Xem mẫu
Financial Modeling Topic #4: Portfolio Risk-Return
Optimization
1
References
• Financial Modeling 3rd Edition by Simon Benninga
– Modeling Support
– Ch. 8: Portfolio Models
– Ch. 9: Efficient Portfolios with Short Sales
– Ch. 12: Efficient Portfolios without Short Sales
2
Learning Objectives
• Compute optimal portfolio weights that combine risky portfolios and risk free assets
– Compute efficient (max return/min risk) and optimal risky portfolios
– Compute optimal complete portfolios that combine a risk free asset or borrowing.
3
Data
Asset ExpRet StdDev Weights Correl. SPY EFA EEM Covar SPY EFA EEM SPY 6.50% 16.00% 33.33% SPY 1 0.89281 0.544844 SPY 0.025596 0.025711 0.021792 EFA 6.75% 18.00% 33.33% EFA 0.89281 1 0.612985 EFA 0.025711 0.0324 0.027584 EEM 7.75% 25.00% 33.33% EEM 0.544844 0.612985 1 EEM 0.021792 0.027584 0.0625
Portfolio 7.00% 17.34% 100.00% vols*transpose(vols)* correl σ=MMULT(MMULT(TRANSPOSE(W),S),W)^0.5
Asset ExpRet StdDev Rf 2.00% 0.00%
Rb 5.50% 0.00%
Sharpe
BSharpe
Portolio Vol ExpRet W(SPY) W(EFA) W(EEM) 17.34% 7.00% 33.33% 33.33% 33.33%
Copy,paste,special value,Alt-h-v-v Envelope:Efficient RiskyPortfolioswithNOshort sales(w >=0)
Portolio Vol #1
#2 #3 #4 #5
#6
ExpRet W(SPY) W(EFA) W(EEM) 6.50%
6.75% 7.00% 7.25% 7.50% 7.75%
CAL-B:Optimal BorrowingPortfolio(Tangencyof RbandEnvelope)
CAL:Optimal RiskyPortfolio(Tangencyof Rf andEnvelope) Portolio Vol ExpRet W(SPY) W(EFA) W(EEM)
Portolio ORP
Rf
Vol ExpRet W(SPY) W(EFA) W(EEM)
0.00% 2.00%
Rb 0.00% 5.50% OBP
1.5OBP*
*Portfoliothat isinvested150%inOBBand-50%Rb Optimal CompletePortfolios--TargetingVol
Portfolio Volatility ExpRet W(Rf) W(Rb) W(SPY) W(EFA) W(EEM) Weights W(Risky)
V1 18.00% V2 9.00%
V3 27.00%
0.00%
nguon tai.lieu . vn