Risk and Return

• Risk and return defined– Average return– Total (absolute) risk – Total (relative) risk

• Portfolio risk and diversification effect

• Systematic Vs. non-systematic risk

• Beta and “reward to risk”

• CAPM

Return • The additional cents on the dollar invested…• k=(profit+additional cash flows)/initial investment• Over a period of time…average return

• Arithmetic Return:

• Geometric Return:

• Why do returns matter?– $ does not mean much…alone

– Cross-comparison between markets

– Are “normally distributed”

n

iknAR

1

1

1)1(

1

1

nn

iikGR

Risk• We need to think in terms of estimates in an uncertain

world: Estimate=average return +/- some volatility

• Uncertainty or volatility of returns• Standard deviation of returns

• Measured in %• What does it mean?

2

1

)(1

1tan

vartan

averagekn

DeviationdardS

ianceDeviationdardS

n

i

Risk and Return• How to compare assets?

• Which one do you pick?

• What is the problem here?

Think…Goal: FUN

Choice 1: Orlando (3 theme parks)Choice 2: Hampshire (biggest inflatable bouncy castle)You equal utility for any of these attractions...Trick: • There is one chance on two that each attraction will be

closed• There is one chance on two that Indianapolis Airport will

be closed1. Which one do you pick?2. Think about the risks of not having fun, which one

really matters?

Portfolio effect• Portfolio Return is the weighted average return of

each asset in the portfolio

• Portfolio Risk is not the weighted average risk of each asset in the portfolio.

• Portfolio risk has to do with each asset’s weight and risk, but also the degree to which they move together (ρ)

n

iii kWturnPortfolio

1

Re

2pp

n

1i

n

1jj,ijiji

n

1i

2i

2i

2p

iiip

WWW

),,W(fRiskPortfolio

Mathematical Explanation

22)

222

44(

: weightequal with stocks 2 of portfolio a agineIm

ba)ba()ab2ba(

,thus

ab2ba)ba(

bab,a

ba2

b2

ap

222

222

Portfolio risk and return…in EnglishPortfolio return=

(weighted) average assets’ return

Portfolio risk =(weighted) average assets’ risk

- (weighted) average assets prices’ propensity to move in opposite direction

OrPortfolio risk =

(weighted) average assets’ risk- Benefits from diversification

Risk and DiversificationAnnouncements and news contain both an expected component and a

surprise component; it is the surprise component that affects a stock’s price and therefore its return.

Return = expected + unexpected

Risk (return)= 0 + market risk + business risk

The trick: if you hold many securities, the particularities of each security becomes irrelevant…thus, in a well diversified portfolio business-specific risk is irrelevant!

Risk that matters…• If only market risk matters, then the risk premium of a

security should be related (somehow) to the market risk premium!

• Let’s assume that those risk premiums are proportional:

security risk premium=β x market risk premium • This β is a multiplier which has to do with the relative

risk premium of a security to the market risk premium…it is a relative Market (systematic) Risk

CAPM• ki=kRF + kRP, then…

– Security risk premium = (ki- kRF)

– Market risk premium = (km- kRF)

• If security risk premium=β x market risk premium

• Then, (ki- kRF) =β x (km- kRF)

• That is,

ki = kRF +β x (km - kRF)

This is also known as the SML (market equilibrium), a component of the CAPM

• As a result, any security’s return can calculated using β, kRF, and km

Some Questions• What if the observed returns are different from the

theoretical returns?• What is the market “relative” risk (β)?• What does a β of 2 mean?• What does a β of .5 mean?• What does a β of –1 mean?• How do we measure β?• What is the β of a portfolio?• Impact of inflation and risk aversion on expected

returns