Compound Growth
Compound Annual Growth Rate
CAGR = (Ending Value ÷ Starting Value)^(1 ÷ Years) − 1
The constant annual rate at which an investment grows from a starting value to an ending value, smoothing out volatility.
Compound Interest
A = P(1 + r/n)^(nt)
Growth that results from earning interest on both the principal and previously earned interest.
SIP Future Value
FV = PMT × [((1 + r)^n − 1) ÷ r]
The future value of making regular equal deposits at fixed intervals with compound interest.
Annualized Return
Annualized Return = (Ending Value ÷ Beginning Value)^(1 ÷ Years) − 1
Multi-period return converted to an equivalent constant annual rate, accounting for compounding.
Debt
Loan Payment Formula
M = P × [r(1+r)^n] / [(1+r)^n − 1]
The fixed monthly payment required to fully amortize a loan over its term.
Amortization Schedule
Interest Payment = Remaining Balance × Monthly Rate | Principal Payment = Total Payment − Interest Payment
The breakdown of loan payments into principal and interest components over the loan term.
APR (Annual Percentage Rate)
APR ≈ Nominal Rate + (Total Fees ÷ Loan Amount) ÷ Years
The true annual cost of borrowing, including interest rate and fees, expressed as an annual percentage.
Options Pricing
Black-Scholes Option Price
C = S₀ × N(d₁) − Ke^(−rT) × N(d₂) where d₁ = [ln(S₀/K) + (r + σ²/2)T] / (σ√T)
Theoretical price of a European-style option based on stock price, strike, time, volatility, and risk-free rate.
Intrinsic Value
Call IV = max(S − K, 0) | Put IV = max(K − S, 0)
The immediate exercise value of an option, floored at zero (cannot be negative).
Time Value of Options
Time Value = Option Premium − Intrinsic Value
The portion of option premium above intrinsic value, reflecting time, volatility, and market forces.
Options Break-Even
Call BE = Strike + Premium Paid | Put BE = Strike − Premium Paid
The stock price at expiration where an option trade neither makes nor loses money (accounting for premium paid/received).
Risk & Performance
Volatility (Standard Deviation)
σ = √[Σ(Rᵢ − R̄)² ÷ n]
A measure of how widely returns vary around their average, indicating investment risk and variability.
Sharpe Ratio
Sharpe Ratio = (Rₚ − Rf) ÷ σₚ
A risk-adjusted return measure showing excess return earned per unit of volatility, comparing investments fairly.
Sortino Ratio
Sortino Ratio = (Rₚ − MAR) ÷ Downside Deviation
Risk-adjusted return focusing only on downside volatility (losses), ignoring upside variability.
Maximum Drawdown
Maximum Drawdown = minₜ [(Valueₜ − Peakₜ) ÷ Peakₜ]
The largest peak-to-trough percentage decline experienced in the portfolio's history.
Beta
β = Cov(Rₐ, Rₘ) ÷ Var(Rₘ)
A measure of how sensitive an asset's returns are to market movements, indicating systematic risk exposure.
Alpha
α = Rₚ − [Rf + βₚ(Rₘ − Rf)]
The excess return of an investment compared to what a risk model (like CAPM) predicts it should earn.
Trading
Risk-Reward Ratio
Risk-Reward = Amount at Risk : Potential Reward
The ratio of potential loss to potential gain on a trade, based on planned stop-loss and profit-target prices.
Win Rate
Win Rate = Winning Trades ÷ Total Closed Trades × 100%
The percentage of closed trades that were profitable, measured as winning trades divided by total trades.
Profit Factor
Profit Factor = Gross Profit ÷ |Gross Loss|
Gross profits divided by absolute gross losses, indicating how much profit a strategy generates per dollar of loss.