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Business Finance(MGT 232)

Lecture 15

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Risk and ReturnRisk and Return

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• Risk attitudes• Portfolio return• Portfolio Risk• Coefficient of correlation• Risk diversification

Overview of the Last Lecture

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Combining securities that are not perfectly, positively correlated reduces risk.

Diversification and the Correlation Coefficient

INVE

STM

ENT

RETU

RN

TIME TIMETIME

SECURITY ESECURITY E SECURITY FSECURITY F CombinationCombinationE and FE and F

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Total Risk Total Risk = SystematicSystematic RiskRisk + UnsystematicUnsystematic RiskRisk

Systematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on

the market as a whole. Also called market risk

Unsystematic Risk Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification.

Also called diversifiable risk

Total Risk = Systematic Risk + Unsystematic Risk

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Total Risk = Systematic Risk + Unsystematic Risk

TotalTotalRiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

STD

DEV

OF P

ORTF

OLIO

RET

URN

NUMBER OF SECURITIES IN THE PORTFOLIO

Systematic risk is due to factors such as changes in nation’s economy, tax reform by the Congress,or a change in the world situation.

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Total Risk = Systematic Risk + Unsystematic Risk

TotalTotalRiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

STD

DEV

OF P

ORTF

OLIO

RET

URN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors unique to a particular companyor industry. For example, the death of akey executive or loss of a governmentaldefense contract.

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An index of systematic risksystematic risk.

It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio.

β measures the tendency of the stock to move up and down with the changes in market

What is Beta?

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If β= 1.0 it shows the security is as risky as the entire market, it is the betaof an average

security

If β= 0.5 it shows the security is half as risky as an average security

If β= 2.0 it shows the security is twice as risky as an average security

What is Beta?

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Characteristic Lines and Different BetasEXCESS RETURN

ON STOCK

EXCESS RETURNON MARKET PORTFOLIO

Beta < 1Beta < 1(defensive)(defensive)

Beta = 1Beta = 1

Beta > 1Beta > 1(aggressive)(aggressive)

Each characteristic characteristic line line has a

different slope.

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The average beta of the security in a market is in the range of 0.5-1.5. The portfolio consists of low beta securities itself will have a lower portfolio beta.

The beta of a portfolio is the weighted average of beta of its individual securities

ββpp = w = w11bb11+w+w22bb22+…..+w+…..+wnnbbnn

Beta of a Portfolio

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Suppose you decided to invest in three stocks, an amount of Rs. 100,000. The stocks has following values of beta:

β1 = 0.7

β2 = 0.7

β3 = 2.0

Find the beta of a portfolio, if you invest equal amount in each stock?

Beta of a Portfolio

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CAPM is a model that describes the relationship between risk and expected (required) return; in

this model, a security’s expected (required) return is the risk-free rate risk-free rate plus a premium a premium based on the

systematic risk systematic risk of the security.

The model was evaluated by Harry Markowitz and William Sharpe

Capital Asset Pricing Model (CAPM)

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1. Capital markets are efficient.

2. Homogeneous investor expectations over a given period.

3. Risk-freeRisk-free asset return is certain

4. Market portfolio contains only systematic risksystematic risk

CAPM Assumptions

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RRjj = RRff + j(RRMM - RRff)RRjj is the required rate of return for stock j,

RRff is the risk-free rate of return,

jj is the beta of stock j (measures systematic risk of stock j),

RRMM is the expected return for the market portfolio.

Security Market Line

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Security Market Line

MM = 1.01.0Systematic Risk (Beta)

RRff

RRMM

Requ

ired

Retu

rnRe

quire

d Re

turn

RiskRiskPremiumPremium

Risk-freeRisk-freeReturnReturn

RRjj = RRff + j(RRMM - RRff)

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Mariam at Basket Wonders is attempting to determine the rate of return required by their stock investors. Mariam is using a 6% R6% Rff and a

long-term market expected rate of return market expected rate of return of 10%10%. A stock analyst following the firm has calculated

that the firm betabeta is 1.21.2. What is the required required rate of returnrate of return on the stock of Basket Wonders?

Determination of the Required Rate of Return

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RRBWBW = RRff + i(RRMM - RRff)

The required rate of return exceeds the market rate of return as BW’s beta exceeds the market

beta (1.0).

BWs Required Rate of Return

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Mariam at BW is also attempting to determine the intrinsic intrinsic value value of the stock. She is using the constant growth model.

Mariam estimates that the dividend next period dividend next period will be Rs.0.50Rs.0.50 and that BW will growgrow at a constant rate of 5.8%5.8%. The

stock is currently selling for Rs.15.

What is the intrinsic value intrinsic value of the stock? Is the stock overover or underpricedunderpriced?

Determination of the Intrinsic Value of BW

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The stock is OVERVALUED as the market price (Rs.15) exceeds the

intrinsic value intrinsic value (Rs.10Rs.10).

Determination of the Intrinsic Value of BW

Rs.0.50Rs.0.5010.8%10.8% - 5.8%5.8%

IntrinsicIntrinsicValueValue =

= Rs.10Rs.10

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Security Market Line

Systematic Risk (Beta)

RRff

Requ

ired

Retu

rnRe

quire

d Re

turn

Direction ofMovement

Direction ofMovement

Stock Y Stock Y (Overpriced)

Stock X (Underpriced)

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Security Market Line

• Underpriced When the offer price is lower than the price of

the first trade, the stock is considered to be underpriced.

• Overpriced• when the offer price is greater than the price

of the first trade, the stock is considered to be overpriced.

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Summary

• Systematic and unsystematic risk• Beta and beta of a portfolio• Capital Asset pricing Model• Security market line and Intrinsic value