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Mathematics of Finance - 1000 Foot View

Time Value of Money

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Future Value of a Lumpsum

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Annuities - Recurring Payments

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Amortisation - Loan Installments

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Present Value of escalating annuity

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Future value of escalating annuity

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Effective rate of return

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Internal rate of return

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Net present value

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Yield to maturity

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Current Yield

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Yield to Call

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Measuring return

Generating a return on your investments is the prime reason why you are investing. Naturally, you would like to measure these returns. Measurements form the basis for other actions such as portfolio construction, liability modelling, attribution analysis and risk management, among others.

Holding Period Return

Measures the relative change of an investments net asset value over the time period under consideration. It can be calcualted over various time horizons.

Annualising Return

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Aggregation of returns

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Compounding

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Continuous compounding

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Arithmetic Mean versus Geometric Mean

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Descriptive Statistics

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Central tendency statistics

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Gains versus losses

Formula for calculating gain versus loss ratio

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Range and Location

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Mean

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Variance

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Volatility

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Skewness

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Kurtosis

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Mathematics of Risk Management

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Downside risk measures

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Value at Risk

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Monte Carlo Simulation

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Stress testing and scenario analysis

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Style, Clusters and Classifications

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Asset Pricing Models

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Single Factor Models

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Multi-Factor Models

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Regression Analysis

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Simple Regression Analysis

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Multiple Linear regression

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Covariance and correlation

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Scatter Plot

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Mu-Sigma

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Snail Trail

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Risk-adjusted performance measures

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Sharp Ratio

Formula for calculating the Sharpe Ratio of a Portfolio

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Treynor Ratio

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Jensen Alpha

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M Performance Measure

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Sortino Ratio

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Information Ratio

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