Risk, Return, and Security
Market Line
Financial Management
Outline
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Risk of an investment
Expected return of an investment
Portfolios:
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Portfolio expected returns
Portfolio risk
Risk: Systematic and Unsystematic Risk
Diversification and Portfolio Risk
The security market line and Capital Asset
Pricing Model
Defining Risk
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Risk refers to the chance that some
unfavorable event will happen
Investment risk is the probability that actual
returns may deviate from expected returns
The chance that actual returns may be lower
than expected return gives rise to investment
risk
Higher the probability of actual returns being
less than expected, higher will be investment
risk
Returns
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Actual Return
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Realized return/historical return/return ex-post
Expected Return
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Return ex-ante/anticipated return
A weighted average of all possible returns, where
weights represent probability of each possible
outcome
Multiply each possible outcome with its probability
and add them up over all possible outcomes
Measuring Expected Return
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E(r) = P1 r1 + P2r2 + … + Pnrn
n
=  Pi ri
i=1
ri is the ith possible outcome and
Pi is the probability of ith outcome
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Examples
Measuring Risk
Risk is measured by standard deviation of
possible returns
n
Variance (2) =  (ri – E(r))2 Pi
i=1
Standard Deviation () = (2)1/2
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Examples
Coefficient of Variation
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Standard deviation is an absolute measure of
risk
We cannot rank investments only on the basis
of standard deviation or on the basis of
expected return
To rank investments, we need a measure of
risk that is based on risk and return
Coefficient of variation is a relative measure
of risk based on risk and expected return
Examples
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Risk and return are always positively
related
Higher return is associated with high
risk
Portfolio Risk and Return
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Meaning of Portfolio
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A combined holding of more than one stock,
bonds, real estate, or any other asset
Why create a portfolio?
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To diversify/reduce/mitigate risk of a single
security
All securities in the portfolio may not move
together
If one goes down, others will go up and
compensate for the loss of the first one
Portfolio Expected Return
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A simple weighted average of the expected
return of each security in the portfolio, where
weights represent the proportion of investment in
each portfolio
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E(rp) = (w1× E(r1)) + (w2× E(r2)) + … +(wn× E(rn))
n
E(rp) =  wi E(ri)
i=1
Examples
Portfolio Risk
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Risk of a portfolio is measured by standard
deviation of the portfolio (p)
Standard deviation of a portfolio is not a
simple weighted average of the standard
deviations of each individual security in the
portfolio
Theoretically, it is possible to combine two
risky securities and create a zero risk portfolio
without compromising returns.
Example
Portfolio Risk
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Total risk as measured by standard deviation
does not matter in a portfolio context
Total risk can be divided into two categories
Total Risk = Unsystematic Risk + Systematic
Risk
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Examples
In a well diversified portfolio, only systematic
risk matters; unsystematic risk disappears
and is zero.
Portfolios Risk and Beta
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Systematic risk of a portfolio is measured by
beta of a security
Meaning of beta
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Tendency of a stock to move with the market
Sensitivity of an asset’s price to the changes in the
market
Beta of a risk free security
Beta of a market portfolio
Beta of a market portfolioBeta of a market
portfolio
Computing Portfolio Beta
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A simple weighted average of the beta of each individual asset
in the portfolio, where weights represent the proportion of
investment in each asset in the portfolio
p = (w1× 1) + (w2× 2) + … +(wn× n)
n
 p =  wi  i
i=1
Where wi represents proportion of total investment in security i
and I represents beta of security i in the portfolio
Examples
Security Market Line and
CAPM
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Positive relationship between systematic
risk and return of a portfolio
The line which gives the expected
returns-systematic risk combinations of
assets is called the security market line