard deviation (volatility). Discuss the similarities/differences
between the two volatility series.
7. Forecast the covariance of the daily ETF returns using the EMA(0.06) approach. Provide
a time series plot of the correlation between the two assets for λ = 0.06 and λ = 0.01 and
discuss:
• if there evidence to argue that the correlation between the ETF is varying over time
• the effect of changing the smoothing parameter
8. Calculate portfolio 99% VaR assuming normality and using the same weight as above. Provide
a time series plot of the individual ETFs and portfolio VaR and discuss the results. Calculate
the violation rate for portfolio VaR and compare the results with the methods considered
earlier.
The assigment should be done in Rstudio by creating a new file: File -> New File -> R Markdown
and in the next window select Word as the output format. Save the file in your drive and compile it
by clicking on the Knit Word button which opens up the document in Word (Office or OpenOffice).
Upload the Word document in Blackboard under Assignment 5.
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First Name
ETF 1 TICKER 1
Abul Fazal
iShares International Treasury Bond
IGOV
Matthew
Vanguard Mid-Cap Value ETF
VOE
Lizi
SPDR\xc2 S&P International Indl Sect ETF
IPN
Han
Columbia Core Bond ETF
GMTB
Duc
United States Short Oil ETF
DNO
Canberk
PowerShares DWA Emerging Markets Mom ETF
PIE
Ryan SPDR\xc2 Dow Jones Global Real Estate ETF
RWO
Cheng
DB Base Metals Double Long ETN
BDD
Haoxiang
PIMCO Short Term Municipal Bond Actv ETF
SMMU
Dung
CurrencyShares\xc2 Swiss Franc ETF
FXF
Jeffrey
First Trust NASDAQ-100 Equal Wtd ETF
QQEW
Qing
iShares Asia Developed Real Estate
IFAS
David
First Trust ISE Global Platinum ETF
PLTM
Yiping
PowerShares Dynamic Food & Beverage ETF
PBJ
Joyce
iShares S&P Mid-Cap 400 Value
IJJ
Indhira
SPDR\xc2 S&P 600 Small Cap ETF
SLY
Kathleen First Trust Cnsmr Staples AlphaDEX\xc2 ETF
FXG
Joshua
Global X China Financials ETF
CHIX
Xingxin
iShares US Financials
IYF
Andrea
iShares MSCI EMU
EZU
Minqi
iShares International Dev Rel Est
IFGL
William
iShares MSCI ACWI
ACWI
Yanran
iPath\xc2 Bloomberg Lead SubTR ETN
LD
Xiaolei
PowerShares Golden Dragon China ETF
PGJ
Ming
ProShares Short MidCap400
MYY
First Name
ETF 2 TICKER 2
Abul Fazal
iShares iBoxx $ Invst Grade Crp Bond
LQD
Matthew
iShares Globl Consumer Discretionary
RXI
Lizi
iShares S&P Small-Cap 600 Value
IJS
Han
PowerShares 1-30 Laddered Treasury ETF
PLW
Duc SPDR\xc2 Barclays Long Term Treasury ETF
TLO
Canberk
Guggenheim S&P Global Div Opps Idx ETF
LVL
Ryan
Vanguard FTSE All-World ex-US ETF
VEU
Cheng
PowerShares DB Gold ETF
DGL
Haoxiang
iShares Russell Mid-Cap Value
IWS
Dung
First Trust ISE Global Platinum ETF
PLTM
Jeffrey
PowerShares S&P SmallCap Energy ETF
PSCE
Qing
PowerShares S&P SmallCap Utilities ETF
PSCU
David
ProShares Ultra Health Care
RXL
Yiping
ProShares Ultra Real Estate
URE
Joyce
iShares Russell Top 200
IWL
Indhira
iShares Interm Government/Credit Bd
GVI
Kathleen
Vanguard Total World Stock ETF
VT
Joshua PowerShares DWA Cnsmr Cyclicals Mom ETF
PEZ
Xingxin
iShares Russell 1000 Growth
IWF
Andrea
ProShares Ultra Russell2000
UWM
Minqi PowerShares DWA Emerging Markets Mom ETF
PIE
William
CurrencyShares\xc2 Japanese Yen ETF
FXY
Yanran
iShares China Large-Cap
FXI
Xiaolei
iShares 1-3 Year International Trs Bd
ISHG
Ming
iPath\xc2 JPY/USD Exchange Rate ETN
JYN
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