1. Investment and portfolio management MGT 531

2. Investment and portfolio management  MGT 531

3.  The course assumes little prior applied knowledge in the area of finance.  Kristina (2010) ‘Investment Analysis and Portfolio Management’,

4. 1. Measures of risk and returns 2. Portfolio theory. 3. Markowitz portfolio theory. 4. The Risk and Expected Return of a Portfolio. 5. Efficient set 6. Opportunity set 7. Capital Market Line 8. Weighted average of expected Return

5.  Risk of the portfolio.  volatility  Measuring Risk in CAPM  Systematic risk  Unsystematic risk  Assumptions of CAPM  market risk

6.  Risk of the portfolio.  As we know, the most often used measure for the risk of investment is standard deviation.,  which shows the volatility of the securities that is:  The difference between actual return from their expected return.  If a portfolio‘s expected rate of return is a weighted average of the expected rates of return of its securities,  standard deviation for the portfolio can‘t simply calculated using the same approach.

7.  But the relationship between the securities in the same portfolio must be taken into account.  the relationship between the assets can be estimated using the covariance and coefficient of correlation.  As covariance can range from “–” to “+” infinity,  it is more useful for identification of the direction of relationship (positive or negative),  coefficients of correlation always lies between -1 and +1 and is the convenient measure of intensity and direction of the relationship between the assets.

8.  CAPM was developed by W. F. Sharpe.  CAPM simplified Markowitz‘s Modern Portfolio theory and,  made it more practical.  Markowitz showed that:  for a given level of expected return and  for a given feasible set of securities,  finding the optimal portfolio with the lowest total risk, measured as variance or standard deviation of portfolio returns,  requires knowledge of the covariance or correlation between all possible security combinations.

9.  When forming the diversified portfolios consisting large number of securities,  investors found the calculation of the portfolio risk using standard deviation technically complicated.  Measuring Risk in CAPM is based on the identification of two key components of total risk (as measured by variance or standard deviation of return):  Systematic risk  Unsystematic risk  Systematic risk is that associated with the market, it has three types.

10. 1. purchasing power risk, 2. interest rate risk, 3. liquidity risk, etc.  Unsystematic risk is unique to an individual asset:  Types: 1. business risk, 2. financial risk, 3. other risks, related to investment into particular asset.  Unsystematic risk can be diversified away by holding many different assets in the portfolio,  however systematic risk can’t be diversified.

11.  In CAPM investors are compensated for taking only systematic risk.  Though, CAPM only links investments via the market as a whole.  Figure (along vertical axis portfolio risk, and along horizontal axis Number of securities in portfolio)

12.  The essence of the CAPM: the more systematic risk the investor carry, the greater is his / her expected return.  The CAPM being theoretical model is based on some important assumptions:  All investors look only one-period expectations about the future;  Investors are price takers and they cant influence the market individually;  There is risk free rate at which an investors may either lend (invest) or borrow money.

13.  Investors are risk-averse,  Taxes and transaction costs are irrelevant.  Information is freely and instantly available to all investors.  Following these assumptions, the CAPM predicts:  what an expected rate of return for the investor should be, given other statistics about: 1. the expected rate of return in the market and 2. market risk (systematic risk):

14.  E(r j) = Rf + β(j) * ( E(rM) - Rf ),  here: E(r j) - expected return on stock j;  Rf - risk free rate of return;  E(rM) - expected rate of return on the market  β(j) - coefficient Beta, measuring undiversified risk of security j.  Several of the assumptions of CAPM seem unrealistic.  Investors really are concerned about taxes and  They are paying the commissions to the broker when buying or selling their securities.  And the investors usually do look ahead more than one period.

15.  Large institutional investors managing their portfolios sometimes can: 1. influence market by buying big amounts of the securities or 2. selling big amounts of the securities.  The empirical studies and especially wide use of the CAPM by practitioners show that:  it is useful instrument for investment analysis and  decision making in reality.