H
AAS
S
CHOOL
OF
B
USINESS
U
NIVERSITY
OF
C
ALIFORNIA
AT
B
ERKELEY
UGBA 103
A
VINASH
V
ERMA
N
OTATION
This note contains a list of the variables used in risk and portfolio theory and the symbols
we have assigned to them.
Symbol
Variable
E
(
),
E
i
,
E
p
,
E
M
E
(
) denotes
expectation
or
expected value
of
, the variable
in parenthesis. For instance, E(
P
) denotes expectation of
P
, the
price (in brief, expected price), E(
R
) denotes expectation of
R
,
the return (in brief,
expected return
).
When there is a subscript on
E
, as in
E
i
, it stands for expected
return on Security
i
(
E
p
stands for expected return on portfolio
p
,
and
E
M
stands for expected return on the market portfolio
M.
)
i, j
i,
and
j,
are index variables running over a set of things such as
events or securities. Thus, a typical event in a set of
n
events is
referred to as
i
th
event, or a typical security in a portfolio of
n
securities is referred to as
i
th
security.
M
Upper case
M
typically stands for the
market
portfolio.
n
n
typically stands for the number of securities in a portfolio.
p, p
i
p
j
P, P
0
,
P
A
Lower case
p
typically stands for
probability
. Thus,
p
i
denotes
the probability of the
i
th
event.
Lower case
p
,
when used as a subscript
, stands for a typical
portfolio,
p
. Thus,
R
p
stands for the
return
on portfolio,
p
.
Upper case
P
typically stands for
price
, and subscripts on it
typically denote, depending on the context, the time at which the
price prevails (
P
0
is the price at
t
=0), or the security to which the
price pertains (
P
A
is the price of Security
A
).
r, r
E
r
A
R,
R
A
, R
i
, R
f
Lower case
r
typically stands for the
discount rate
or the
cost of
capital
.
(Later in the course subscripts on
r
will denote the category to
which the cost of capital pertains. This,
r
E
will denote the cost of
capital for
E
, the equity, and
r
A
will denote the cost of capital for
A
, the assets of the firm.)
Upper case
R
typically stands for the
return
, and subscripts on it
typically denote the security to which the return pertains (
R
A
is