Lecture 6: Risk and Return
RSM 332
Capital Market Theory
Rotman School of Management
University of Toronto
Mike Simutin
October 19/20, 2011
Risk and Return
RSM 332, 1/26
Why Is This Important?
I
Investors and investment professionals want to measure
performance of investment strategies and account for their risk
I
This allows us to distinguish between diFerent investment
alternatives
I
It also permits us to evaluate mutual fund and other money
managers
I
Investors and investment professionals would like to construct
portfolios that maximize expected return without taking on
unnecessary risk
I
Understanding and taking advantage of the bene±ts of
diversi±cation helps improve portfolio performance
I
Understanding risk and return forms the basis of
understanding Modern Portfolio Theory, which dominates
today’s investment philosophy
Risk and Return
RSM 332, 2/26
A Couple CoinTossing Games
Game 1
I
I’ll toss a fair coin, and if either heads or tails come up, I’ll
give you a $100
I
How much will you be willing to pay to play this game?
Game 2
I
Now I’ll toss the same coin, and if it comes up heads, I’ll give
you $1,000,200
I
But if it comes up tails, you’ll have to pay me $1,000,000
I
How much will you be willing to pay to play this game?
Risk and Return
RSM 332, 3/26
More Coin Tossing: St. Petersburg Paradox
I
I will toss a coin repeatedly until tails appear
I
I will put $1 in the payoF pot if the ±rst toss is heads and
then double the pot every time heads appear
I
WhenItossata
i
l
,youwa
lkawayw
ithwhateverisinthepot
I
So if I toss four straight heads and then a tail, I’ll pay you
1
·
2
·
2
·
2=$2
3
=$8
I
If I toss
n
straight heads and then a tail, I’ll pay you $2
n
−
1
I
Your expected payoF is
1
2
·
1+
1
4
·
2+
1
8
·
4+
1
16
·
8+
...
=
1
2
+
1
2
+
1
2
+
1
2
+
...
=
∞
±
n
=1
1
2
=
∞
I
How much will you be willing to pay to play such a game with
an in±nite expected payoF?
Risk and Return
RSM 332, 4/26
Risk and Return
I
Investors dislike risk: they are
risk averse
I
Returns on investment vary with risk: you should require more
return if you take on more risk
I
So returns is only half the story in ±nance: we also need to
take into account risk
I
Discount rates should therefore reﬂect not only the time value
of money, but also the riskiness of the underlying security
I
How should we measure returns and risk?
Risk and Return
RSM 332, 5/26
Measuring Returns
I
Returns can either be
ex post
, meaning returns were already
realized
,o
r
ex ante
, which means they are
expected
I
Let’s ±rst look at
ex post
returns
I
Holding period return if you bought a stock at time
t
−
1and
sold it at time
t
is
R
t
=
P
t
+
D
t
−
P
t
−
1
P
t
−
1
=
P
t
+
D
t
P
t
−
1
−
1
Year 0
Year 1
Year 2
Dividends at yearend,
D
t
456
Price at yearend,
P
t
100
110
112
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Return during year 1 is
R
1
=
110 + 5
−
100
100
= 15%
I
Return during year 2 is
R
2
=
112 + 6
−
110
110
=7
.
27%
Risk and Return
RSM 332, 6/26
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View Full DocumentMeasuring Realized (Ex Post) Returns
I
Holding period return realized
over two years
is
1
.
15
·
1
.
0727
−
1=23
.
36%
I
Holding period return
per year
is
(1
.
15
·
1
.
0727)
1
/
2
−
1=11
.
07%
I
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