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Chapter 1
I ntroduction to Risk Management
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ReturnThe gain or loss of a security in a particular
period.
The return consists of the income and thecapital gains relative on an investment.
It is usually quoted as a percentage.
The general rule is that the more risk you
take, the greater the potential for higher
return - and loss.
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Forms of ReturnInterest
Investments like saving accounts,
GICsand bonds pay interest.
Dividends
Some stocks pay dividends, which give
investors a share of what the company makes.The amount of the dividend depends on how
well the company did that year and what type
of stock one owns.
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Forms of ReturnCapital gains
As an investor, if one sells an investment like a
stock, bond, mutual fund or ETF, for morethan one has paid for it, it will result in capital
gain.
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Meaning of RiskThe chance that an investment's actual return will
be different than expected.
Risk includes the possibility of losing some or allof the original investment.
Different versions of risk are usually measured by
calculating the standard deviation of the historicalreturns or average returns of a specific investment.
A high standard deviation indicates a high degree
of risk.
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Meaning of RiskMany companies now allocate large amounts of
money and time in developing risk
management strategies to help manage risksassociated with their business and investment
dealings.
A key component of the risk mangementprocess is risk assessment, which involves the
determination of the risks surrounding a
business or investment.
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Risk Versus UncertaintyUncertaintyinvolves a doubtful outcome
What you will get for your birthday
If a particular horse will win at the track
Risk involves the chance of loss
If a particular horse will win at the track if youmade a bet
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Measurement of RiskVariance
Standard Deviation
Value at Risk (VaR)
Beta
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Risk-Return ProfileThe more risk someone bears, the higher the
expected return
The r isk-less rate of interestcan be earnedwithout bearing any risk
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Risk-Return ProfileA fundamental idea in finance is the
relationship between risk and return. The
greater the amount of risk that an investor iswilling to take on, the greater the potential
return.
The reason for this is that investors need to becompensated for taking on additional risk.
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Risk-Return Profile
Risk
Expected return
Rf
0
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BetaBeta coefficient is a measure of sensitivity of a
share price to movement in the market price.
It measures systematic risk which is the riskinherent in the whole financial system.
Beta coefficient is an important input in capital
asset pricing model to calculate required rate ofreturn on a stock.
It is the slope of the security market line.
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Beta
Beta coefficient is given by the followingformulas:
=Covariance of Market Return with Stock
Return / Variance of Market Return =(Correlation Coefficient between Market and
stock Standard Deviation of Stock Returns) /
Standard Deviation of Market ReturnsAnalysis
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Beta
A beta coefficient of 1 suggests that the stockcarries the same risk as the overall market and will
earn market return only.
A coefficient below 1 suggests a below averagerisk and return (where the average means the
overall market)
A coefficient higher than 1 suggests an aboveaverage risk and return.
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It is the equilibrium model that underlies all modernfinancial theory
Derived using principles of diversification with
simplified assumptionsMarkowitz, Sharpe, Lintner and Mossin are
researchers credited with its development
Capital Asset Pricing Model (CAPM)
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Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assetsNo taxes and transaction costs
Information is costless and available to all
investors Investors are rational mean-variance optimizers
There are homogeneous expectations
Assumptions
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A model that describes the relationship between
risk and expected return and that is used in the
pricing of risky securities.
The CAPM says that the expected return of a
security or a portfolio equals the rate on a risk-free
security plus a risk premium. If this expected
return does not meet or beat the required return,then the investment should not be undertaken.
The security market line plots the results of the
CAPM for all different risks (betas).
CAPM
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Using the CAPM model and the following
assumptions, we can compute the expected return
of a stock in this CAPM example: if the risk-free
rate is 3%, the beta (risk measure) of the stock is 2and the expected market return over the period is
10%, the stock is expected to return 17%
(3%+2(10%-3%)).
CAPM
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Capital Market LineTHE CAPITAL MARKET LINE
M
rP
sP
CML
rfr
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All investors will hold the same portfolio for
risky assetsmarket portfolio
Market portfolio contains all securities and theproportion of each security is its market value
as a percentage of total market value
Resulting Equilibrium Conditions
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Risk premium on the market depends on the
average risk aversion of all market participants
Risk premium on an individual security is afunction of its covariance with the market
Resulting Equilibrium Conditions
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THE SECURITY MARKET
LINE (SML)FOR AN INDIVIDUAL RISKY ASSET
the relevant risk measure is its covariance with
the market portfolio (si, M)
DEFINITION: the security market line
expresses the linear relationship between
the expected returns on a risky asset and
its covariance with the market returns
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Security Market Line (SML)THE SECURITY MARKET LINESML
b
E(r)
rrf
rM
b =1.0