Risk & Performance Metrics

The excess return of an investment relative to the return predicted by CAPM for its level of systematic risk. Positive alpha indicates outperformance above risk-adjusted expectations, while negative alpha indicates underperformance. Calculated as: α = R_portfolio - [R_f + β(R_market - R_f)].

Example: A mutual fund with a beta of 1.2 returns 15% annually. If the risk-free rate is 3% and the market re...

The strategy of dividing investments among different asset classes (stocks, bonds, cash) to balance risk and return based on investment objectives, time horizon, and risk tolerance. Research shows asset allocation determines over 90% of portfolio return variability over time.

Example: A 60/40 portfolio allocates 60% to stocks and 40% to bonds, balancing growth potential with stabilit...

A measure of a security's volatility relative to the overall market (systematic risk). Beta of 1.0 means the security moves in line with the market; >1.0 indicates higher volatility; <1.0 indicates lower volatility. Beta does not measure unsystematic (company-specific) risk.

Example: A stock with beta of 1.5 is expected to rise 15% when the market rises 10%, but also fall 15% when t...

A statistical measure of how two securities move in relation to each other, expressed as a coefficient ranging from -1.0 to +1.0. Perfect positive correlation (+1.0) means securities move together identically, perfect negative correlation (-1.0) means they move in exact opposite directions, and zero correlation (0) means no relationship exists. Low or negative correlation between holdings is essential for effective portfolio diversification.

Example: Stocks and bonds typically have low or negative correlation, making them effective diversification p...

A statistical measure of how two securities move together, indicating the direction of their relationship but not its strength. Positive covariance means securities tend to move in the same direction, negative covariance means they move in opposite directions, and zero covariance indicates no linear relationship. Used in Modern Portfolio Theory for portfolio construction and diversification analysis, though correlation is preferred for interpretation because covariance magnitude depends on the securities being measured.

Example: If Stock A and Stock B have positive covariance, when Stock A rises 5%, Stock B tends to rise as wel...

A liquidity ratio that measures a company's ability to pay short-term obligations, calculated as Current Assets ÷ Current Liabilities. A ratio above 1.0 indicates sufficient assets to cover liabilities due within one year; below 1.0 may signal financial stress. Widely used in fundamental analysis and credit evaluation.

Example: A company with $500,000 in current assets (cash, receivables, inventory) and $250,000 in current lia...

A financial leverage metric calculated as Long-term Debt divided by Total Capitalization (D/E = Long-term Debt ÷ Total Capitalization, where Total Capitalization = Long-term Debt + Shareholders' Equity). Measures the proportion of long-term debt financing relative to permanent capital. Short-term debt is excluded. Higher ratios indicate greater financial leverage, which amplifies both potential gains and losses for equity holders.

Example: Company A has $50 million in long-term debt and $100 million in shareholder equity, giving total cap...

The practice of spreading investments across different securities, sectors, or asset classes to reduce unsystematic risk. Does not eliminate systematic (market) risk. Effective diversification requires low or negative correlation between holdings.

Example: A portfolio with 60% stocks (across 8 sectors), 30% bonds, and 10% real estate provides diversificat...

A financial metric showing the percentage of earnings paid to shareholders as dividends, calculated as Dividends per Share ÷ Earnings per Share (or Total Dividends ÷ Net Income). A high payout ratio (70-90%) may indicate limited growth reinvestment or mature company status, while a low ratio (20-40%) suggests the company is retaining earnings for growth.

Example: A company with $5.00 EPS paying $2.00 per share in annual dividends has a 40% payout ratio ($2.00 ÷ ...

A measure of a bond's price sensitivity to interest rate changes, expressed in years. Macaulay duration measures the weighted average time to receive all cash flows, while modified duration measures the approximate percentage price change for a 1% change in yield. Duration increases with longer maturity and decreases with higher coupon rates. For zero-coupon bonds, duration equals maturity; for coupon-paying bonds, duration is always shorter than maturity.

Example: A 10-year Treasury bond with a 6% coupon has a modified duration of approximately 7.4 years. If inte...

The risk that a bond's market value will decline when interest rates rise, reflecting the inverse relationship between bond prices and yields. Interest rate risk is measured by duration, which estimates the percentage price change for each 1% change in interest rates. Bonds with longer maturities and lower coupon rates have greater interest rate risk because their cash flows are weighted further into the future.

Example: When the Federal Reserve raises interest rates from 3% to 4%, a 20-year Treasury bond with a 3% coup...

A risk-adjusted measure of excess return beyond what CAPM predicts, developed by Michael Jensen. Uses beta to adjust for systematic risk. Formula is: Actual Return - [Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)]. Positive Jensen's Alpha indicates outperformance above risk-adjusted expectations.

Example: A portfolio manager generates a 16% annual return with a beta of 1.3. With a risk-free rate of 3% an...

A framework developed by Harry Markowitz for constructing portfolios that maximize expected return for a given level of risk through diversification. MPT emphasizes that risk can be reduced by combining assets with low or negative correlation, and that portfolios should be evaluated based on their overall risk-return characteristics rather than individual securities in isolation. The efficient frontier represents the set of optimal portfolios offering the highest expected return for each risk level.

Example: An adviser using MPT principles constructs a client portfolio with 60% stocks and 40% bonds. The bon...

A statistical measure indicating the percentage of a portfolio's movements that can be explained by movements in a benchmark index. Ranges from 0 to 1 (or 0% to 100%), with higher values indicating stronger correlation. High R-squared (above 0.85) means beta is a reliable predictor of portfolio behavior; low R-squared indicates significant unsystematic risk that beta does not capture.

Example: An S&P 500 index fund typically has an R-squared near 1.0 (100%) relative to the S&P 500, meaning vi...

A profitability ratio measuring how efficiently a company generates profits from shareholder equity, calculated as Net Income ÷ Shareholder Equity. Higher ROE indicates better management performance in using equity capital to generate earnings. Commonly used in fundamental analysis to compare companies within the same industry.

Example: A company with $5 million in net income and $25 million in shareholder equity has an ROE of 20% ($5M...

A measure of risk-adjusted return calculated as (portfolio return - risk-free rate) / standard deviation. Higher ratios indicate better risk-adjusted performance, with values above 1.0 generally considered good.

Example: A fund returning 12% with 8% standard deviation and 2% risk-free rate has Sharpe ratio of 1.25....

A measure of risk-adjusted return that penalizes only downside deviation (volatility below a target return) rather than total volatility like the Sharpe ratio. Calculated as (portfolio return - target return) / downside deviation. Higher ratios indicate better risk-adjusted performance, focusing specifically on harmful volatility.

Example: Two portfolios both return 10% annually. Portfolio A has 12% total volatility with 6% downside devia...

A statistical measure of the dispersion of returns for a security or portfolio. Indicates total risk (both systematic and unsystematic). Higher standard deviation means greater volatility. Under normal distribution, 68% of returns fall within 1 standard deviation, 95% within 2, and 99.7% within 3.

Example: A fund with 12% average annual return and 8% standard deviation would have returns between 4% and 20...

Systematic risk (market risk) affects the entire market and cannot be eliminated through diversification, measured by beta. Unsystematic risk (specific or idiosyncratic risk) affects individual securities or sectors and can be reduced or eliminated through diversification. Effective portfolio management focuses on diversifying away unsystematic risk while accepting systematic risk.

Example: During the 2008 financial crisis, the entire market declined (systematic risk) regardless of diversi...

The standard deviation of the difference between a portfolio's returns and its benchmark's returns, measuring how consistently a fund follows (or deviates from) its benchmark. Low tracking error (1-2%) indicates passive management closely following the benchmark, while high tracking error (4-7%) indicates active management with significant deviations. Expressed as an annualized percentage.

Example: An S&P 500 index fund with 0.5% tracking error closely mimics the index, with return differences sta...

A measure of risk-adjusted return calculated as (portfolio return - risk-free rate) / beta. Higher ratios indicate better risk-adjusted performance per unit of systematic risk. Only valid for well-diversified portfolios where beta is the relevant risk measure.

Example: A diversified mutual fund returns 14% with beta of 1.2, while the risk-free rate is 3%. The Treynor ...

The total annual return an investor would receive if a bond is held until maturity, expressed as an annualized percentage. YTM includes both coupon payments and any capital gain (discount bonds) or capital loss (premium bonds) from purchasing above or below par. Critical assumption: all coupon payments are reinvested at the same YTM rate. For premium bonds, YTM is lower than current yield and coupon rate. For discount bonds, YTM is higher than current yield and coupon rate.

Example: An investor purchases a $1,000 par corporate bond with a 5% coupon at $950 (discount). The bond matu...