Risk Management and Investment Management
Investment risk management evaluates returns relative to objectives, benchmarks and constraints. Distinguish total risk from active risk, consider leverage and liquidity, and ask whether a manager’s results reflect compensated exposures or repeatable skill.
The topic at a glance
| Concept | How it works | Watch for |
|---|---|---|
| Total risk | Measure variability and downside relative to the investor’s obligations. | Choosing a portfolio only by its historical return. |
| Active risk | Measure portfolio returns relative to the chosen benchmark. | Using total volatility as tracking error. |
| Constraints | Incorporate leverage, liquidity, concentration and mandate limits. | Assuming a favorable ratio removes implementation risk. |
01Total risk
How it works: Measure variability and downside relative to the investor’s obligations.
Watch for: Choosing a portfolio only by its historical return.
02Active risk
How it works: Measure portfolio returns relative to the chosen benchmark.
Watch for: Using total volatility as tracking error.
03Constraints
How it works: Incorporate leverage, liquidity, concentration and mandate limits.
Watch for: Assuming a favorable ratio removes implementation risk.
Original worked example
Sharpe and information ratio answer different questions
A portfolio returns 10%, the risk-free rate is 2%, and total volatility is 16%. Its benchmark returns 8%, with tracking error of 4%. Assume consistent annual measures.
- STEP 1
Sharpe ratio = (10% - 2%)/16% = 0.50.
- STEP 2
Active return = 10% - 8% = 2%.
- STEP 3
Information ratio = 2%/4% = 0.50.
The numerical ratios coincide here, but one uses excess return and total risk; the other uses active return and active risk.
Illustrative assumptions and calculations for learning. Not observed market data or an official exam item.
How the ideas fit together
Before you start: Portfolio return, benchmarks, volatility and covariance.
Match the risk denominator to the mandate
Total volatility measures dispersion of portfolio returns. Tracking error measures dispersion of active returns relative to a specified benchmark. A broad market portfolio can have substantial total risk and very little active risk. Changing the benchmark changes the interpretation of active performance without changing the underlying holdings.
Separate return attribution from evidence of skill
A result can reflect exposure to common factors, market timing, security selection or implementation costs. A short period of outperformance cannot distinguish these reliably by itself. Review leverage, drawdowns, liquidity and whether reported prices adjust slowly. Use consistent horizons and return definitions when comparing performance ratios.
Evaluate how the return was earned
A manager can outperform by taking an unrecognized factor exposure or by holding illiquid assets whose reported prices adjust slowly. Compare like horizons and benchmarks, assess fees and implementation costs, and inspect drawdowns and liquidity alongside summary ratios. Historical performance alone does not establish skill or future results.
Work through the topic
Connect portfolio objectives, benchmark-relative risk, liquidity and performance evaluation. Treat a ratio as evidence about a defined question, not a complete assessment of an investment process.
Translate the mandate into a risk problem
A portfolio’s relevant risk depends on the obligation it serves. A fund tracking an equity index cares about deviations from that benchmark; a liability-focused investor cares about its assets relative to future payments; an absolute-return mandate may impose a drawdown or capital-preservation objective. The same holdings can look acceptable under one objective and inappropriate under another.
Specify the benchmark, horizon, allowable instruments, liquidity needs and constraints before calculating performance. A manager cannot be evaluated fairly against a benchmark selected after observing the result. Likewise, a high return obtained by taking exposure outside the mandate is not evidence that the approved strategy worked. Risk evaluation starts with the comparison the investor actually authorized.
An original pension example has long-dated benefit obligations and near-term cash payments. A longer-duration asset allocation may reduce sensitivity of the funding surplus to rate changes, yet leave a need for liquid resources to pay benefits and collateral. Asset risk, liability risk and cash-flow risk therefore need connected but distinct measures.
Distinguish allocation weights from contributions to risk
A 50/50 capital allocation is not generally a 50/50 risk allocation. Portfolio variance combines weights, individual volatilities and covariances. A volatile asset can dominate total risk even with a modest capital weight, while an offsetting position can reduce the total. Interpret component contributions within the model used to calculate them and examine whether the dependence estimate is stable.
Suppose a portfolio holds 50% in an asset with 20% volatility and 50% in an asset with 5% volatility, with zero correlation. Portfolio variance is 0.5² × 0.20² + 0.5² × 0.05² = 0.010625, so volatility is about 10.31%. The first asset contributes 0.01 of the variance and the second 0.000625. Equal invested amounts clearly do not produce equal variance contributions in this deliberately simple case.
Changing correlation to 0.5 adds 0.0025 to variance, raising volatility to about 11.46%. This sensitivity is a reason to examine a range of dependence assumptions and shared stress exposures. A risk budget based on one covariance estimate is a conditional plan. Constraints, transaction costs and changes in market conditions influence whether it remains feasible.
| Input or outcome | Zero correlation | Correlation 0.5 |
|---|---|---|
| Capital weights | 50% and 50% | 50% and 50% |
| Asset volatilities | 20% and 5% | 20% and 5% |
| Portfolio variance | 0.010625 | 0.013125 |
| Portfolio volatility | 10.31% | 11.46% |
Original equal-weight portfolio: capital and risk differ
- Capital weights
- Zero correlation: 50% and 50%
- Correlation 0.5: 50% and 50%
- Asset volatilities
- Zero correlation: 20% and 5%
- Correlation 0.5: 20% and 5%
- Portfolio variance
- Zero correlation: 0.010625
- Correlation 0.5: 0.013125
- Portfolio volatility
- Zero correlation: 10.31%
- Correlation 0.5: 11.46%
Choose a performance denominator that matches the question
A Sharpe ratio compares excess return over a risk-free reference with total return volatility. An information ratio compares active return over a selected benchmark with tracking error. The different denominators can produce different rankings. Use consistent periods and return conventions; a monthly numerator divided by an annualized denominator has no useful interpretation.
For an original illustration, annual portfolio return is 9%, the risk-free return is 3%, total volatility is 12%, benchmark return is 7% and tracking error is 4%. Sharpe is (9% - 3%)/12% = 0.50. The information ratio is (9% - 7%)/4% = 0.50. Their equality here is coincidental. If the benchmark return changes to 8%, the information ratio becomes 0.25 while the stated Sharpe ratio is unchanged.
Review the return-generating process as well as the ratio. Fees, valuation lags, concentrated exposures and infrequent large losses can affect interpretation. A favorable sample outcome does not establish persistent skill. Examine whether the strategy followed its mandate, whether results are robust to the chosen period and whether investors could actually hold or redeem the position under stressed conditions.
Can low tracking error coexist with substantial losses?
Yes. A portfolio that closely follows a falling benchmark can have low active risk and a large absolute loss. Tracking error describes deviations from the benchmark, not protection of invested capital.
Does diversification eliminate liquidity risk?
No. Many differently named investments may rely on the same trading venues, dealers or funding conditions. Review how assets can be sold and how obligations are funded in a shared adverse scenario, as well as their ordinary return covariance.
Try a changed assumption
A portfolio exactly tracks its benchmark before fees. Is its total volatility necessarily zero?
Show answer and reasoning
No. Its active return and tracking error can be zero while both portfolio and benchmark fluctuate substantially. An information ratio with zero denominator is not a meaningful finite score.
Original learning check. No email or account needed.
Can I compare information ratios against different benchmarks?
Only with care. The benchmark defines both active return and tracking error. Different benchmarks can make apparently similar ratios describe different decisions.
Sources and scope
Links checked 2026-10-10. GARP establishes exam scope; the technical references support the methods identified below. These are selected study notes and original examples, not complete curriculum coverage or official exam questions.
- GARP FRM study materials and 2026 learning objectives
Exam-domain scope and the official route to the annual learning objectives. This page does not certify coverage of every reading.
- MIT OpenCourseWare: portfolio theory
Portfolio variance, covariance and diversification.
- MIT OpenCourseWare: quantitative lecture index
Further reading across quantitative methods. Specific technical references are linked beside the explanations below.
- MIT: Factor Modeling, lecture 15
Factor exposures and covariance-based portfolio risk decomposition.
- CFA Institute: Sharpe ratio and information ratio
Risk-adjusted performance ratios, benchmark selection and interpretation limits. Numerical cases on these pages are original.
Prepared by MiloPrep editorial team. MiloPrep is independent of GARP. References do not imply endorsement or independent review of these notes.