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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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Usage of Statistics To DetermineRisk and Return (Cont.) Probability and Its Distribution (Cont.)
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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Usage of Statistics To DetermineRisk and Return (Cont.) Probability and Its Distribution (Cont.)
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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Measuring The Expected Returnand Risk of Investing in OneSecurity (Cont.)
Variance
Financial Asset of A
= [0.2(12% - 14.2%)
2
] + [0.5(14% - 14.2%)
2
]+ [0.3(16% - 14.2%) 2]
= 1.96%
Financial Asset of B
= [0.2(6% - 13.9%)2] + [0.5(14% - 13.9%) 2]+ [0.3(19% - 13.9%) 2]
= 20.29%
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Measuring The Expected Returnand Risk of Investing in OneSecurity (Cont.)
Standard Deviation
Financial Asset of A
= Variance A= 1.96%= 1.4%
Financial Asset of B
= 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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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)
Formula for Portfolio Variance is
Formula for Portfolio Standard Deviation
is
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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)
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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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)
Expected Return for Each Financial Asset
Financial Asset of A
= (0.45 x 11%) + (0.55 x 9%)
= 9.90%
Financial Asset of B
= (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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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)
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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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)
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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Measuring The Expected Returnand Risk of Security Portfolio(Cont.)
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.)