List of Frequently Used Symbols and Notation
A text such as Intermediate Financial Theory is, by nature, relatively notation intensive. We have adopted a strategy to minimize the notational burden
within each individual chapter at the cost of being, at times, inconsistent in our
use of symbols across chapters. We list here a set of symbols regularly used
with their specific meaning. At times, however, we have found it more practical
to use some of the listed symbols to represent a different concept. In other instances, clarity required making the symbolic representation more precise (e.g.,
by being more specific as to the time dimension of an interest rate).
Roman Alphabet
a
Amount invested in the risky asset;
in Chapter 14, fraction of wealth invested in the risky asset or portfolio
AT
Transpose of the matrix (or vector)A
c
Consumption; in Chapter 14 only, consumption is represented by C,
while c represents ln C
ckθ
Consumption of agent k in state of nature θ
CE
Certainty equivalent
CA
Price of an American call option
CE
Price of a European call option
d
Dividend rate or amount
∆
Number of shares in the replicating portfolio (Chapter xx
E
The expectations operator
ekθ
Endowment of agent k in state of nature θ
f
Futures position (Chapter 16);
pf
Price of a futures contract (Chapter 16)
F, G Cumulative distribution functions associated with densities:
f, g
Probability density functions
K
The strike or exercise price of an option
K(x̃) Kurtosis of the random variable x̃
L
A lottery
L
Lagrangian
m
Pricing kernel
M
The market portfolio
M Uθk Marginal utility of agent k in state θ
p
Price of an arbitrary asset
P
Measure of Absolute Prudence
q
Arrow-Debreu price
qb
Price of risk-free discount bond, occasionally denoted prf
e
q
Price of equity
rf
Rate of return on a risk-free asset
Rf
Gross rate of return on a risk-free asset
r̃
Rate of return on a risky asset
R̃
Gross rate of return on a risky asset
1
RA
RR
s
S
S(x̃)
T
U
U
V
Vp
VF
wi
Y0
Absolute risk aversion coefficient
Relative risk aversion coefficient
Usually denotes the amount saved
In the context of discussing options, used to denote the price of the underlying stock
Skewness of the random variable x̃
Transition matrix
Utility function
von Neuman-Morgenstern utility function
Usually denotes variance-covariance matrix of asset returns;
occasionally is used as another utility function symbol; may also signify value as in
The value of portfolio P or
The value of the firm
Portfolio weight of asset i in a given portfolio
Initial wealth
Greek Alphabet
α
Intercept coefficient in the market model (alpha)
β
The slope coefficient in the market model (beta)
δ
Time discount factor
η
Elasticity
λ
Lagrange multiplier
µ
Mean
πθ
State probability of state θ
πθRN
Risk-neutral probability of state θ
Π
Risk premium
ρ(x̃, ỹ) Correlation of random variables x̃ and ỹ
ρ
Elasticity of intertemporal substitution (Chapter 14)
σ
Standard deviation
σij
Covariance between random variables i and j
θ
Index for state of nature
Ω
Rate of depreciation of physical capital
ψ
Compensating precautionary premium
Numerals and Other Terms
1
Â
Â
GBM
F SD
SSD
Vector of ones
Is strictly preferred to
Is preferred to (non strictly, that is allowing for indifference)
Geometric Brownian Motion stochastic process
First-order stochastic dominance
Second-order stochastic dominance
2