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