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:
1 n
AR    ki
n 1
1
n
n
GR    (1  ki )  1
i 1

• Why do returns matter?
– $ does not mean much…alone
– Cross-comparison between markets
– Are “normally distributed”
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
S tan dard Deviation  var iance
n
1
S tan dard Deviation 
  (ki  average) 2
n 1 1
• Measured in %
• What does it mean?
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 closed
1. 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
n
Portfolio Re turn   Wi  ki
i 1
• Portfolio Risk is not the weighted average risk of
each asset in the portfolio.
Portfolio Risk   p  f ( Wi ,  i , i )
 2p

p 
n
2
 Wi
i 1
  i2
n n
   Wi  W j   i   j  i, j
i 1 j1
 2p
• Portfolio risk has to do with each asset’s weight
and risk, but also the degree to which they move
together (ρ)
Mathematical Explanation
(a  b) 2  a 2  b 2  2ab
thus,
(a  b  2ab)  (a  b)  a  b
2
2
2
Im agine a portfolio of 2 stocks with equal weight :
a 2 b 2
a b
a b
p  (

 2

  a ,b ) 

4
4
2
2
2
2
Portfolio risk and return…in English
Portfolio return=
(weighted) average assets’ return
Portfolio risk =
(weighted) average assets’ risk
- (weighted) average assets prices’ propensity to move
in opposite direction
Or
Portfolio risk =
(weighted) average assets’ risk
- Benefits from diversification
Risk and Diversification
Announcements 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 =
Risk (return)=
expected
0
+
+
unexpected
market risk + business risk
The trick: if you hold many securities, the particularities of each security
becomes irrelevant…thus, in a well diversified portfolio businessspecific 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