Investment Terms Glossary

Essential investment terminology and concepts for understanding quantitative investing, factor strategies, and portfolio management

A comprehensive guide to key investment terms and concepts used throughout the Parallax platform and in quantitative investing. These are the standard terms you'll encounter in portfolio reporting, performance analysis, and investment strategy documentation.

Note:

Understanding Risk Measurement: No single metric captures all dimensions of portfolio risk. Each measure provides a different perspective, and together they create a comprehensive picture of portfolio characteristics. This glossary emphasizes the multi-dimensional nature of risk and return analysis.

Quick Navigation

Jump to any category to explore related concepts:

πŸ“Š Risk-Adjusted Performance

Metrics that evaluate returns relative to risk

πŸ“‰ Risk & Volatility Measures

Quantifying uncertainty and downside potential

πŸ”— Portfolio Construction

Building and managing diversified portfolios

⚑ Investment Strategies

Systematic approaches to security selection

πŸ“ˆ Performance Measurement

Evaluating investment results

πŸ”¬ Advanced Analytics

Sophisticated portfolio analysis techniques

Detailed Terms

Each term below includes Beginner explanations with practical portfolio examples, and Advanced sections with mathematical formulas, historical context, limitations, and cross-references.

Alpha

What it means: Alpha measures how much better (or worse) your portfolio performed compared to a benchmark index, after accounting for the risk you took.

Portfolio Example: Your portfolio returned 15% this year while the S&P 500 returned 12%. If your portfolio has the same risk profile as the S&P 500, your alpha is 3% - you added 3% of value beyond what the market provided.

Why it matters: Alpha tells you if your investment strategy or portfolio manager is actually adding value, or if returns are just coming from general market movements.

↑ Back to top

Beta

What it means: Beta measures how much your portfolio moves compared to the overall market. A beta of 1.0 means your portfolio moves exactly with the market.

Portfolio Example: Your portfolio has a beta of 0.4. If the market goes up 10%, your portfolio typically goes up 4% (0.4 Γ— 10%). If the market falls 10%, your portfolio typically falls only 4%. This portfolio is less volatile than the market.

Another Example: A portfolio with beta of 1.5 amplifies market moves - when the market rises 10%, this portfolio typically rises 15%. When the market falls 10%, it falls 15%. Higher risk, higher potential returns.

Why it matters: Beta tells you how much market risk you're taking. Lower beta = more stability. Higher beta = more volatility and potential returns.

↑ Back to top

Sharpe Ratio

What it means: The Sharpe Ratio tells you how much return you're getting for each unit of risk you're taking. Higher is better - you're getting more "bang for your buck" in terms of risk.

Portfolio Example:

  • Portfolio A: 12% return, 8% volatility β†’ Sharpe Ratio = 1.25 (assuming 2% risk-free rate)
  • Portfolio B: 15% return, 15% volatility β†’ Sharpe Ratio = 0.87
  • Even though Portfolio B has higher returns, Portfolio A is better on a risk-adjusted basis

Why it matters: It helps you compare different investments fairly. A 20% return with 30% volatility isn't necessarily better than a 12% return with 8% volatility.

↑ Back to top

Standard Deviation

What it means: Standard deviation measures how much your portfolio's returns jump around. Higher standard deviation = more unpredictable returns = more risk.

Portfolio Example:

  • Portfolio A: Average return 10%, standard deviation 5% β†’ Returns typically range from 5% to 15%
  • Portfolio B: Average return 10%, standard deviation 20% β†’ Returns typically range from -10% to 30%
  • Both have the same average return, but Portfolio B is much riskier (more volatile)

Rule of Thumb: About 68% of the time, returns fall within 1 standard deviation of the average. About 95% of the time within 2 standard deviations.

Why it matters: It helps you understand how bumpy the ride will be. Lower standard deviation = smoother, more predictable returns.

↑ Back to top

Correlation

What it means: Correlation measures whether two investments tend to move together, move in opposite directions, or move independently.

Portfolio Example:

  • Stock A and Stock B have correlation of +0.9: When A goes up, B strongly tends to go up too. They move together.
  • Stock A and Stock C have correlation of -0.7: When A goes up, C strongly tends to go down. They move in opposite directions.
  • Stock A and Stock D have correlation of 0.0: A's movements tell you nothing about D's movements. They're independent.

Important Note: Correlation doesn't tell you the magnitude of movements, only the direction and strength of the relationship. The actual percentage moves depend on each stock's volatility.

Why it matters: Lower correlation between your holdings means better diversification. When one investment falls, others may hold steady or rise, reducing overall portfolio risk.

↑ Back to top

Drawdown

What it means: Drawdown measures how much your portfolio fell from its highest point to its lowest point before recovering. It shows the worst loss you experienced.

Portfolio Example: Your portfolio hits an all-time high of $100,000. Over the next 6 months, it falls to $75,000 before starting to recover. Your maximum drawdown is 25% ($25,000 loss / $100,000 peak).

Why it matters: Drawdown tells you the psychological and financial pain you'll need to endure during rough patches. A 50% drawdown requires a 100% gain just to get back to even - much harder than it sounds.

Recovery Reality:

  • 20% drawdown needs 25% gain to recover
  • 30% drawdown needs 43% gain to recover
  • 50% drawdown needs 100% gain to recover

↑ Back to top

Information Ratio

What it means: The Information Ratio measures how much excess return you're generating per unit of risk you're taking relative to a benchmark. It tells you how efficiently a strategy or manager beats their benchmark.

Portfolio Example:

  • Your portfolio returns 14% vs. S&P 500's 10% (4% excess return)
  • Your tracking error (active risk) is 5%
  • Information Ratio = 4% / 5% = 0.80

This means for every 1% of additional risk taken relative to the S&P 500, you're generating 0.80% of excess return.

Why it matters: It separates skilled active management from luck. A high Information Ratio means consistent outperformance, not just occasional big wins.

↑ Back to top

Treynor Ratio

What it means: The Treynor Ratio measures return per unit of systematic (market) risk, focusing only on risk that can't be diversified away.

Portfolio Example:

  • Portfolio A: 14% return, beta = 1.2 β†’ Treynor Ratio = (14% - 2%) / 1.2 = 10.0
  • Portfolio B: 12% return, beta = 0.8 β†’ Treynor Ratio = (12% - 2%) / 0.8 = 12.5
  • Portfolio B is better - generating more return per unit of market risk taken

When to use it: Best for evaluating well-diversified portfolios where unsystematic risk has been eliminated through diversification.

Why it matters: If your portfolio is well-diversified, beta (systematic risk) is what matters most. The Treynor Ratio tells you if you're being compensated fairly for that market exposure.

↑ Back to top

Diversification

What it means: Diversification is spreading investments across different assets, sectors, or strategies to reduce risk. It's the only "free lunch" in investing - you can reduce risk without reducing expected returns.

Core Principle: Different investments don't move in perfect lockstep. When some are down, others may be up or stable, smoothing overall portfolio returns.

Portfolio Example:

  • Portfolio A: $100,000 in one tech stock β†’ High risk, all eggs in one basket
  • Portfolio B: $100,000 split among 50 stocks across 10 sectors β†’ Much lower risk, same expected return

Diversification Math:

For N equally-weighted stocks:
Οƒportfolio = Οƒstock Γ— √[(1/N) + ((N-1)/N) Γ— ρavg]

If uncorrelated (ρ = 0):
Οƒp = Οƒs / √N  β†’ For N=30: 5.5Γ— risk reduction

If realistic correlation (ρ = 0.3):
Οƒp = Οƒs Γ— 0.54 β†’ For N=30: only 1.85Γ— risk reduction

Reality Check: Real stocks within a market exhibit 0.3-0.5 average correlation, limiting diversification benefits to approximately 2Γ— risk reduction. Systematic market risk (beta) cannot be diversified away, regardless of number of holdings.

Cross-References: See Correlation, Standard Deviation, Systematic Strategy

↑ Back to top

(Continuing with remaining terms in simpler format for brevity...)

Factor Investing

What it means: Factor investing systematically targets specific stock characteristics (factors) that historically predict higher returns: value, momentum, quality, size, and low volatility.

Portfolio Example: Instead of picking individual stocks, you build a portfolio emphasizing companies that are:

  • Undervalued (value factor)
  • Rising in price (momentum factor)
  • High quality (quality factor)
  • Defensive (low volatility factor)

Why it works: Decades of research show these characteristics predict returns because they represent either risk premiums or behavioral inefficiencies.

Cross-References: See Systematic Strategy, Value Investing, Momentum

↑ Back to top

Market Capitalization

What it means: Market cap = Share Price Γ— Total Shares Outstanding. It's the total market value of a company.

Categories:

  • Large-cap: Greater than $10 billion (Microsoft, Apple)
  • Mid-cap: $2B - $10B
  • Small-cap: Less than $2 billion

Portfolio Example: A $100M company trading at $50/share has 2 million shares outstanding. If price rises to $60, market cap increases to $120M.

Factor Connection: Small-cap stocks historically outperform large-caps over long periods, though with higher volatility (the "size premium").

↑ Back to top

Momentum

What it means: Momentum is the tendency for assets that have outperformed recently to continue outperforming over intermediate horizons (3-12 months).

Time Horizon Matters - Different horizons show opposite effects:

  • Short-term (1 week - 1 month): Reversal effect (mean reversion) - recent winners become losers
  • Intermediate (3-12 months): Momentum effect (continuation) - recent winners keep winning
  • Long-term (3-5 years): Reversal effect again - value reversion

Typical Implementation:

  • Formation period: 12-month lookback (skip most recent month to avoid short-term reversal)
  • Holding period: 3-6 months
  • Works better cross-sectionally (relative momentum) than time-series (absolute momentum)

Portfolio Example: Stock X rose 30% over months 2-13 (skipping month 1). Momentum strategies buy it, expecting continued outperformance over next 3-6 months.

Why it works: Behavioral biases (underreaction to news, herding) and institutional factors (slow capital allocation) cause trends to persist.

Risk Warning: Momentum strategies experience severe crashes during market reversals (e.g., 2009: 50-80% losses in 2 months during rally from market bottom).

Cross-References: See Factor Investing

↑ Back to top

Value Investing

What it means: Value investing targets stocks trading below their intrinsic worth based on fundamentals like earnings, book value, or cash flow.

Portfolio Example: Company trades at $40 but analysis suggests worth $60 based on assets and earnings power. Value investors buy, expecting price to rise toward $60.

Classic Metrics: P/E ratio, P/B ratio, EV/EBITDA - lower is more "value"

Cross-References: See Factor Investing

↑ Back to top

Volatility

What it means: Volatility measures how much prices fluctuate. Same concept as standard deviation but often used specifically for describing market conditions.

Portfolio Example:

  • Low volatility period: Market moves Β±0.5% most days
  • High volatility period: Market moves Β±2-3% most days

VIX Index: The "fear gauge" - measures expected S&P 500 volatility. VIX greater than 30 = high volatility, VIX less than 15 = low volatility.

Cross-References: See Standard Deviation, Risk-Adjusted Returns

↑ Back to top

Portfolio Rebalancing

What it means: Periodically selling winners and buying losers to maintain target allocations.

Portfolio Example: Start with 60% stocks / 40% bonds. After stocks rally, you're now 70% stocks / 30% bonds. Rebalancing sells 10% stocks and buys 10% bonds to return to 60/40.

Why it matters: Rebalancing enforces "buy low, sell high" discipline and maintains desired risk level.

Frequency Trade-off: More frequent = maintains targets better but higher transaction costs.

↑ Back to top

Risk-Adjusted Returns

What it means: Returns evaluated relative to risk taken. A 15% return with 20% volatility may be worse than 10% return with 5% volatility.

Key Metrics:

  • Sharpe Ratio (return per unit of total risk)
  • Sortino Ratio (return per unit of downside risk)
  • Calmar Ratio (return per unit of maximum drawdown)

Cross-References: See Sharpe Ratio, Standard Deviation, Information Ratio

↑ Back to top

Tracking Error

What it means: How much a portfolio's returns deviate from its benchmark. Higher tracking error = more active management.

Mathematical Definition: Standard deviation of (Portfolio Return - Benchmark Return)

Portfolio Example:

  • Portfolio returns: 12%, 8%, -3%, 15%
  • Benchmark returns: 10%, 10%, -2%, 14%
  • Differences: +2%, -2%, -1%, +1%
  • Tracking Error = Standard deviation of differences = ~1.7%

Interpretation: With 1.7% tracking error, about 68% of the time the portfolio will perform within Β±1.7% of the benchmark.

Cross-References: See Information Ratio, Beta

↑ Back to top

Hit Ratio

What it means: Hit Ratio measures what percentage of the time your portfolio outperformed its benchmark. It's like a batting average in baseball.

Portfolio Example:

  • Over 12 months, your portfolio beat the S&P 500 in 8 months and underperformed in 4 months
  • Hit Ratio = 8/12 = 67% (or "hit rate" of 0.67)

Interpretation:

  • 50% = Random / no skill (coin flip)
  • 60%+ = Consistent outperformance
  • 70%+ = Very consistent

Why it matters: Shows consistency of your strategy. You can have high returns but low hit ratio (few big wins, many small losses) or high hit ratio but low returns (many small wins, few big losses).

↑ Back to top

Information Coefficient

What it means: Information Coefficient (IC) measures how good you are at predicting which stocks will outperform. It's the correlation between your predictions and actual outcomes.

Portfolio Example:

  • You predict expected returns for 100 stocks at start of quarter
  • Quarter ends, you calculate correlation between your predictions and actual returns
  • IC = 0.05 means weak but positive predictive ability
  • IC = 0.10 means strong predictive ability (rare in practice)

Interpretation:

  • IC = 0: No predictive ability (random guessing)
  • IC = 0.03-0.05: Typical for skilled managers
  • IC = 0.10+: Exceptional (very rare)

Why it matters: IC directly measures forecasting skill, the core of active management value. Higher IC means better stock selection ability.

↑ Back to top

Style Analysis R-Squared

What it means: Style Analysis R-squared (R-squared) measures how much of your portfolio's performance can be explained by systematic factors (market, value, size, momentum). Higher R-squared means your returns are mostly driven by known factors, not unique stock picking.

Portfolio Example:

  • Portfolio with R-squared = 0.95 (95%): Almost all performance explained by factor exposures - likely a closet index fund
  • Portfolio with R-squared = 0.60 (60%): Moderate factor exposure with significant active stock selection
  • Portfolio with R-squared = 0.30 (30%): Highly active, returns driven more by individual picks than broad factors

Interpretation:

  • R-squared greater than 0.90: Essentially a factor/index fund, paying active fees for passive exposure
  • R-squared = 0.60-0.90: Mix of factor exposure and active selection
  • R-squared less than 0.60: Truly active management

Why it matters: Helps identify "closet indexers" charging active fees for passive strategies. Also reveals if your "active" manager is just riding known factor exposures.

↑ Back to top

Factor-Adjusted Alpha

What it means: Factor-Adjusted Alpha is the return you generated that can't be explained by known investment factors like market exposure, value tilt, size tilt, or momentum. It's a more sophisticated version of regular alpha.

Portfolio Example:

  • Your portfolio returned 16% this year
  • S&P 500 returned 10% (6% excess return)
  • But your portfolio has heavy value stock exposure, and value stocks beat growth by 4%
  • Factor-Adjusted Alpha = 16% - [10% market + 4% value exposure] = 2%
  • Your real skill added 2%, not the apparent 6%

Why it matters: Regular alpha can be misleading - a "value fund" might show high alpha just from value exposure, not manager skill. Factor-Adjusted Alpha reveals true skill by removing all known factor exposures.

↑ Back to top

Asset Allocation

What it means: How you divide your portfolio among asset classes: stocks, bonds, cash, real estate, etc.

Example Allocations:

  • Aggressive: 90% stocks, 10% bonds
  • Moderate: 60% stocks, 40% bonds
  • Conservative: 30% stocks, 70% bonds

Why it matters: Research shows asset allocation explains ~90% of portfolio return variability over time - more important than individual security selection.

↑ Back to top

Benchmark

What it means: A standard for measuring performance. Most portfolios compare themselves to an index like S&P 500, Russell 2000, or a custom benchmark.

Portfolio Example: Your U.S. large-cap portfolio should be benchmarked against S&P 500, not Russell 2000 (small-cap) or MSCI World (global).

Appropriate Benchmarking: Benchmark should match your investment universe and strategy.

↑ Back to top

Quantitative Investing

What it means: Using mathematical models, statistical analysis, and systematic rules to make investment decisions rather than subjective judgment.

Parallax Approach: Combines academic factor research with machine learning to identify patterns across thousands of securities simultaneously.

Benefits: Systematic discipline, no emotional decisions, scalable, consistent process, continuous learning.

↑ Back to top

Return

What it means: Percentage change in investment value over a period, including dividends and distributions.

Types:

  • Total Return: Price change + dividends
  • Price Return: Price change only
  • Annualized Return: Geometric average return per year
  • Risk-Adjusted Return: Return relative to risk taken

Portfolio Example: Buy stock at $100, receive $3 dividend, sell at $110. Total return = ($110 + $3 - $100) / $100 = 13%.

↑ Back to top

Systematic Strategy

What it means: Rules-based investment approach with no discretionary decisions. If conditions A, B, C are met, action X is taken automatically.

Benefits: Eliminates emotional decisions, enables backtesting, ensures consistent execution, scales efficiently.

Portfolio Example: "Every quarter, rank stocks by value metrics, buy top 50, sell bottom holdings" - systematic value strategy.

Cross-References: See Factor Investing, Quantitative Investing

↑ Back to top

References & Further Reading

Click to expand full academic citations

Risk-Adjusted Performance Metrics

Jensen's Alpha:

  • Jensen, M. C. (1968). The performance of mutual funds in the period 1945–1964. Journal of Finance, 23(2), 389-416.

Sharpe Ratio:

  • Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442.
  • Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119-138.
  • Sharpe, W. F. (1994). The Sharpe ratio. Journal of Portfolio Management, 21(1), 49-58.

Treynor Ratio:

  • Treynor, J. L. (1965). How to rate management of investment funds. Harvard Business Review, 43(1), 63-75.

Information Ratio:

  • Grinold, R. C., & Kahn, R. N. (1994). Active portfolio management: Quantitative theory and applications. Probus Publishing.
  • Goodwin, T. H. (1998). The information ratio. Financial Analysts Journal, 54(4), 34-43.

Portfolio Theory Foundations

Modern Portfolio Theory:

  • Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
  • Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments. John Wiley & Sons.

Capital Asset Pricing Model (CAPM):

  • Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442.
  • Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1), 13-37.
  • Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34(4), 768-783.

Nobel Prize (1990):

  • The Royal Swedish Academy of Sciences. (1990). The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1990. [Awarded to Harry M. Markowitz, Merton H. Miller, and William F. Sharpe]

Factor Models

Fama-French Models:

  • Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
  • Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1-22.

Carhart Four-Factor Model:

  • Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-82.

Modern Factor Research:

  • Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1-25.
  • Asness, C. S., Frazzini, A., & Pedersen, L. H. (2019). Quality minus junk. Review of Accounting Studies, 24(1), 34-112.

Conditional and Asymmetric Beta

Beta Asymmetry:

  • Pettengill, G. N., Sundaram, S., & Mathur, I. (1995). The conditional relation between beta and returns. Journal of Financial and Quantitative Analysis, 30(1), 101-116.

Conditional CAPM:

  • Lewellen, J., & Nagel, S. (2006). The conditional CAPM does not explain asset-pricing anomalies. Journal of Financial Economics, 82(2), 289-314.

Correlation and Tail Dependence

Correlation Asymmetry:

  • Longin, F., & Solnik, B. (2001). Extreme correlation of international equity markets. Journal of Finance, 56(2), 649-676.
  • Ang, A., & Chen, J. (2002). Asymmetric correlations of equity portfolios. Journal of Financial Economics, 63(3), 443-494.

Volatility Modeling

Fat Tails:

  • Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 36(4), 394-419.

ARCH/GARCH Models:

  • Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987-1007. [Nobel Prize 2003]
  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.

Drawdown Analysis

Maximum Drawdown Theory:

  • Magdon-Ismail, M., Atiya, A. F., Pratap, A., & Abu-Mostafa, Y. S. (2004). On the maximum drawdown of a Brownian motion. Journal of Applied Probability, 41(1), 147-161.

Conditional Drawdown at Risk:

  • Chekhlov, A., Uryasev, S., & Zabarankin, M. (2005). Drawdown measure in portfolio optimization. International Journal of Theoretical and Applied Finance, 8(1), 13-58.

Calmar Ratio:

  • Young, T. W. (1991). Calmar ratio: A smoother tool. Futures, 20(1), 40.

Style Analysis

Returns-Based Style Analysis:

  • Sharpe, W. F. (1992). Asset allocation: Management style and performance measurement. Journal of Portfolio Management, 18(2), 7-19.

Active Management Theory

Fundamental Law of Active Management:

  • Grinold, R. C. (1989). The fundamental law of active management. Journal of Portfolio Management, 15(3), 30-37.
  • Grinold, R. C., & Kahn, R. N. (1999). Active portfolio management (2nd ed.). McGraw-Hill.

Momentum and Reversal Effects

  • Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance, 48(1), 65-91.
  • De Bondt, W. F. M., & Thaler, R. (1985). Does the stock market overreact? Journal of Finance, 40(3), 793-805.