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

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.

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.

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.

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.

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.

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.).

Stock Returns Holding Period Return During Period (t) – (R t ) where: P t = price per share at the end of period (t) D t = dividends per share during period (t) Price Relative – (1 + R t ) Often used to avoid working with negative numbers.

Stock Returns (Continued) Arithmetic Mean Return – ( ) An unweighted average of holding period returns

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.”

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.

Stock Returns (A Numerical Example) Assume that a stock that pays no dividends experiences the following pattern of price levels: T 0 = Current Time Period T 1 = End of Period (1) T 2 = End of Period (2)

Stock Returns (A Numerical Example - Continued) Holding Period Returns: Price Relatives:

Stock Returns (A Numerical Example - Continued) Arithmetic Mean Return: Geometric Mean Return: