Introduction to Modern Investment Theory (Chapter 1)

1
Introduction to Modern Investment Theory
(Chapter 1)

• Purpose of the Course
• Evolution of Modern Portfolio Theory
• Efficient Frontier
• Single Index Model
• Capital Asset Pricing Model (CAPM)
• Arbitrage Pricing Theory (APT)
• Stock Returns

2
Purpose of the Course

• Develop an understanding of the strengths and
  weaknesses of modern investment theory and
  various models which are currently being employed
  to make investment decisions.

3
Introductory Quote

• This is a book about the theory of investment
  management. Among other things, the theory
  provides the tools to enable you to manage
  investment risk, detect mispriced securities, . .
  . modern investment theory is widely employed
  throughout the investment community by investment
  and portfolio analysts who are becoming
  increasingly sophisticated.

4
Evolution of Modern Portfolio Theory

• Efficient Frontier
• Markowitz, H. M., Portfolio Selection, Journal
  of Finance (December 1952).
• Rather than choose each security individually,
  choose portfolios that maximize return for given
  levels of risk (i.e., those that lie on the
  efficient frontier). Problem When managing large
  numbers of securities, the number of statistical
  inputs required to use the model is tremendous.
  The correlation or covariance between every pair
  of securities must be evaluated in order to
  estimate portfolio risk.

5
Evolution of Modern Portfolio Theory(Continued)

• Single Index Model
• Sharpe, W. F., A Simplified Model of Portfolio
  Analysis, Management Science (January 1963).
• Substantially reduced the number of required
  inputs when estimating portfolio risk. Instead of
  estimating the correlation between every pair of
  securities, simply correlate each security with
  an index of all of the securities included in the
  analysis.

6
Evolution of Modern Portfolio Theory (Continued)

• Capital Asset Pricing Model (CAPM)
• Sharpe, W. F., Capital Asset Prices A Theory of
  Market Equilibrium Under Conditions of Risk,
  Journal of Finance (September 1964).
• Instead of correlating each security with an
  index of all securities included in the analysis,
  correlate each security with the efficient market
  value weighted portfolio of all risky securities
  in the universe (i.e., the market portfolio).
  Also, allow investors the option of investing in
  a risk-free asset.

7
Evolution of Modern Portfolio Theory (Continued)

• Arbitrage Pricing Theory (APT)
• Ross, S. A., The Arbitrage Theory of Capital
  Asset Pricing, Journal of Economic Theory
  (December 1976).
• Instead of correlating each security with only
  the market portfolio (one factor), correlate each
  security with an appropriate series of factors
  (e.g., inflation, industrial production, interest
  rates, etc.).

8
Stock Returns

• Holding Period Return During Period (t) (Rt)
• where Pt price per share at the end of period
  (t)
• Dt dividends per share during
  period (t)
• Price Relative (1 Rt)
• Often used to avoid working with negative
  numbers.

9
Stock Returns(Continued)

• Arithmetic Mean Return ( )
• An unweighted average of holding period returns

10
Stock Returns(Continued)

• Geometric Mean Return ( )
• A time weighted average of holding period returns
• Assumes reinvestment of all intermediate cash
  flows
• The return that makes an amount at the beginning
  of a period grow to the amount at the end of the
  period
• Note that stands for summation of the
  products.

11
Stock Returns(Continued)

• Arithmetic Mean Versus Geometric Mean
• Arithmetic Mean
• Assuming that the past is indicative of the
  future, the arithmetic mean is a better measure
  of expected future return.
• Geometric Mean
• A better measure of past performance over some
  specified period of time.

12
Stock Returns(A Numerical Example)

• Assume that a stock that pays no dividends
  experiences the following pattern of price
  levels
• T0 Current Time Period
• T1 End of Period (1)
• T2 End of Period (2)

13
Stock Returns(A Numerical Example - Continued)

• Holding Period Returns
• Price Relatives

14
Stock Returns(A Numerical Example - Continued)

• Arithmetic Mean Return
• Geometric Mean Return