Bayesian Updating in Investment Analysis: Revising Probabilities with New Information
Bayesian Updating in Investment Decisions Investment analysis rarely begins with complete information. An analyst may start with a view about the probability that a company will beat earnings expectations, that a bond issuer will be downgraded, or that an equity…
Unconditional Expected Values in Finance: Mean, Variance, and Covariance
Introduction to Random Variables A random variable assigns a numerical value to an uncertain outcome. In finance, the random variable might be a stock return next month, the number of defaults in a bond portfolio, the return on a cryptocurrency…
Semi-Deviation and Coefficient of Variation: Downside Risk and Risk per Unit of Return
Why Additional Dispersion Measures Are Needed Standard deviation is the most familiar measure of volatility, but it treats upside and downside variability symmetrically. A return that is far above the mean increases standard deviation just as much as a return…
Covariance and Correlation in Finance: Measuring Co-Movement and Diversification
Why Co-Movement Matters A portfolio is not simply a collection of individual risks. Two investments may each be volatile, yet still work well together if their returns do not move in the same direction at the same time. Conversely, two…
Skewness and Kurtosis in Asset Returns: Interpreting Asymmetry and Tail Risk
Why Shape Matters Mean and standard deviation are powerful, but they are not enough. Two investment strategies can have the same average return and the same volatility while exposing investors to very different experiences. One strategy may have many small…
Statistical Measures of Asset Returns: Mean, Median, Variance, Standard Deviation, and Dispersion
Why Statistical Characteristics Matter A return series is rarely understood by looking at a single observation. A portfolio may earn 8% in one year, lose 12% the next year, and then recover sharply. An analyst therefore needs summary measures that…
Cash Flow Additivity and No-Arbitrage Pricing: Forward Rates, FX Forwards, and Options
Cashflow Additivity Principle According to the cashflow additivity principle, the present value of any sum of any future cashflows is equivalent to the sum of the present values of the associated cashflows. The cash flow additivity principle ensures that the…
Implied Return, Required Return, and Implied Growth in Bond and Equity Valuation
The growth rate is the rate at which the market expects an asset to grow. On the other hand, implied return is based on the current price and future security cash flows. When investors know the price and future value…
Present Value of Bonds and Stocks: Discounting Expected Future Cash Flows
Introduction to Time Value of Money The time value of money (TVM) is a fundamental financial concept. It emphasizes that a sum of money is worth more in the present than in the future. There are three key reasons supporting…
Index Construction and Index Returns: Price, Equal, Market-Cap, Float, and Fundamental Weighting
Why Index Construction Matters A security market index is a financial indicator designed to summarize the performance of a selected group of securities. It may represent a broad market, a sector, an asset class, an investment style, or a custom…
