Mean-Variance Analysis and Efficient Frontier for Investments Chapter 8
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The document discusses mean-variance analysis and the efficient frontier for portfolio optimization. It introduces the assumptions and concepts of mean-variance analysis, including indifference curves, efficiency criteria, and computing the mean and variance of portfolios. It then explains how to find the efficient frontier by solving a quadratic programming problem and examines the return and risk of individual securities and portfolios consisting of different asset allocations.
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Mean-Variance Analysis and Efficient Frontier for Investments Chapter 8
- 1. Investments Chapter 8: Mean-Variance Analysis
- 14. Expected Return, Variance, and Covariance
- 15. Expected Return, Variance, and Covariance
- 16. Expected Return, Variance, and Covariance
- 17. Expected Return, Variance, and Covariance
- 18. Expected Return, Variance, and Covariance
- 19. Expected Return, Variance, and Covariance
- 20. The Return and Risk for Portfolios Note that stocks have a higher expected return than bonds and higher risk. Let us turn now to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks.
- 21. The Return and Risk for Portfolios The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:
- 22. The Return and Risk for Portfolios The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.
- 23. The Return and Risk for Portfolios The variance of the rate of return on the two risky assets portfolio is where BS is the correlation coefficient between the returns on the stock and bond funds .
- 24. The Return and Risk for Portfolios Observe the decrease in risk that diversification offers. An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than stocks or bonds held in isolation.
- 25. The Efficient Set for Two Assets We can consider other portfolio weights besides 50% in stocks and 50% in bonds … 100% bonds 100% stocks
- 26. The Efficient Set for Two Assets We can consider other portfolio weights besides 50% in stocks and 50% in bonds … 100% bonds 100% stocks
- 27. The Efficient Set for Two Assets 100% stocks 100% bonds Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less. These compromise the efficient frontier .
- 28. Two-Security Portfolios with Various Correlations 100% bonds return 100% stocks = 0.2 = 1.0 = -1.0