Description
It also explains Harry Markoitz portfolio selection model, portfolio risk, impact of correlation on portfolio risk-return. It also covers efficient frontier.
THE PROCESS OF INVESTMENT MANAGEMENT
SOME BASIC ASSUMPTIONS
• An investor wants to maximize the returns from investments for a given level of risk i.e. the investors are risk averse. • The full spectrum of investments must be considered. • Your portfolio should include all of your assets and liabilities, not only your stocks. • A good portfolio is not simply a collection of individually good investments.
SOME BASIC ASSUMPTIONS
• Creation of an optimum investment portfolio is not simply a matter of combining a lot of unique individual securities that have desirable risk-return characteristics. • Relationship among the investments is extremely important in portfolio construction. n • E (R Port) = ? Wi E(R i)
i=1
EXPECTED RETURN FROM INDIVIDUAL ASSETS VS. PORTFOLIO
MEASURING RISK
• The variance, or standard deviation, is a measure of the variation of possible rates of return, Ri , from the expected rate of return [E(Ri)] as • Covariance is a measure of the degree to which two variables “move together” relative to their individual mean values over time. • In portfolio analysis, we usually are concerned with the covariance of rates of return rather than prices or some other variable. • Standardizing the covariance by the individual standard deviations yields the correlation coefficient (rij), which can vary only in the range –1 to +1.
VARIANCE AND STANDARD DEVIATION OF INDIVIDUAL ASSETS
COVARIANCE
COVARIANCE
COVARIANCE VS. CORRELATION
COVARIANCE VS. CORRELATION
HARRY MARKOITZ’S PORTFOLIO SELECTION MODEL
Assumptions:
1. Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period. 2. Investors maximize one-period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth. 3. Investors estimate the risk of the portfolio on the basis of the variability of expected returns. 4. Investors base decisions solely on expected return and risk, so their utility curves are a function of expected return and the expected variance (or standard deviation) of returns only. 5. For a given risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected return, investors prefer less risk to more risk.
Under these assumptions, a single asset or portfolio of assets is considered to be efficient if no other asset or portfolio of assets offers higher expected return with the same (or lower) risk, or lower risk with the same (or higher) expected return.
PORTFOLIO RISK
The standard deviation for a portfolio of assets is a function of the weighted average of the individual variances (where the weights are squared), plus the weighted covariances between all the assets in the portfolio. • The standard deviation for a portfolio of assets encompasses not only the variances of the individual assets but also includes the covariances between pairs of individual assets in the portfolio. Further, it can be shown that, in a portfolio with a large number of securities, this formula reduces to the sum of the weighted covariances. • The important factor to consider when adding an investment to a portfolio that contains a number of other investments is not the investment’s own variance but its average covariance with all the other investments in the portfolio.
•
PORTFOLIO RISK
Impact of changing correlations on risk:
Example: E(R1) = 0.20 ?1 = 0.10 E(R2) = 0.20 ?2 = 0.10 Consider the following alternative correlation coefficients and the covariances they yield. The covariance term in the equation will be equal to r1,2 (0.10)(0.10) because both standard deviations are 0.10. a. r1,2 = 1.00; Cov1,2 = (1.00)(0.10)(0.10) = 0.010 b. r1,2 = 0.50; Cov1,2 = (0.50)(0.10)(0.10) = 0.005 c. r1,2 = 0.00; Cov1,2 = 0.000(0.10)(0.10) = 0.000 d. r1,2 = –0.50; Cov1,2 = (–0.50)(0.10)(0.10) = –0.005 e. r1,2 = –1.00; Cov1,2 = (–1.00)(0.10)(0.10) =–0.01
PORTFOLIO RISK
PORTFOLIO RISK
PORTFOLIO WITH PERFECTLY NEGATIVE CORRELATED SECURITIES
•
IMPACT OF CORRELATION ON PORTFOLIO RISK-RETURN
Combining assets that are not perfectly correlated does not affect the expected return of the portfolio • But it does reduce the risk (standard deviation) of the portfolio. • Risk is eliminated when we reach the ultimately combination of perfectly negative correlation.
•
RISK-RETURN OF PORTFOLIO OF STOCKS WITH VARIED RISK AND RETURN
RISK-RETURN OF PORTFOLIO OF STOCKS WITH VARIED RISK AND RETURN
RISK-RETURN OF PORTFOLIO OF STOCKS WITH VARIED RISK AND RETURN
RISK-RETURN OF CONSTANT PORTFOLIO OF STOCKS CHANGING WEIGHTS
CONSTANT PORTFOLIOS WITH CHANGING WEIGHTS
STANDARD DEVIATIONS WITH CHANGING WEIGHTS
RISK-RETURN OF CONSTANT PORTFOLIO OF STOCKS CHANGING WEIGHTS
PORTFOLIO RISK AND RETURN PLOTS FOR DIFFERENT WEIGHTS
THE EFFICIENT FRONTIER
THE EFFICIENT FRONTIER
THE EFFICIENT FRONTIER
doc_185675356.pptx
It also explains Harry Markoitz portfolio selection model, portfolio risk, impact of correlation on portfolio risk-return. It also covers efficient frontier.
THE PROCESS OF INVESTMENT MANAGEMENT
SOME BASIC ASSUMPTIONS
• An investor wants to maximize the returns from investments for a given level of risk i.e. the investors are risk averse. • The full spectrum of investments must be considered. • Your portfolio should include all of your assets and liabilities, not only your stocks. • A good portfolio is not simply a collection of individually good investments.
SOME BASIC ASSUMPTIONS
• Creation of an optimum investment portfolio is not simply a matter of combining a lot of unique individual securities that have desirable risk-return characteristics. • Relationship among the investments is extremely important in portfolio construction. n • E (R Port) = ? Wi E(R i)
i=1
EXPECTED RETURN FROM INDIVIDUAL ASSETS VS. PORTFOLIO
MEASURING RISK
• The variance, or standard deviation, is a measure of the variation of possible rates of return, Ri , from the expected rate of return [E(Ri)] as • Covariance is a measure of the degree to which two variables “move together” relative to their individual mean values over time. • In portfolio analysis, we usually are concerned with the covariance of rates of return rather than prices or some other variable. • Standardizing the covariance by the individual standard deviations yields the correlation coefficient (rij), which can vary only in the range –1 to +1.
VARIANCE AND STANDARD DEVIATION OF INDIVIDUAL ASSETS
COVARIANCE
COVARIANCE
COVARIANCE VS. CORRELATION
COVARIANCE VS. CORRELATION
HARRY MARKOITZ’S PORTFOLIO SELECTION MODEL
Assumptions:
1. Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period. 2. Investors maximize one-period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth. 3. Investors estimate the risk of the portfolio on the basis of the variability of expected returns. 4. Investors base decisions solely on expected return and risk, so their utility curves are a function of expected return and the expected variance (or standard deviation) of returns only. 5. For a given risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected return, investors prefer less risk to more risk.
Under these assumptions, a single asset or portfolio of assets is considered to be efficient if no other asset or portfolio of assets offers higher expected return with the same (or lower) risk, or lower risk with the same (or higher) expected return.
PORTFOLIO RISK
The standard deviation for a portfolio of assets is a function of the weighted average of the individual variances (where the weights are squared), plus the weighted covariances between all the assets in the portfolio. • The standard deviation for a portfolio of assets encompasses not only the variances of the individual assets but also includes the covariances between pairs of individual assets in the portfolio. Further, it can be shown that, in a portfolio with a large number of securities, this formula reduces to the sum of the weighted covariances. • The important factor to consider when adding an investment to a portfolio that contains a number of other investments is not the investment’s own variance but its average covariance with all the other investments in the portfolio.
•
PORTFOLIO RISK
Impact of changing correlations on risk:
Example: E(R1) = 0.20 ?1 = 0.10 E(R2) = 0.20 ?2 = 0.10 Consider the following alternative correlation coefficients and the covariances they yield. The covariance term in the equation will be equal to r1,2 (0.10)(0.10) because both standard deviations are 0.10. a. r1,2 = 1.00; Cov1,2 = (1.00)(0.10)(0.10) = 0.010 b. r1,2 = 0.50; Cov1,2 = (0.50)(0.10)(0.10) = 0.005 c. r1,2 = 0.00; Cov1,2 = 0.000(0.10)(0.10) = 0.000 d. r1,2 = –0.50; Cov1,2 = (–0.50)(0.10)(0.10) = –0.005 e. r1,2 = –1.00; Cov1,2 = (–1.00)(0.10)(0.10) =–0.01
PORTFOLIO RISK
PORTFOLIO RISK
PORTFOLIO WITH PERFECTLY NEGATIVE CORRELATED SECURITIES
•
IMPACT OF CORRELATION ON PORTFOLIO RISK-RETURN
Combining assets that are not perfectly correlated does not affect the expected return of the portfolio • But it does reduce the risk (standard deviation) of the portfolio. • Risk is eliminated when we reach the ultimately combination of perfectly negative correlation.
•
RISK-RETURN OF PORTFOLIO OF STOCKS WITH VARIED RISK AND RETURN
RISK-RETURN OF PORTFOLIO OF STOCKS WITH VARIED RISK AND RETURN
RISK-RETURN OF PORTFOLIO OF STOCKS WITH VARIED RISK AND RETURN
RISK-RETURN OF CONSTANT PORTFOLIO OF STOCKS CHANGING WEIGHTS
CONSTANT PORTFOLIOS WITH CHANGING WEIGHTS
STANDARD DEVIATIONS WITH CHANGING WEIGHTS
RISK-RETURN OF CONSTANT PORTFOLIO OF STOCKS CHANGING WEIGHTS
PORTFOLIO RISK AND RETURN PLOTS FOR DIFFERENT WEIGHTS
THE EFFICIENT FRONTIER
THE EFFICIENT FRONTIER
THE EFFICIENT FRONTIER
doc_185675356.pptx