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Pertemuan 3 effisien frontier. harry m
1.
2. Readings for this week
▫ Chapters Seven and Eight in book draft
▫ Online to the various sites that define
statistics like mean, variance, standard
deviation, covariance and correlation
September
28, 2017
3. Harry Markowitz
September
28, 2017
As a graduate student in Economics
at University of Chicago in the 1950s,
Harry wanted to know how to optimally
construct a portfolio of stocks
In order to make any headway,
Harry had to decide how to describe
(define) a stock. So, what to do?
4. A Stock is a Probability Distribution of
Returns
according to Harry
September
28, 2017
Returns
mean
9. Mean-Variance (Harry Markowitz, 1955)
• Each asset defined as:
▫ Probability distribution of returns
▫ Mean and Variance of the distribution known
▫ Covariances of returns between any two assets are known
▫ Assume no riskless asset (all variances > 0)
• Portfolio is
▫ A collection of assets with a mean and a variance that can be
calculated
▫ Also an asset (no difference between portfolio and an asset)
September
28, 2017
10. Diagram with 2 Assets September
28, 2017
Mean
Standard Deviation = √(Variance)
Asset 1 (μ1, σ1)
Asset 2 (μ2, σ2)
11. and 2
September
28, 2017
September 15, 17, 2015
Mean
Asset 1 (μ1, σ1)
Asset 2 (μ2, σ2)
Portfolio (μP, σP)
σ
Where should the portfolio be in the diagram?
Asset 1 (μ1, σ1)
Asset 2 (μ2, σ2)
Portfolio (μP, σP)
σ
12. Investors will Choose some portfolio among those on the efficient frontier
• Those who wish less risk choose portfolios that are further to the
left on the efficient frontier. These portfolios are those with lower
mean and lower standard deviation
• Investors desiring more risk move to the right along the efficient
frontier in search of higher mean, higher standard deviation
portfolios
September
28, 2017
September 15, 17, 2015