intro to investment theory

7/30/2019 Intro to Investment Theory

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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


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Purpose of the Course

Develop an understanding of the

strengths and weaknesses of modern

investment theory and various modelswhich are currently being employed to

make investment decisions.


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Introductory Quote

This is a book about thetheoryof

investment management. Among other

things, the theory provides the tools toenable you to manage investment risk,

detect mispriced securities, . . . modern

investment theory is widely employedthroughout the investment community by

investment and portfolio analysts who

are becoming increasingly sophisticated.


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Evolution of Modern Portfolio Theory

Efficient Frontier

Markowitz, H. M., Portfolio Selection,Journal ofFinance (December 1952).

Rather than choose each security individually,choose portfolios that maximize return forgiven levels of risk (i.e., those that lie on theefficient frontier). Problem: When managing

large numbers of securities, the number ofstatistical inputs required to use the model istremendous. The correlation or covariancebetween every pair of securities must be

evaluated in order to estimate portfolio risk.


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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.


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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.


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Arbitrage Pricing Theory (APT)

Ross, S. A., The Arbitrage Theory of Capital Asset

Pricing,Journal of Economic Theory (December1976).

Instead of correlating each security with only

the market portfolio (one factor), correlate

each security with an appropriate series offactors (e.g., inflation, industrial production,

interest rates, etc.).


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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.

1t

t1tt

tP

DPPR

1t

ttt

P

DP)R(1


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Stock Returns(Continued)

Arithmetic Mean Return( )

An unweighted average of holding period returns

AR

n

R...RRR

n

R

R

n321

n

1t

t

A


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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 aperiod grow to the amount at the end of the period

Note that stands for summation of the products.

GR

1)R(1...)R)(1R(1

1)R(1R

/n1

n21

/n1n

1t

tG

n

1t


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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 somespecified period of time.


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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)

100

50

100

210 TTT


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Stock Returns(A Numerical Example - Continued)

Holding Period Returns:

Price Relatives:

100%or1.0050

50100R

50%-or.50100

10050R

2

1

2.00

50

100)R(1

.50100

50)R(1

2

1


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Stock Returns(A Numerical Example - Continued)

Arithmetic Mean Return:

Geometric Mean Return:

25%or.25

2

1.00.50RA

0%1)(.50)(2.00R 2/1G

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