FV_n = PV * (e^r_s*N)

r_BD = [D/F] * [360/t]

r_BD = annualized yield on a bank discount basis

D = dollar discount (face value - purchase price)

F = face value of the bill

t = number of days until maturity

EAY = [(1+HPY)^365/t] - 1

HPY = holding period yield

t = number of days until maturity

R_mm = [360*r_BD] / [360-(t*r_BD)]

R_mm = HPY*(360/t)

X = Number of observations / Σ(1/x_i)

*Find what this measures/when it's used

L_y = [(n+1)*y] / 100

y = percentage point at which we are dividing the distribution

L_y = location (L) of the percentile (P_y) in the data set sorted in ascending order

MAD = Σ|x_i-X| / n

n = number of items in the data set

X = mean

| | = absolute value

σ^{2 =} Σ(x_i-μ)² / N

Variances = observation - population mean

σ ⁼ [Σ(x_i-μ)² / N]^1/2

s/X

Sample standard deviation / sample mean

[r_p-r_f] / s_p

(mean portfolio return - risk free return) / standard deviation of portfolio returns

s_k = [n / [(n-1)(n-2)]]  *  [Σ(x_i-X)³ / s³]

As n becomes large, the first term reduces to 1/2

[ [ [n*(n+1)] / [(n-1)(n-2)(n-3)] ] * [(Σ(x_i-X)⁴ / s⁴] ]   -  [ [3(n-1)²] / [(n-2)(n-3)] ]

As n becomes large, the first term becomes 1/n and the third term becomes 3

P(E) = a / (a+b)

Odds of "a" to "b"; switch numerator to b for probability of "b" to "a"

P(A|B) = P(AB) / P(B)

Probability of A given B is the probability of A and B over Probability of B

P(AB) = P(A|B) * P(B)

Probability of A and B is the probability of A given B times the probability of B

P(A|B) = P(A)

P(A or B) = P(A) + P(B) - P(AB)

P(A and B) = P(A) * P(B)

P(A) = P(AS) + P(AS^c)

*Don't know what this is at all

P(A) = P(A|S₁) * P(S₁) + P(A|S₂) * P(S₂) + ...+ P(A|S_n) * P(S_n)

Where set of events s is mutually exclusive and exhaustive

E(X) = Σ P(x_i)*x_i

xi = one of n possible outcomes

1. E(X) = E(X|S)P(S) + E(X|S^c)P(S^c)

2. E(X) = E(X|S₁) * P(S₁) + E(X|S₂) * P(S₂) + ...+ E(X|S_n) * P(S_n)

Where: E(X) = the unconditional expected value of X

E(X|S₁) = the expected value of X given Scenario 1

P(S₁) = the probability of Scenario 1 occurring

The set of events {S₁, S₂,..., S_n} is mutually exclusive and exhaustive.

Cov (XY) = E{[X - E(X)][Y - E(Y)]}

Cov (R_A,R_B) = E{[R_A - E(R_A)][R_B - E(R_B)]}

Corr (R_A,R_B) = Cov (R_A,R_B) / [(σ_A)(σ_B)]

_nC_r = (n over r) = n! / [(n-r)!*(r!)]

Used when the order in which the items assigned the labels is not important

F(x) = n * p(x)

For the nth observation

P(X=x) = _nC_x*(p)^x*(1-p)^n-x

p = probability of success

1-p = probability of failure

nCx = number of possible combinations of having x successes in n trials. Aka number of ways to choose x from n when the order does not matter

90% - x ± 1.65s

95% - x ± 1.96s

99% - x ± 2.58s

Mean ± ...

Approximately 50% of all observations lie in the interval mean ± (2/3)σ

Approximately 68% of all observations lie in the interval mean ± 1σ

Approximately 95% of all observations lie in the interval mean ± 2σ

Approximately 99% of all observations lie in the interval mean ± 3σ

Minimize P(R_pT)

Where:

R_p = portfolio return

R_T = target return

(E(R_p)-R_t) / σ_p

E(R_p) = expected portfolio return

R_t = target return

EAR = e^r_cc - 1

Where:

r_cc = continuously compounded annual rate

HPRt = e^(r_cc*t) - 1

Sampling error of the mean = Sample mean - Population mean

= X - μ

Sample mean ± (reliability factor * standord error)

Reliability factor = The standard normal random variable for which the probability of an observation lying in either tail is α / 2

[(X-μ₀)] / [(s / n^1/2)]

X = sample mean

μ₀ = hypothesized population mean

s = standard deviation of the sample

 n = sample size

M = (V-V_x) * 100

M = momentum oscillator value

V = last closing price

V_x = closing price x days ago (typically 10)

RSI = 100 - [100 / (1+RS)]

RS = sum of up changes for the period / sum of absolute value of down changes for the period

%k = 100*[(C-L14)/(H14-L14)]

C = last closing price

L14 = lowest price in last 14 days

H14 = highest price in last 14 days

%D (signal line) = Average of the last three %K values calculated daily