Excel project
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PortfolioOptimizationProject14.pptxPortfolio Optimization
Excel Project
Portfolio Mean-Variance Analysis
To construct a n-Asset portfolio
The expected return on a portfolio is the weighted average of the expected returns of the individual assets in the portfolio.
w1 + w2 + w3 …+ wn = 1
Portfolio variance is the weighted sum of all the variances and covariances:
There are n variances, and n2 – n covariances
All feasible/Attainable portfolios
All feasible/Attainable portfolios lie inside a bullet-shaped region, called the minimum-variance boundary or frontier.
Feasible set
Efficient Portfolios and Efficient Frontier
Mean-Variance Criterion suggests that investors should only choose efficient portfolios. An efficient portfolio is one that offers:
the most return for a given amount of risk, or
the least risk for a give amount of return.
The collection of efficient portfolios is called the efficient frontier for risky securities.
Minimum Variance Portfolio (MVP)
How can we find the weights of the securities so that we can minimize the variance of the portfolio?
The Optimal Risky Portfolio With A Risk-Free Asset
With a risk-free asset available, investors choose the efficient portfolios on the capital allocation line with the steepest slope
E(rA)
A
E(r)
Efficient Frontier for risky portfolio
E(rP)
CAL (M)
P
E(r)
s
The Capital Market Line (CML)
M
E(rP&F)
F
Risk Free
P&F
Efficient Frontier for risky portfolio
E(rP)
P
P&F
E(rP&F)
CAL (M) = CML
The optimal CAL is called the Capital Market Line or CML
The CML dominates the EF for risky portfolio
6-
The Capital Market Line (cont.)
The Capital Market Line (CML) is all linear combinations of the risk-free asset and Tangent Portfolio M and it is the new efficient frontier.
Slope =Sharpe Ratio = (E(rp) - rf) / standard deviation of portfolio, that is the return per unit of risk.
CML maximizes the slope or the return per unit of risk or it equivalently maximizes the Sharpe ratio
What does the CML tell us?
The expected rate of return on any efficient portfolio (p) is equal to the risk-free rate plus Slope of Tangent Portfolio times the risk of the portfolio (p).
Return on P = Risk free rate + Sharpe ratio of Tangent Portfolio x Risk of P
=++×××+=
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