Financial Management I_Chapter 5

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Financial ManagementIBBPW3103Chapter 5

Risk Analysis


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Definition of Risk Risk : Probability of change to the return

receivable by an investor in a specific period

Return : The profit level receivable by aninvestor during the period of its investment

Types of return

Expected Return : Return based on the information

available that can be expected by an investor

Unexpected Return : Created from information that

is beyond he expectation of investor


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Usage of Statistics ToDetermine Risk and Return Random Variable

Statistic data that is difficult to predict

accurately The estimation of real value difficult to obtain


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Usage of Statistics To DetermineRisk and Return (Cont.) Probability and Its Distribution

Used to measure the probability of random variablethat uncertainty

The concept of probability outlines several of thefollowing issue Probability cannot be in negative form

The total overall probabilities are equal 1 @ 100%

The value 0 shown the probability of a specific occurrencethat definitely would not occur

The value 0.1 show the probability of a specificoccurrence occurring is 10%

The value 1 show the probability of a specific occurrencedefinitely to occur


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Usage of Statistics To DetermineRisk and Return (Cont.) Probability and Its Distribution (Cont.)

Probability distribution is categorized into 2

types of distribution that is Discrete Probability : Distribution that has a

matching probability value and random variable

that are limited

Continuous Probability : Calculation of value thatis related with the random variable that will create

an unlimited number of possibility return


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Usage of Statistics To DetermineRisk and Return (Cont.)Probability and Its Distribution (Cont.)

Example 5.1 : Nusa Company is currently

weighing 2 alternative investment, which arethe project to rear fish (PRF) and project to

rear sheep (PRS). The following are the

discrete probability distribution of return for

both investment alternatives.Probability PRF Return (RM) PRS Return (RM)0.25 8,000 2,000

0.25 12,000 18,000

0.50 10,000 10,000


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Based on the prediction by NC, both the

investment alternatives showed that theopportunity to obtain the estimated return of

RM10,000 is higher than as it stated a

higher probability percentage.

Figure below displayed the information in the

form of the bar chart


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Usage of Statistics To DetermineRisk and Return (Cont.)


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Usage of Statistics To DetermineRisk and Return (Cont.)


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Figure 5.1 show that the probability

distribution gap of return for PRS isbigger RM16,000 (RM18,000 RM2,000)

compared to PRF RM4,000 (RM12,000

RM8,000)

Figure 5.2 show that the probability

distribution of return for PRS is higher

than PRF

So, the PRS riskier compare to PRF


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Usage of Statistics To DetermineRisk and Return (Cont.) Expected Return (Mean)

Is the mean for random variable that is

average of probability for all the possibilitiesin the value of random variable

The formula for Expected Return @ Mean is


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Usage of Statistics To DetermineRisk and Return (Cont.) Expected Return (Mean)

Where


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Usage of Statistics To DetermineRisk and Return (Cont.) Variance

Is a measure of dispersion of distribution of

all possible result around expected return. The formula for Variance is


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Usage of Statistics To DetermineRisk and Return (Cont.) Standard Deviation

Measurement of dispersion around the

expected value of a probability or itsfrequency, which is the square root of

variances

Formula for Standard Deviation


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Usage of Statistics To DetermineRisk and Return (Cont.) Coefficient of Variance

Is a standard deviation ratio of expected

return. Used as the comparison basis for two

investment in financial statement

Formula for CV is


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Usage of Statistics To DetermineRisk and Return (Cont.) Covariance

Show the relationship of returns among the financial assetsand how far two random variables are different from each other

+ Covariance : One of the random variables states a valuemore than mean & the other random variable inclined towardthe value ofmore than mean

- Covariance : One of the random variable stated a value ofmore than mean & the other random variable incline towardsthe value ofless than mean

0 Covariance : No relationship between the two randomvariable

The formula for Covariance is


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Usage of Statistics To DetermineRisk and Return (Cont.) Correlation Coefficient

Used to measure the relationship movement

magnitude between 2 variable that is movement of

return on financial assets

Perfect Negative Correlation (Corr = -1.0) : Two

variables moving in the opposite direction

Perfect Positive Correlation (Corr = +1.0) : Two

variables moving in the same direction

Positive Correlation (Ex. 0.4) : Two variable moving

in the same direction but at different magnitudes


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Measuring The Expected Returnand Risk of Investing in OneSecurity

When we measure only one security, there are

3 types of analysis to be made that is Expected

Return, Variance and Standard Deviation

Example 5.2

Economy

Situation

Probability

(P)

Rate of Return (r) For

Financial Asset

A B

Weak 0.20 12% 6%

Moderate 0.50 14% 14%

Strong 0.30 16% 19%


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Measuring The Expected Returnand Risk of Investing in OneSecurity (Cont.)

Expected Return

Financial Asset of A

= (0.20 x 0.12) + (0.50 x 14%)+ (0.30 x 16%)

= 14.2%

Financial Asset of B

= (0.20 x 6%) + (0.50 x 14%)

+ (0.30 x 19%)

= 13.9%


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Variance


= [0.2(12% - 14.2%)

2

] + [0.5(14% - 14.2%)

2

]+ [0.3(16% - 14.2%) 2]

= 1.96%


= [0.2(6% - 13.9%)2] + [0.5(14% - 13.9%) 2]+ [0.3(19% - 13.9%) 2]

= 20.29%


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Standard Deviation


= Variance A= 1.96%= 1.4%


= Variance B= 20.29%= 4.50%


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Reducing Risk ThroughDiversification Portfolio refer combination several

securities in the capital market

Objective of portfolio is to reduce risk andincrease return for investor


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Principle of Systematicand Unsystematic Risk Systematic Risk : Cannot be diversified

and effect to all financial market. For

example, interest rate risk, purchasingpower risk and all market risk

Unsystematic Risk : Can be diversified.

For example, business risk that related tothe company operation


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Measuring The Expected Returnand Risk of Security Portfolio The expected rate of return for

investment in the securities portfolio is

the weighted average expected return onthe financial assets held in the portfolio

The formula is


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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)

Where


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Formula for Portfolio Variance is

Formula for Portfolio Standard Deviation

is


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Example 5.3 : Investment made with 50% of

the financial asset of A, 25% in the financial

asset of B and 25% in the financial asset of C.

Economy

Situation

Probability

(P)

Rate of return (r) for Financial

Asset (%)

A B C

Strong 0.45 11 16 21

Weak 0.55 9 5 0


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Expected Return for Each Financial Asset


= (0.45 x 11%) + (0.55 x 9%)

= 9.90%


= (0.45 x 16%) + (0.55 x 5%)

= 9.95% Financial Asset of C

= (0.45 x 21%) + (0.55 x 0%)

= 9.45%


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Expected Return for the Portfolio

= (0.50 x 9.9%) + (0.25 x 9.95%) + (0.25 x

9.45%)= 9.8%


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Portfolio Variance For Strong Economic Situation

= (0.50 x 11%) + (0.25 x 16%) + (0.25 x 21%)

= 14.75%

For Weak Economic Situation

= (0.50 x 9%) + (0.25 x 5%) + (0.25 x 0%)

= 5.75%

Portfolio Variance

= [0.45(14.75% - 9.8%)2] + [0.55(5.57% - 9.8%)2]

= 20.05%


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Portfolio of Standard Deviation

= Portfolio Variance

= 20.05%= 4.477%


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Capital Asset PricingModel (Cont.) According to the CAPM model, an investor will choose

any combination of assets along the capital market line

At this line, investor will get optimum risk-return

replacement.


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Capital Asset PricingModel (Cont.) From the graph, the straight line is known as Capital

Market Line (CML) starting from the point marked rf(the asset did not have risk or risk-free asset) andtouches the efficiency frontier curve (that is the

market portfolio known as M) This point will give the optimum risk-return to the

investor.

The gradient of the CML can measure the amount ofexpected return for a unit of total risky investment.The formula is


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Capital Asset PricingModel (Cont.) There are a few assumption in used of CAPM

Model that is There are many investor and all the investor is the

price taker (No one investor can influence themarket price)

All investor have a same holding period of securities

All assets in the market which is the investor can be

a borrower or lender at fixed risk free rate No tax and no transaction cost

All investor make the decision based on the meanand variance

All investor have a same expectation


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Measuring SystematicRisk (Beta) Assume the investor successfully chosen one

of the portfolio that consist of Risky Assets ofA,B,C,D and one Non-Risky Asset

All risky assets has a combination ofsystematic and unsystematic risks. When theportfolio is formed, the unsystematic risk canbe fully distributed.

The result, the only systematic risk leftaccumulated is due to the combination ofsystematic risk


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Measuring SystematicRisk (Beta) (Cont.) Systematic risk can be measured using the

Coefficient Beta () that is the relative sharesdiversification index. The following indicator

used to interpret the result of beta multiplier

= 0.0 : Securities without risk (risk-free assets)

= 0.5 : The level of securities risk is half of the

market risk = 1.0 : Securities have the same level of risk with

the average market risk

= 2.0 : The level of securities risk is twice the

average market risk


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Measuring SystematicRisk (Beta) (Cont.) Total expected return for a unit of risk

can be measured by the CML gradientand enable us to determine the premiumrisk for a risky asset.

The formula is

= (Systematic Risk) (CML Gradient)

=


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Measuring SystematicRisk (Beta) (Cont.) Example 5.4 : Assume you hade determined the beta multiplier

including the weighted investment for each of the financial risky

asset. Based on this information, you can then calculate the

portfolio beta multiplier for the investment of assets x, y and z.

Beta portfolio = (1.20 x 0.25) + (0.90 x 0.20) + (0.80 x 0.55)

= 0.92

Security % Portfolio Beta

X 25 1.20

Y 20 0.90

Z 55 0.80


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Security Market Line(SML) Shows the relationship between rate of return

and systematic risk (beta multiplier as follow:-


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Security Market Line(SML) (Cont.) The formula for SML is

Example 5.5 : Assume the portfolio comprise of

investment in security X (Beta=1.5 & Expected

Return=18%) and risk-free security (rf=7%). 30% of the

investment is invested in security X and 70% invested

in the risk-free security. So,


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Security Market Line(SML) (Cont.) Then, Reward-to-Risk Ratio can be

calculated based on the following formula


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Security Market Line(SML) (Cont.) Example 5.6 : Assume the portfolio comprise of

investment in security Y (Beta=1.1 & Expected

Return=14%) and risk-free security (rf=7%). 30% of the

investment is invested in security Y and 70% investedin the risk-free security. So

Reward-to-Risk Ratio can be calculated based on the

SML gradient:

= (rx rf) x = (14% - 7%) 1.1 = 6.36%


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Security Market Line(SML) (Cont.)

Financial Management I_Chapter 5

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