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Introduction

Chapter 1

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Risk vs Return

There is a trade off between risk and

expected return The higher the risk, the higher the

expected return

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www.pse.com.ph

RISK-REWARDCONCEPT

Return shouldcompensate forbearing this risk

The higher the risk,the more you should

receive for holdingthe investment, andthe lower the risk,

the less you should

receive

Stocks

RISK & REWARD

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Probabilities:

an attitude of mind towards someproposition of whose truth we are not

certain - "Will a specific event occur?"

The higher the probability of an event, the

more certain we are that the event willoccur.

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Broad Categories ofprobability interpretations

Frequentists deals with experiments thatare random and well-defined ; it denotes the relativefrequency of occurrenceof an experiment's outcome,when repeating the experiment; deals with relative

frequency "in the long run" of outcomes.

Subjectivists assign numbers per subjective probability,i.e., as a degree of belief.

Bayesians include expert knowledge w/c is representedby a prior probability distribution. The data is incorporatedin a likelihood function.

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Example (Table 1.1, page 2)

Suppose Treasuries yield 5% and thereturns for an equity investment are:

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Probability Return0.05 +50%

0.25 +30%

0.40 +10%0.25 10%

0.05 30%

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Example continued

We can characterize investments by theirexpected return and standard deviation of

return For the equity investment:

Expected return =10%

Standard deviation of return =18.97%

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Probability Distribution - Normal

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Probability Distribution -Skellam

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Combining Risky Investments

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2121

2

2

2

2

2

1

2

122112 wwwwww

PP

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30

Standard Deviation

of Return (%)

Expected

Return (%)

2.0

%24

%16

%15

%10

2

1

2

1

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Efficient Frontier of Risky

Investments (Figure 1.3, page 5)

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Efficient

FrontierExpected

Return

S.D. of

Return

Investments

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Efficient Frontier of All Investments(Figure 1.4, page 6)

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Expected

Return

S.D. of Return

RF

E(RM

)

M

Previous Efficient

FrontierF

M

I

J

New Efficient

Frontier

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Systematic vs Non-Systematic Risk(equation 1.3, page 7)

We can calculate the best fit linearrelationship between return frominvestment and return from market

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M

RR

Systematic Risk

(non-diversifiable)Non-systematic risk

(diversifiable)

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The Capital Asset Pricing Model

(Figure 1.5, page 9)

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Expected

Return

E(R)

1.0

Beta

RF

E(RM)

])([)(FMF

RRERRE

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Assumptions

Investors care only about expected return and SD ofreturn

The s of different investments are independent

Investors focus on returns over one period All investors can borrow or lend at the same risk-free

rate

Tax does not influence investment decisions

All investors make the same estimates of s, s ands.

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Alpha

Alpha measure the extra return on aportfolio in excess of that predicted byCAPM

so that

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)()(FMFPRRRRE

)( FMFP RRRR

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Arbitrage Pricing Theory

Returns depend on several factors

We can form portfolios to eliminate the

dependence on the factors Leads to result that expected return is

linearly dependent on the realization of the

factors

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Risk vs Return for Companies

If shareholders care only about systematic risk shouldthe same be true of company managers?

In practice companies are concerned about total risk

Earnings stability and company survival are importantmanagerial objectives

Bankruptcy costs arguments show that that managersare acting in the best interests of shareholders when

they consider total risk

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What Are Bankruptcy Costs?

Lost sales (There is a reluctance to buyfrom a bankrupt company.)

Key employees leave Legal and accounting costs

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Approaches to Bank Risk

Management

Risk aggregation: aims to get rid of non-

systematic risks with diversification Risk decomposition: tackles risks one by

one

In practice banks use both approaches

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