Risk & Probability Cheat Sheet

The core ideas of Risk & Probability distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Probability

The mathematical measure of the likelihood that a specific event will occur, expressed as a value between 0 (impossible) and 1 (certain), or equivalently as a percentage between 0% and 100%. In finance, probabilities are assigned to different investment outcomes to calculate expected returns and assess risk.

Expected Value

The probability-weighted average of all possible outcomes of an uncertain event. It is calculated by multiplying each possible outcome by its probability of occurring, then summing the results. Expected value represents the long-run average result if the same decision were repeated many times.

Risk-Return Tradeoff

The principle that potential investment returns tend to increase as risk increases. Investors who want higher returns must accept greater uncertainty and the possibility of larger losses. This tradeoff is fundamental to portfolio theory and explains why different asset classes offer different return profiles.

Standard Deviation (as Risk Measure)

A statistical measure of how spread out investment returns are around their average value. A higher standard deviation means returns vary more widely from year to year, indicating greater risk. In finance, standard deviation is the most common quantitative measure of investment volatility.

Diversification

The strategy of spreading investments across different assets, industries, or geographic regions to reduce the impact of any single investment's poor performance on the overall portfolio. Diversification reduces unsystematic risk but cannot eliminate systematic (market-wide) risk.

Systematic Risk

Risk that affects the entire market or economy and cannot be eliminated through diversification. Also called market risk or non-diversifiable risk, it includes factors like recessions, interest rate changes, inflation, and geopolitical events that impact virtually all investments simultaneously.

Unsystematic Risk

Risk that is specific to a particular company, industry, or sector and can be reduced or eliminated through diversification. Also called specific risk or diversifiable risk, it includes factors like management decisions, product failures, regulatory changes affecting one industry, or competitive pressures.

Risk Tolerance

An individual's willingness and ability to endure fluctuations in the value of their investments. Risk tolerance is influenced by factors including time horizon, financial goals, income stability, and psychological comfort with uncertainty. It determines the appropriate asset allocation for each investor.

Key Terms at a Glance

Probability:The mathematical measure of how likely an event is to occur, expressed as a value between 0 and 1.

Expected Value:The probability-weighted average of all possible outcomes of an uncertain event, representing the long-run average result.

Risk-Return Tradeoff:The principle that higher potential investment returns are associated with higher levels of risk.

Standard Deviation:A statistical measure of how spread out values are from the average, used in finance as the primary measure of investment volatility.

Diversification:The strategy of spreading investments across multiple assets to reduce unsystematic risk.

Systematic Risk:Market-wide risk that cannot be eliminated through diversification, including recessions and interest rate changes.

Unsystematic Risk:Risk specific to a particular company or industry that can be reduced or eliminated through diversification.

Risk Tolerance:An individual willingness and financial ability to endure fluctuations in investment value.

Probability Distribution:A mathematical function that describes all possible outcomes and their associated probabilities for an uncertain event.

Volatility:The degree of variation in an investment returns over time, commonly measured by standard deviation.

Tail Risk:The risk of rare but extreme events that fall in the statistical tails of a probability distribution.

Sharpe Ratio:A measure of risk-adjusted return: (return minus risk-free rate) divided by standard deviation. Higher values indicate better return per unit of risk.

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