R = [(P_T + D_T) / P₀] - 1

P_T = Price at end

D_T = Dividends paid

P₀ = Price at the beginning of the period

R = [(1 + R₁)*(1 + R₂)*...*(1 + R_N)] - 1

Rs are sub-period returns

**Return for WHOLE period

R = [[(1 + R₁)*(1 + R₂)*...*(1 + R_N)]^(1/n)] - 1

**ANNUAL return

r_annual = [(1 + r_period)ⁿ] - 1

r = Return on Investment

n = Number of periods in a year

Rp = w₁R₁ + w₂R₂

w = Weight of asset

R = Return on asset

σ² = [Σ(R_t - μ)²] / T

R_t = Return for period t

T = total number of period

u = Mean of T returns

σ² = [Σ(R_t - R)²] / [T - 1]

R = mean return of the sample observations

σ² = sample variance

σ = [[∑(R_t - μ)²] / T]^1/2

For a sample, denominator is T - 1

σ_p^{2 =} ∑wiwjCov(Ri,Rj)

or

σ_p^{2 =} Σw_i²Var(R_i) + Σw_iw_jCov(R_i,R_j)

σ_p = [w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ_1,2]^1/2

or

[w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2]^1/2

U = E(R) - (1/2)Aσ²

Where:

U = utility of an investment

E(R) = Expected Return

σ² = Variance of Returns

A = Additional return required by the investor to accept an additional unit of risk

[E(R_i) - Rf] / σ_i

CAL has intercept of Rf and a constant slope given by the above formula

E(R_p) = w₁R_f + (1-w₁)E(R_m)

w₁ = Weight in risk free asset

E(R_m) = expected market return

E(R_p) = R_f + [(E(R_m) - R_f)/σ_m] * σ_p

Slope ((E(R_m) - R_f)/σ_m) is the market price of risk

[R_p - R_f] / βp