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ECO204 real Risky Asset
Creation date：2024-05-20 16:38:25
Belonging category：经济Economics
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real Risky Asset

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ECO204

A STEP-BY-STEP GUIDE TO PROJECT 2(04)
Project 2(04): Construct a one-month-holding-period financial portfolio in February 2023 with:
Fraction 1 − of funds invested in a “Risk-Free Asset”
Fraction of funds (with ≥ 0) invested in a “Synthetic
Risky Asset” (SRA) which consists of four risky assets with
investment weights 1, . . , 4 ( ⋛ 0 and σ = 1)
1 in “Equity #1” 2 in “Equity #2”
3 in “Equity #3”
OR “Oil”
4 in a
“Corporate-
Bond”
• You are the CIO at a “family-fund”.
• This morning (“today” = Jan 31st 2023), the (risk-averse) Board of Directors (Ivey &
Queens graduates) put you in-charge of Project 2(04):
• Project 2(04) harkens back to time you took ECO204 and aced the “Shred Ivey-
Queens Project” by constructing a financial portfolio by four different methods.
• You’re going to prove your mettle – and once again shred those Queens & Ivey
snobs – by constructing four different models of the Project 2(04) financial portfolio. 2
Project 2(04): “Synopsis”
Ajaz Hussain, Economics, University of Toronto (STG)
ECO204 2022-2023
Lecture & Tutorial Portfolios: Quick Review
4Agent invests $ of her own funds in a financial portfolio consisting of:
Fraction (1 − ) invested in a Risk Free Asset Fraction invested in ONE actual risky asset
A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:
Fraction 1 of “SRA” in a
real Risky Asset 1
Fraction 2 of “SRA” in a
real Risky Asset 2
Fraction 3 of “SRA” in a
real Asset 3
Agent invests $ of her own funds in a financial portfolio consisting of:
Fraction (1 − ) invested in a Risk
Free Asset
Fraction invested in a “SRA”
consisting of ≥ 1 actual risky
assets:
Fraction 1 of
“SRA” in Risky
Asset 1
Fraction 2 of
“SRA” in Risky
Asset 2
Fraction 3 of
“SRA” in Risky
Asset 3
Portfolio “A”
Portfolio “B”
Portfolio “C”
Portfolio A
Portfolio B
Portfolio C
Use Portfolio A algebra by
treating SRA as “the” risky asset
Recall: The “Algebra” of Constructing Portfolio of a Risk Free and Synthetic Risky Asset
For the sake of illustration,
suppose the SRA consists
of 3 risky assets
Calculate optimal investment weights of risky assets in
SRA by maximizing the SRA’s Sharpe Ratio
Calculate optimal fraction invested in “risk free asset”
and “SRA as the risky asset” (with return-risk and
) by maximizing Mean-Variance Utility.
In practice, you’d need the value of parameter [see W12
Lecture, W14 Tutorial]
Result
“Optimal Portfolio” of a Risk-Free-Asset and a SRA
consisting of ≥ 1 risky assets
5
A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:
Fraction 1 of “SRA” in a
real Risky Asset 1
Fraction 2 of “SRA” in a
real Risky Asset 2
Fraction 3 of “SRA” in a
real Asset 3
Agent invests $ of her own funds in a financial portfolio consisting of:
Fraction (1 − ) invested in a Risk
Free Asset
Fraction invested in a “SRA”
consisting of ≥ 1 actual risky
assets:
Fraction 1 of
“SRA” in Risky
Asset 1
Fraction 2 of
“SRA” in Risky
Asset 2
Fraction 3 of
“SRA” in Risky
Asset 3
Agent invests $ of her own funds in a financial portfolio consisting of:
Fraction (1 − ) invested in a Risk Free Asset Fraction invested in SRA
Recall: The “Mechanics” of Constructing Portfolio of Risk Free and Synthetic Risky Asset
Ajaz Hussain, Economics, University of Toronto (STG)
ECO204 2022-2023
“Minimal Data” Required to Construct Portfolio
of a Risk Free and a Synthetic Risky Asset
7“Minimal Data” for Constructing Portfolio with a Risk Free and a Synthetic Risky Asset
A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:
Fraction 1 of “SRA” in a
real Risky Asset 1
Fraction 2 of “SRA” in a
real Risky Asset 2
Fraction 3 of “SRA” in a
real Asset 3
Agent invests $ of her own funds in a financial portfolio consisting of:
Fraction (1 − ) invested in a Risk Free Asset Fraction invested in SRA
max
1,2,3
Sharpe Ratio of SRA =
Risk Premium of SRA
Risk of SRA
=
−

=
1 1 + 2 2 + 3 3 −
1
21
2 + 2
22
2 + 3
23
2 + 21212 + 21313 + 22323
max

U = −
2 = + [] − −
2
“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)
for = , . . , for , = , . . ,
“You”
Risk Free:
FRED Series
DGS3MO
Randomly
assigned
“Equity #1”
from CRSP
Randomly
assigned
“Equity #2”
from CRSP
Randomly
assigned
“Equity #3”
from CRSP
Randomly
assigned a
Corporate
Bond from a
Blackrock ETF
“Commodity”:
Oil FRED
Series
DCOILWTICO
8
Project 2(04) Assets & “Project 2-Excel-Template”
Project 2(04): Construct a one-month-holding-period financial portfolio in February 2023 with:
Fraction 1 − of funds invested in
a “Risk-Free Asset”
Fraction of funds (with ≥ 0) invested in a “Synthetic Risky
Asset” (SRA) consisting of four risky assets with investment
weights , = 1, . . , 4
1 in
“Equity #1”
2 in
“Equity #2”
3 in
“Equity #3”
OR “Oil”
4 in a
“Corporate-
Bond”
Project 2(04) Excel-Template-Demo-Portfolio: Construct a one-month-holding-period financial portfolio in February 2023 with:
Fraction 1 − of funds invested in
a “Risk-Free Asset” FRED Series DGS3MO
Fraction of funds (with ≥ 0) invested in a “Synthetic Risky Asset” (SRA)
consisting of five risky assets with investment weights , = 1, . . , 5
1 in Equity #1:
APTV
2 in “Equity
#2”: CCL
3 in “Equity
#3”: MTN
4 in a “Equity
#4”: EXAS
5 in a
“Corporate-
Bond”: SPRINT
To help you, I’ve posted an “Excel-Template” for the following “DEMO” portfolio 
9“Asset” Comment
“Risk Free Asset”
FRED Series DGS3MO
• Download monthly data via FRED Excel Add-in or FRED website. See FRED-DGS3MO tab and W14 Tutorial on how to
transform FRED data to obtain monthly (by “compounded method”) in Feb 2023.
• By definition: = 0, = 0 for all = 1, . . .
CRSP “Equities”
• See Equity-Bond-Assign tab for CRSP equities assigned to you and download data from CRSP.
• Currently, CRSP reports “returns” through June 2022. See Lecture Delivered W11 on “cleaning” and “pruning” CRSP
data for a common “date range” (see Equities-CRSP-Jun22 tab for demo example).
• For July 2022 – Jan 2023 “data”, use Google Sheets in Equities-Google-Jan23 tab to download “daily prices” 
assume no dividends  calculate monthly −1, =
−−1
−1
[Urge you to look at the Excel “setup” and “formulas”]
• Combine CRSP and Google equities data sets (see Equities-Data tab).
S&P500
• For reasons to be explained later, we will need data on SP500 returns.
• Best option is to download SP500 Nominal Index from multpl.com and compute returns for the date range of the “final
equities” data set (See Lecture Delivered W11 and SP500 tab)
“Corporate-Bond”
• Download the Blackrock-IBHC-ETF file (updated daily) from here “clean/format” the data (see Blackrock-IBHC-
ETF tab)  Extract the row corresponding to your bond  copy & paste & transpose that row in new worksheet
(see DEMO-Sprint tab)
• Use the bond’s ISIN # to find “today’s price” (be creative and put some elbow grease).
• Use “Solver” to compute a “finely-tuned” YTM monthly rate (see Table in Columns H-L in DEMO-Sprint tab).
• Research your corporate-bond rating (AAA, AA, A, B, BB, BBB, CCC)  Go to Corp-Bonds-Quandl tab and take
note of data-series (monthly yields) corresponding to your bond rating
“Commodity -- Oil”:
FRED Series
DCOILWTICO
• NOT in Excel-Template. Download monthly data of Oil prices ($/barrel) via FRED Excel Add-in or FRED website 
Forecast next month’s Oil price by assuming growth rate of Oil prices is Normally distributed and “picking” a growth
rate at random from this distribution (see Gold Claims Case)
Combine the final equities returns data set, SP500 returns data set, Quandl-Bond monthly yield data series corresponding to your bond’s rating,
and the Oil returns data set, over the date range of the “final equities” data set to obtain a “unified” data set (see ALL-DATA tab).
“Minimal Data” for Constructing Portfolio with a Risk Free and a Synthetic Risky Asset
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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