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ECO204 real Risky Asset
创建日期：2024-05-20 16:38:25
所属分类：经济Economics
标签： ECO204
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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ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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