1 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Fin 2802: Investments Spring, 2010 Dragon Tang Lecture 18 Optimal Investment Portfolio March 30, 2010 Readings: Chapter 7 Practice Problem Sets: 1-15, 17-21

2 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Optimal Portfolio Choice Objectives: Show how covariance and correlation affect the power of diversification Construct efficient portfolio Calculate the composition of the optimal risky portfolio Take risk wisely!

3 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Diversification and Portfolio Risk Market risk or beta risk –Systematic or Nondiversifiable Firm-specific risk –Diversifiable or nonsystematic

4 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Portfolio Risk as a Function of the Number of Stocks

5 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Portfolio Risk as a Function of Number of Securities

6 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Two Asset Portfolio Return – Stock and Bond

7 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Covariance  1,2 = Correlation coefficient of returns  1,2 = Correlation coefficient of returns Cov(r 1 r 2 ) =    1  2  1 = Standard deviation of returns for Security 1  2 = Standard deviation of returns for Security 2  1 = Standard deviation of returns for Security 1  2 = Standard deviation of returns for Security 2

8 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Correlation Coefficients: Possible Values If  = 1.0, the securities would be perfectly positively correlated If  = - 1.0, the securities would be perfectly negatively correlated Range of values for  1, <  < 1.0

9 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Two Asset Portfolio St Dev – Stock and Bond

10 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio r p = Weighted average of the n securities r p = Weighted average of the n securities  p 2 = (Consider all pair-wise covariance measures)  p 2 = (Consider all pair-wise covariance measures) In General, For an n-Security Portfolio:

11 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Numerical Example: Bond and Stock Returns Bond = 6%Stock = 10% Standard Deviation Bond = 12%Stock = 25% Weights Bond =.5Stock =.5 Correlation Coefficient (Bonds and Stock) = 0

12 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Return and Risk for Example Return = 8%.5(6) +.5 (10) Standard Deviation = 13.87% [(.5) 2 (12) 2 + (.5) 2 (25) 2 + … 2 (.5) (.5) (12) (25) (0)] ½ [192.25] ½ = 13.87

13 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Investment Opportunity Set for Stock and Bonds

14 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Investment Opportunity Set for Stock and Bonds with Various Correlations

15 Table 7.1 Descriptive Statistics for Two Mutual Funds FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio

16 Table 7.3 Expected Return and Standard Deviation with Various Correlation Coefficients FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio

17 Figure 7.3 Portfolio Expected Return as a Function of Investment Proportions FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio

18 Figure 7.4 Portfolio Standard Deviation as a Function of Investment Proportions FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio

19 Figure 7.5 Portfolio Expected Return as a function of Standard Deviation FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio

20 Table 7.4 Risk Reduction of Equally Weighted Portfolios in Correlated and Uncorrelated Universes FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio

21 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Portfolio Selection Asset allocation Security selection These two are separable!

22 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Asset Allocation John Bogle: “Asset allocation accounts for 94% of the differences in pension fund performance” Identify investment opportunities (risk-return combinations) Choose the optimal combination according to investor’s risk attitude

23 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Optimal Portfolio Construction Step 1: Using available risky securities (stocks) to construct efficient frontier. Step 2: Find the optimal risky portfolio using risk- free asset Step 3: Now We have a risk-return tradeoff, choose your most favorable asset allocation Step 4: Calculate optimal portfolio weights

24 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Portfolios Constructed from Three Stocks A, B and C

25 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio The Efficient Frontier of Risky Assets and Individual Assets

26 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Optimal Capital Allocation Line for Bonds, Stocks and T-Bills

27 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio The Complete Portfolio

28 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio The Complete Portfolio – Solution to the Asset Allocation Problem

29 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Discussion: Practical Portfolio Rules Rule #1: do not be a amateur stock trader (don’t do it or do it full time!), choose to be a trader or investor first! Investment philosophy: define value! Be cost cautious! Investment psychology: do not chicken out! –Don’t get sentimental, history doesn’t matter –Stop loss and let your winner run –… Research, research, research! Sector rotation, familiarity, estimation risk Offense wins game, defense wins championship Amateurs practice until they get it right, pros practice until they can’t get it wrong.

30 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Investor Personalities Measured investors: Rich and greedy Reluctant investors: Rich and humble Competitive investors: Like to trade, which is hazardous Unprepared investors: Poor, greedy, and ignorant

31 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Mistakes Investors Make Overconfident, underestimate market force Short-sighted, resulting in unnecessary transactions Mental accounting, do not see the big picture Can’t see “everyone is unique, just like everyone else” Disposition: holding on losers too long and selling winner too fast Averaging down in price rather than up in buying Buying on tips and rumors Speculating too heavily in options or futures wanting to get rich quick No investment strategy, or having one without persistence

32 FIN 2802, Spring 10 - Tang Chapter 7: Optimal Investment Portfolio Summary Diversification Optimal risky portfolio and efficient frontier Allocation among risky and risk-free assets Next Class: Practical Portfolio Management