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) – (Rt)
Pt Pt 1 Dt
Rt
Pt 1
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.
Pt Dt
(1 R t )
Pt 1
Stock Returns
(Continued)
Arithmetic Mean Return – (R A)
An unweighted average of holding period returns
R t
R A t 1
n
R1 R 2 R 3 . . . R n
n
Stock Returns
(Continued)
Geometric Mean Return – ( R G )
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
1 /n
n
R G (1 R t ) 1
t 1
(1 R 1 )(1 R 2 ) . . . (1 R n )
1 /n
1
n
Note that stands for “summation of the products.”
t 1
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:
T0 T1 T2
100 50 100
T0 = Current Time Period
T1 = End of Period (1)
T2 = End of Period (2)
Stock Returns
(A Numerical Example - Continued)
Holding Period Returns:
50 100
R1 .50 or - 50%
100
100 50
R2 1.00 or 100%
50
Price Relatives:
50
(1 R 1 ) .50
100
100
(1 R 2 ) 2.00
50
Stock Returns
(A Numerical Example - Continued)
Arithmetic Mean Return:
.50 1.00
RA .25 or 25%
2
Geometric Mean Return:
R G (.50)(2.00)
1/ 2
1 0%
