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Risk, Return, and Security Market Line
Financial Management
Outline Risk of an investment Expected return of an investment Portfolios:
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 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 Actual Return
Realized return/historical return/return ex-post Expected Return
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
E(r) = P1 r1 + P2r2 + … + Pnrn n
= Pi ri
i=1ri is the ith possible outcome and
Pi is the probability of ith outcome Examples
Measuring Risk Risk is measured by standard deviation
of possible returns nVariance (2) = (ri – E(r))2 Pi
i=1Standard Deviation () = (2)1/2
Examples
Coefficient of Variation 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
Risk and return are always positively related
Higher return is associated with high risk
Portfolio Risk and Return Meaning of Portfolio
A combined holding of more than one stock, bonds, real estate, or any other asset
Why create a portfolio? 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 A simple weighted average of the expected
return of each security in the portfolio, where weights represent the proportion of investment in each portfolio
E(rp) = (w1× E(r1)) + (w2× E(r2)) + … +(wn× E(rn)) n E(rp) = wi E(ri) i=1 Examples
Portfolio Risk 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 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
Examples
In a well diversified portfolio, only systematic risk matters; unsystematic risk disappears and is zero.
Portfolios Risk and Beta Systematic risk of a portfolio is measured
by beta of a security Meaning of beta
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 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 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