0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Portfolio Selection, Wealth Management And Market Risk

1,019

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
1,019
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
26
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. THE PORTFOLIO SELECTION PROBLEM
• 2. INTRODUCTION
• THE BASIC PROBLEM:
• given uncertain outcomes, what risky securities should an investor own?
• 3. INTRODUCTION
• THE BASIC PROBLEM:
• The Markowitz Approach
• assume an initial wealth
• a specific holding period (one period)
• a terminal wealth
• diversify
• 4. INTRODUCTION
• Initial and Terminal Wealth
• recall one period rate of return
• where r t = the one period rate of return
• w b = the beginning of period wealth
• w e = the end of period wealth
• 5. INITIAL AND TERMINAL WEALTH
• DETERMINING THE PORTFOLIO RATE OF RETURN
• similar to calculating the return on a security
• FORMULA
• 6. INITIAL AND TERMINAL WEALTH
• DETERMINING THE PORTFOLIO RATE OF RETURN
• Formula:
• where w 0 = the aggregate purchase price at time t=0
• w 1 = aggregate market value at time t=1
• 7. INITIAL AND TERMINAL WEALTH
• OR USING INITIAL AND TERMINAL WEALTH
• where
• w 0 =the initial wealth
• w 1 =the terminal wealth
• 8. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
• portfolio return (r p ) is a random variable
• 9. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
• defined by the first and second moments of the distribution
• expected return
• standard deviation
• 10. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
• First Assumption:
• nonsatiation: investor always prefers a higher rate of portfolio return
• 11. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
• Second Assumption
• assume a risk-averse investor will choose a portfolio with a smaller standard deviation
• in other words, these investors when given a fair bet (odds 50:50) will not take the bet
• 12. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
• INVESTOR UTILITY
• DEFINITION : is the relative satisfaction derived by the investor from the economic activity.
• It depends upon individual tastes and preferences
• It assumes rationality, i.e. people will seek to maximize their utility
• 13. THE MARKOWITZ APPROACH
• MARGINAL UTILITY
• each investor has a unique utility-of-wealth function
• incremental or marginal utility differs by individual investor
• 14. THE MARKOWITZ APPROACH
• MARGINAL UTILITY
• Assumes
• diminishing characteristic
• nonsatiation
• Concave utility-of-wealth function
• 15. THE MARKOWITZ APPROACH
• UTILITY OF WEALTH FUNCTION
Wealth Utility Utility of Wealth
• 16. INDIFFERENCE CURVE ANALYSIS
• INDIFFERENCE CURVE ANALYSIS
• DEFINITION OF INDIFFERENCE CURVES :
• a graphical representation of a set of various risk and expected return combinations that provide the same level of utility
• 17. INDIFFERENCE CURVE ANALYSIS
• INDIFFERENCE CURVE ANALYSIS
• Features of Indifference Curves:
• no intersection by another curve
• “ further northwest” is more desirable giving greater utility
• investors possess infinite numbers of indifference curves
• the slope of the curve is the marginal rate of substitution which represents the nonsatiation and risk averse Markowitz assumptions
• 18. PORTFOLIO RETURN
• CALCULATING PORTFOLIO RETURN
• Expected returns
• Markowitz Approach focuses on terminal wealth (W 1 ), that is, the effect various portfolios have on W 1
• measured by expected returns and standard deviation
• 19. PORTFOLIO RETURN
• CALCULATING PORTFOLIO RETURN
• Expected returns:
• Method One:
• r P = w 1 - w 0 / w 0
• 20. PORTFOLIO RETURN
• Expected returns:
• Method Two:
• where r P = the expected return of the portfolio
• X i = the proportion of the portfolio’s initial value invested in security i
• r i = the expected return of security i
• N = the number of securities in the portfolio
• 21. PORTFOLIO RISK
• CALCULATING PORTFOLIO RISK
• Portfolio Risk:
• DEFINITION : a measure that estimates the extent to which the actual outcome is likely to diverge from the expected outcome
• 22. PORTFOLIO RISK
• CALCULATING PORTFOLIO RISK
• Portfolio Risk :
• where  ij = the covariance of returns between security i and security j
• 23. PORTFOLIO RISK
• CALCULATING PORTFOLIO RISK
• Portfolio Risk:
• COVARIANCE
• DEFINITION : a measure of the relationship between two random variables
• possible values:
• positive: variables move together
• zero: no relationship
• negative: variables move in opposite directions
• 24. PORTFOLIO RISK
• CORRELATION COEFFICIENT
• rescales covariance to a range of +1 to -1
• where