TAILIEUCHUNG - Lecture Financial modeling - Topic 4: Portfolio risk-return optimization

Lecture Financial modeling - Topic 4: Portfolio risk-return optimization. In this chapter students will 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. | Financial Modeling Topic #4: Portfolio Risk-Return Optimization L. Gattis 1 2 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 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 4 Envelope An efficient risky portfolio is one that maximizes return for a given volatility or minimizes volatility for a given return A set of efficient portfolios is called the portfolio envelope or efficient frontier You find an efficient portfolio by running Excel’s Solver add-in. Objective: Max Expected (Mean) Return (or minimize vol) Constraint: Vol = X (or return = Y) Constraint: Sum of Weights = 1 (100%) Optional Constraint: Weights non-negative (no short sales) 5 Envelope – Optimal Risky Portfolio (Minimize σ, given µ, . Ʃwi=1, Wi=0) 6 Insert XY Scatter with Lines (for Envelope Vols and Returns Adding Asset Data Points on graph - Right click on graph, Select data / add - Add series label by editing data Portfolio Choice With No Risk-Free Asset 7 Select an efficient portfolio that meets your risk or return preferences Notice how EFA is dominated Optimal Portfolios With a Risk-Free Asset When you combine a risk free asset and a risky asset (or portfolio), the combined portfolio mean is the weighted average mean and the volatility is the weight in the risky asset times the volatility of the risky asset σCombined = Wrisky x σRisky Portfolio combination of risky and risk free plot along a straight line There is only one portfolio that you will choose to combine with a risk free assets -- the portfolio is at a tangency between a line extending from Rf and the top surface of the envelope. 8 Envelope Rf Tangency – Optimal Risky .

• Tài chính doanh nghiệp
• Financial modeling
• Lecture Financial modeling
• Asset expected return
• Portfolio optimization
• Portfolio risk return optimization
• Modeling support
• Indirect prices
• Direct prices
• Advanced financial modeling
• Financial applications
• VBA variables
• Option explicit
• Financial simulations
• Retirement ratios
• Changing asset allocation
• Financial statement simulation
• Cash flow
• Cash flow models
• User defined function
• Calculating cost of capital
• Portfolio models
• Estimating asset risk
• Asset risk
• Portfolio risk
• Computing portfolio risk
• Portfolio value at risk
• Random walk simulations
• Monte Carlo simulation
• Advanced excel awesomeness
• Web queries
• Array functions
• Bond fundamental value
• Macaulay duration
• Modified duration function
• Income portfolio
• Portfolio duration
• Bond functions
• Default adjusted bond return
• Bond returns
• Adjusting returns
• Accrued interest
• Yield curve models
• Forward rates
• Forward contracts
• Random variables
• Forward contract
• Option contracts
• Monte carlo valuation
• Option contract
• Option pricing model
• Implied vols
• Volatility estimation
• BSM option greeks
• Dynamic delta hedging
• Short sales
• Distribution fitting
• Selecting distributions
• Simulation process