Chapter 6. Mean-Variance Portfolio Theory || Part 3

Diagram of a Portfolio

• Combinations of assets 1 and 2 trace out a curve that includes the two assets
• Exact shape of the curve depends on the covariance of assets 1 and 2
• Solid portion corresponds to positive combinations of the two assets

6.5 The Feasible Set

Feasible Set

• Suppose that there are n basic assets
• We can plot them as points on the mean-standard deviation diagram
• Next imagine forming portfolios from these n assets, using every possible weighting scheme
• Hence, there are portfolios consisting of each of the n assets alone, combinations of two assets, combinations of three, and so forth
• These portfolios are made by letting the weighting coefficients w_i range over all possible combinations
  이 포트폴리오는 모든 가능한 조합에 대한 가중 계수 w_i 범위를 허용함으로써 만들어집니다
• Set of points that correspond to portfolios is called the feasible set or feasible region

Asset이 3개 있을 때(not perfectly correlated and with different mean)

Feasible Set

• Feasible region is convex to the left
• Feasible region is shaped differently based on whether short selling of assets is allowed or not allowed

 

Minimum-Variance Set

• Left boundary of a feasible set is called the minimum-variance set

   

• For any value of the mean rate of return, the feasible point with the smallest variance (or standard deviation) is the corresponding left boundary point

• There is a special point on this set having minimum variance => Minimum-variance point or global minimum-variance (GMV) portfolio

 

Risk Aversion

• For a given mean rate of return, most investors will prefer the portfolio  corresponding to the leftmost point on the line
• ==> Point with the smallest standard deviation for the given mean
• An investor who agrees with this viewpoint is said to be risk averse(리스크 싫엉)
• An investor who would select a point other than the one of minimum standard deviation is said to be risk preferring (or risk seeking)
  minimum standard 이외에 다른 지점을 투자하면 => risk preferring

• We can turn the argument around 90 degrees and consider portfolios corresponding to the various points on a vertical line (portfolios with a fixed standard deviation and various mean values)

• Most investors will prefer the highest point on such a linea => Select the largest mean for a given level of standard deviation

• This arguments imply that only the upper part of the minimum-variance set will be of interest to investors

• Upper portion of the minimum-variance set is termed the efficeint frontier of the feasible region

Efficient frontier: 효율적 투자선, 효율적 경계선