Chapter 1 Financial Math

Sharpe Ratio

Measures the risk-adjusted return of a portfolio. Formula: (Portfolio Return - Risk-Free Rate) / Standard Deviation.

Holding Period Return

The total return earned on an investment over a specific period. Formula: (End Value - Beginning Value) / Beginning Value (ignoring timeframe).

Dollar-Weighted Return

A measure of return that accounts for the timing and size of cash flows using IRR calculations.

Time-Weighted Return (Geometric)

Measures compounding returns over time, unaffected by cash flow timings. Formula: TWR = [(1 + PR1) x (1 + PR2) x ...]^1/n - 1.

Alpha

The value that a portfolio manager adds or subtracts relative to a benchmark. Formula: Portfolio Return - Benchmark Return

CAPM Alpha (Jensen's Alpha)

The excess return of a portfolio over its expected return. Formula: Actual Return - CAPM Expected Return.

CAPM Expected Return

The expected return on an asset given its systematic risk. Formula: Risk-Free Rate + (Beta x Market Risk Premium)

Beta

Measures an asset's volatility relative to the overall market (systematic risk). Beta > 1 is more volatile than the market.

Treynor Ratio

Measures risk-adjusted return based on systematic risk. Formula: (Portfolio Return - Risk-Free Rate) / Beta.

Holding Period Return with Cash Flows

A calculation where cash distributions or contributions are added to the valuation changes to find the absolute return during the period.

Time-Weighted Return Market Valuation

The process of valuing a portfolio immediately before any new contribution or withdrawal to isolate manager performance from cash flows.