Ch. 7

1
Ch. 7 MODERN PORTFOLIO THEORY (MPT) I.
Investor assumptions A. Utility
B. Risk aversion
 
risk
risk
highly risk tolerant
highly risk averse
 
return
return
 
           
2
INVESTMENT SUMMARY STATISTICS I. Individual
security measures A. Ex-ante (for n
outcomes/states) 1. Expected
return E(ri) S pnrn where pn
probability of state n occurring rn
return expected in state n 2.
Risk (standard deviation) si S pnrn -
E(ri)2 1/2 B. Ex-post (for T historical
observations) 1. Mean
(average) return ra (S rit ) / T
2. Standard deviation siT S rit
- ra2 / T - 11/2 a. Sample vs. population
3
PORTFOLIO MEASURES I. Portfolio
measures (ex-post) A. Covariance sij,T
S (rit - riT) (rjt - rjT) / T-1 (rij
si sj) B. Correlation coefficient rij
(sij,T / si sj ) C. Portfolio return rpT
S wiriT where wi percentage of portfolio
invested in security i D. Portfolio
standard deviation sp S wi2 si2 S S wi wj
si sj rij1/2 II. Portfolio risk decomposition
Weighted average portfolio risk
S wi siT - Portfolio standard deviation
- sp Diversified
risk III. Minimum variance portfolio (MVP)
4
EFFICIENT FRONTIER
40
35
30
25
Return
20
15
10
5
0
0
5
10
15
20
25
30
35
40
Volatility
5
PORTFOLIO SELECTION I. Efficient frontier
A. Quadratic optimization B. Optimal
(market) portfolio max (rp - Rf) / sp
C. MVP D. Use s as risk measure
1. Type of risk(s) sP reflects in well-
diversified portfolio? II. Practical
considerations A. Time period selected (T)
1. Will history repeat? a.
Returns b. Correlations 2.
observations a. Daily/Weekly/Monthly
B. Potential impact on turnover