ECON6101模型算法

构建一个为期一个月的持有期金融投资组合3带：分数投资于“无风险资产”的基金的1投资于“综合风险资产”（SRA）的基金的一部分（≥0），该资产由四种投资权重为1的风险资产组成，4（？0和σ=1）“权益#1”中的1“股权#2”中的2个“权益#3”或“石油”中的34在“公司债券”中你是“家族基金”的首席信息官。今天上午（“今天”=2023年1月31日），（规避风险的）董事会（Ivey&Queens毕业生）让你负责项目2（04）：项目02）让我们回到你参加ECO20的时候4并通过四种不同的方法构建金融投资组合，成功实施了“Shred Ivey Queens项目”4 2022-2023A 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 “SyntheticRisky Asset” (SRA) which consists of four risky assets withinvestment 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 & Iveysnobs – by constructing four different models of the Project 2(04) financial portfolio. 2Project 2(04): “Synopsis”Ajaz Hussain, Economics, University of Toronto (STG)ECO204 2022-2023Lecture & Tutorial Portfolios: Quick Review4Agent 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 assetA “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:Fraction 1 of “SRA” in areal Risky Asset 1Fraction
2 of “SRA” in areal Risky Asset 2Fraction 3 of “SRA” in areal Asset 3Agent invests $ of her own funds in a financial portfolio consistingof:Fraction (1 ? ) invested in a RiskFree AssetFraction invested in a “SRA”consisting of ≥ 1 actual riskyassets:Fraction
1 of“SRA” in RiskyAsset 1Fraction 2 of“SRA” in RiskyAsset 2Fraction
3 of“SRA” in RiskyAsset 3Portfolio “A”Portfolio “B”Portfolio “C”Portfolio APortfolio BPortfolio CUse Portfolio A algebra bytreating SRA as “the” risky assetRecall: The “Algebra” of Constructing Portfolio of a Risk Free and Synthetic Risky AssetFor the sake of illustration,suppose the SRA consistsof 3 risky assetsCalculate optimal investment weights of risky assets inSRA by maximizing the SRA’s Sharpe RatioCalculate 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 W12Lecture, W14 Tutorial]Result“Optimal Portfolio” of a Risk-Free-Asset and a SRAconsisting of ≥ 1 risky assets5A “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:Fraction 1 of “SRA” in areal Risky Asset 1Fraction 2 of “SRA” in areal Risky Asset 2Fraction 3 of “SRA” in areal Asset 3Agent invests $ of her own funds in a financial portfolio consisting of:Fraction (1 ? ) invested in a RiskFree AssetFraction invested in a “SRA”consisting of ≥ 1 actual riskyassets:Fraction 1 of“SRA” in RiskyAsset 1Fraction 2 of“SRA” in RiskyAsset 2Fraction 3 of“SRA” in RiskyAsset 3Agent invests $ of her own funds in a financial portfolio consisting of:Fraction (1 ? ) invested in a Risk Free Asset Fraction invested in SRARecall: The “Mechanics” of Constructing Portfolio of Risk Free and Synthetic Risky AssetAjaz Hussain, Economics, University of Toronto (STG)ECO204 2022-2023“Minimal Data” Required to Construct Portfolioof a Risk Free and a Synthetic Risky Asset7“Minimal Data” for Constructing Portfolio with a Risk Free and a Synthetic Risky AssetA “Synthetic Risky Asset” (SRA) consisting of ≥ 1 actual risky assets:Fraction 1 of “SRA” in areal Risky Asset 1Fraction 2 of “SRA” in areal Risky Asset 2Fraction 3 of “SRA” in areal Asset 3Agent invests $ of her own funds in a financialportfolio consisting of:Fraction (1 ? ) invested in a Risk Free Asset Fraction invested in SRAmax1,2,3Sharpe Ratio of SRA =Risk Premium of SRARisk of SRA“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)for = , . . , for , = , . . ,“You”Risk Free:FRED SeriesDGS3MORandomlyassigned“Equity #1”from CRSPRandomlyassigned“Equity #2”fromCRSPRandomlyassigned“Equity #3”from CRSPRandomlyassigned aCorporateBond from aBlackrock ETF“Commodity”:OilFREDSeriesDCOILWTICO8Project 2(04) Assets & “Project 2-ExcelTemplate”Project 2(04): Construct a one-month-holding-periodfinancial portfolio in February 2023 with:Fraction 1 ? of funds invested ina “Risk-Free Asset”Fraction of funds (with ≥ 0) invested in a “Synthetic RiskyAsset” (SRA) consisting of four risky assets with investmentweights , = 1, . . , 41 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-holdingperiod financial portfolio in February 2023 with:Fraction
1 ? of funds invested ina “Risk-Free Asset” FRED Series DGS3MOFraction of funds (with ≥ 0) invested in a “Synthetic RiskyAsset” (SRA)consisting of five risky assets with investment weights , = 1, . . , 51 in Equity #1:APTV3 in “Equity#3”: MTN4 in a “Equity#4”: EXAS5 in a“Corporate-Bond”: SPRINTTo 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 totransform 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 W1
1 on “cleaning” and “pruning” CRSPdata for a common “date range” (see Equities-CRSP-Jun22 tab for demo example). For July 202
2 – Jan 2023 “data”, use Google Sheets in Equities-Google-Jan2
3 tab to download “daily prices”[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 SP50
0 Nominal Index from multpl.com and compute returns for the date range of the “finalequities” data set (See Lecture Delivered W1
1 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 takenote of data-series (monthly yields) corresponding to your bond rating“Commodity -- Oil”:FRED SeriesDCOILWTICO 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 growthrate 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 Asset10“Minimal Data” for Constructing Portfolio with a Risk Free and a SyntheticRisky Asset(Shown for illustrative purposes) The “unified data set of monthly returns” (see ALL-DATA tab)“Month” Equity
1 # # # # # #…Month-N # # # # # #See ALL-DATA tab.Ajaz Hussain, Economics, University of Toronto (STG)ECO204 2022-2023Four Methods for “Estimating” the “Data Required toConstruct Portfolio of a Risk Free Asset and a SyntheticRisky Asset (with = , . . , Risky Assets)Four Methods for “Estimating” the “Data Required to Construct Portfolio of a Risk FreeAsset and a Synthetic Risky Asset (with = , . . , Risky Assets)Stats Stats-ShrinkageMonte-CarloSimulations WienerProcessMonte-CarloSimulations ItoProcessCalculate fraction of funds allocated to SRAFour Methods for “Estimating” the “Data Required to Construct Portfolio of a Risk FreeAsset and a Synthetic Risky Asset”13Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Stats Approach”“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)Asset Expected Return: Future Risk: Future CovarianceRisk Free Asset 0 , = 0Equities ,?Corporate-Bond (Monthly) YTM of Quandl Bond with thesame ratingWhere +1 estimatedby technique used in “GoldClaims” caseoil ,?See Portfolio-Stats tab.Note: Using “baseline ” value such that 100% invested in SRA14Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Stats-Shrinkage Approach”“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)Asset Expected Return: Future Risk: Future CovarianceRisk Free Asset 0 , = 0Equities + 500Corporate-Bond (Monthly) YTM of Quandl Bond with thesame ratingWhere +1 estimatedby technique used in “GoldClaims” caseoil ,?See Portfolio-Stats-Shrinkage tab.Note: Using “baseline ” value such that 100% invested in SRA15Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Monte-Carlo Simulations WienerProcess” Approach”“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)Asset Expected Return: Future Risk: Future CovarianceRisk Free Asset 0 , = 0Equities of the simulations of the simulations ,?Using equity simulationsCorporate-Bond (Monthly) YTM of Quandl Bond with the samerating,?Using equity simulationsOil Prices +1 estimated bytechnique used in “Gold Claims”caseoil ,?Using equitysimulationsAssume equity ~ ,2Simulate (say) 1,000 rounds ofRandomly select simulationsSee RET-Wiener-Process tab and Portfolio-Wiener-Process tab.Note: Using “baseline ” value such that 100% invested in SRA16Constructing Portfolio with a Risk Free and a Synthetic Risky Asset: “Monte-Carlo Simulations WienerProcess” Approach”“Data” for Constructing Portfolio of a Risk Free Asset and a Synthetic Risky Asset (with = , . . , risky assets)Asset Expected Return: Future Risk: Future CovarianceRisk Free Asset 0 , = 0Equities of the simulations of the simulations ,?Using equity simulationsCorporate-Bond (Monthly) YTM of Quandl Bond with the sameratingUsing equity simulationsOil Prices +Where +1 estimated bytechnique used in “Gold Claims”caseoil ,Using equitysimulationsAssume equity ~ 22, 2Simulate (say) 1,000 roundsofRandomly select simulationsSee RET-Ito-Process tab and Portfolio-Ito-Process tab.Note: Using “baseline ” value such that 100% invested in SRA
WX：codehelp