© K. Cuthbertson and D. Nitzsche Chapter 13 CAPM and APT Investments.

© K. Cuthbertson and D. Nitzsche

Chapter 13

CAPM and APTInvestments

Quiz

RA = 11.2% βA=.82

RB = 17.6% βB=1.46 What is the risk free rate? What is the return on the market? What is the Market Risk Premium?


Learning Objectives

Link between CAPM and mean-variance portfolio theory

Beta as a measure of undiversifiable riskLinear relationship between expected returns

and beta of stocks- SMLUse of CAPM for portfolio construction; for

market risk in a portfolio; for estimation of discount factor in DFCF valuation methods, for market timing strategies


Capital Market Theory: An Overview

Capital market theory extends portfolio theory and develops a model for pricing all risky assets, while capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset based on the systematic risk in the asset

2

2

( , )

where return on the market index

variance of the market returns

return on Security

i mi

m

m

m

i

COV R R

R

R i

CAPM

CAPM states that the expected excess return on a stock is defined by the stock’s market risk beta and by the expected excess return on the market:

(ER-r)=β(ERm –r) or ER=r+β(ERm –r)


Systematic Risk

Risk factors that affect a large number of assets

Also known as non-diversifiable risk or market risk

Examples: changes in GDP, inflation, interest rates, general economic conditions

6

Portfolio Diversification (1)7

Portfolio Diversification (2)8

Measuring Systematic Risk

Beta (β) is a measure of systematic risk

Interpreting beta: β = 1 implies the asset has the same systematic risk

as the overall market βm=Cov(Rm; Rm)/σm2

but Cov(Rm; Rm)=σm2

β < 1 implies the asset has less systematic risk than the overall market

β > 1 implies the asset has more systematic risk than the overall market

9

High and Low Betas10

Portfolio Betas

Consider the previous example with the following four securitiesSecurity Weight BetaA .133 3.69B .2 0.64C .267 1.64D .4 1.79

What is the portfolio beta? 1.773

11

CAPM and SIM

SIM is statistical relationship (regression of excess returns of a stock and a benchmark)

The intercept of the regression line of SIM is a performance measure Jensen’s alpha


Market Index in the SIM

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

Excess Return on Market

Ex

ce

ss

Re

turn

on

BA

Sh

are

s

Security Market Line

CAPM is an asset pricing equation that explains the systematic risk and the role of diversification E(Ri) = Rf + βi(Rm-Rf)

Rearrange CAPM in terms of market riskCalculate beta on historical stock returns or

from financial information vendorReturn averages from historical data serve as

estimates of expected returns



Expected/Average Returns

SML

Beta, βi

Q (buy)

S (sell)

P

Average historic return for S

SML/CAPMreturn, ERP

0.5 1 1.2

T (sell)

M

The larger is βi, the larger is the CAPM expected return ERi

r = 5%

9%

13%

4%

14%

Figure 1 : Security market line (SML)

Matrix

Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column


Applications of CAPM

Market timingPortfolio constructionValue at riskPerformance measure

Treynor measure for excess return (uses market risk β)

Sharpe measure (uses total risk σ) Jansen’s α


Two Fund Separation and CML


Return and Risk of Two Fund Portfolio

Return is weighted average of Risk free rate and market return; portfolio weights sum to one Rp= wRf (Rf) + (1- wRf )(Rm)

Risk on this portfolio is also weighted average (covariance zero; σRf =0 σRp = wRf (σRf ) + (1- wRf )(σ Rm )


Using the CML to Invest: An Example

• How much to invest in the riskless How much to invest in the riskless security?security?

11.5%= w11.5%= wRF RF (4%) + (1-w(4%) + (1-wRFRF )(9%) )(9%)

wwRFRF= -0.5= -0.5

• The investment strategy is to borrow The investment strategy is to borrow 50% and invest 150% of equity in the 50% and invest 150% of equity in the

market portfoliomarket portfolio

Background to Capital Market Theory

Assumptions: All investors are Markowitz efficient investors who

want to target points on the efficient frontier Investors can borrow or lend any amount of money

at the risk-free rate of return (RFR) All investors have homogeneous expectations; that

is, they estimate identical probability distributions for future rates of return

All investors have the same one-period time horizon such as one-month, six months, or one year

Continued…


Assumptions: All investments are infinitely divisible, which

means that it is possible to buy or sell fractional shares of any asset or portfolio

There are no taxes or transaction costs involved in buying or selling assets

There is no inflation or any change in interest rates, or inflation is fully anticipated

Capital markets are in equilibrium, implying that all investments are properly priced in line with their risk levels


Development of the Theory The major factor that allowed portfolio theory to

develop into capital market theory is the concept of a risk-free asset An asset with zero standard deviation Zero correlation with all other risky assets Provides the risk-free rate of return (RFR) Will lie on the vertical axis of a portfolio graph

Risk-Return Possibilities

One can attain a higher expected return than is available at point M

One can invest along the efficient frontier beyond point M, such as point D

Risk-Return Possibilities

With the risk-free asset, one can add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M to achieve a point like E

Point E dominates point D One can reduce the investment risk by lending money at the risk-free

asset to reach points like C

Risk, Diversification & the Market Portfolio: The Market Portfolio

Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line

Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML

It must include ALL RISKY ASSETS

Risk, Diversification & the Market Portfolio: The Market Portfolio

Since the market is in equilibrium, all assets in this portfolio are in proportion to their market values

Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away

Risk, Diversification & the Market Portfolio

Systematic Risk Only systematic risk remains in the market

portfolio Variability in all risky assets caused by

macroeconomic variables Variability in growth of money supply Interest rate volatility Variability in factors like (1) industrial production (2) corporate

earnings (3) cash flow

Can be measured by standard deviation of returns and can change over time


How to Measure Diversification All portfolios on the CML are perfectly positively

correlated with each other and with the completely diversified market Portfolio M

A completely diversified portfolio would have a correlation with the market portfolio of +1.00

Complete risk diversification means the elimination of all the unsystematic or unique risk and the systematic risk correlates perfectly with the market portfolio

Risk, Diversification & the Market Portfolio:

Eliminating Unsystematic Risk

The purpose of diversification is to reduce the standard deviation of the total portfolio

This assumes that imperfect correlations exist among securities


The CML & the Separation Theorem The CML leads all investors to invest in the M

portfolio Individual investors should differ in position on the

CML depending on risk preferences How an investor gets to a point on the CML is

based on financing decisions


The CML & the Separation Theorem Risk averse investors will lend at the risk-free rate

while investors preferring more risk might borrow funds at the RFR and invest in the market portfolio

The investment decision of choosing the point on CML is separate from the financing decision of reaching there through either lending or borrowing


A Risk Measure for the CML The Markowitz portfolio model considers the average

covariance with all other assets The only important consideration is the asset’s

covariance with the market portfolio

© K. Cuthbertson and D. Nitzsche Chapter 13 CAPM and APT Investments.

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Transcript of © K. Cuthbertson and D. Nitzsche Chapter 13 CAPM and APT Investments.