A private real estate fund reports a Sharpe ratio of 1.8 with near-zero correlation to equities. Sounds like the perfect diversifier. Then you set it beside a market-priced index of comparable assets: twice the volatility, correlation near 0.45, drawdowns the appraisal series never shows. Same assets, same period, completely different risk picture, because appraisal smoothing can understate measured risk and overstate risk-adjusted performance. As you work through this lesson, learn to recognize how smoothing can lower reported volatility and correlation and can inflate risk-adjusted ratios.
Standard deviation treats every deviation from the mean the same. A 5% gain above average contributes just as much to measured risk as a 5% loss. For alternative investments with asymmetric return profiles, that symmetry is misleading.
Semivariance is the variance formula computed using only the observations that fall below the mean. Take the square root of semivariance and you get semistandard deviation (sometimes called semideviation), which puts the measure back in return units.
Three more downside measures often appear under different names:
Common mistakes
- Confusing the threshold for semivariance vs target semivariance. Semivariance uses the mean. Target semivariance (and TSSD/downside deviation) uses an investor-chosen target. Shortfall risk is a probability, not a dispersion. Check which threshold each measure uses before you compute it.
- Dropping √Days from parametric VaR. Parametric VaR is Z × σ × √Days × Value. Forgetting √Days gives a one-day VaR when the question asks for ten days. When returns are normal with zero mean, constant daily variance, and no autocorrelation, risk scales with the square root of time, not linearly.
- Adding VaRs without checking correlation. Adding two $100,000 VaRs only gives $200,000 when correlation is +1. In a normal, zero-mean framework with a common horizon, zero correlation gives $141,421. Perfect negative correlation gives the absolute difference of the two VaRs, which is $0 here only because the exposures are matched.
Bottom line
- Seven risk measures: semivariance, semistandard deviation, semivolatility, shortfall risk (a probability), target semivariance, TSSD (downside deviation), and tracking error; semivariance uses the mean, semivolatility uses the mean or a set threshold with − 0.5, target measures use a chosen...
- Parametric VaR = Z × σ × √Days × Value (assumes zero expected return), with Z = 2.33 (99%) and 1.65 (95%); factor-based VaR uses factor volatilities, correlations, and sensitivities; VaR is a threshold, not the maximum loss, and CVaR...
- Portfolio VaR (common horizon, normal, zero mean) = √(VaR1² + VaR2² + 2ρ·VaR1·VaR2): sum at ρ=+1, root-sum-of-squares at ρ=0, absolute difference at ρ=−1 (zero only for matched exposures)
- Two families: return-to-risk ratios and risk-adjusted returns (Jensen's alpha, M²); Sharpe, Sortino, Treynor, Information, and RoVaR each pair a specific numerator with a specific denominator; Sharpe has 5 named properties, Treynor 4; positive Jensen's alpha can coexist with M² below...
Exam shortcut
When a question gives downside risk, match the threshold to the measure: mean → semivariance/semistandard deviation; mean or a specified threshold, counted as with − 0.5 in the denominator → semivolatility; investor target → target semivariance/TSSD; probability of falling short → shortfall risk; benchmark → tracking error.
The full lesson (about 8,657 words, 58 min read) adds 2 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- defining alts
- blurred lines
- risk return characteristics
- goals
- history us
- history asia
- buy sell side
- service providers
- legal structures
- fund types
- fund features
- fund terms
- drawdown fees
- waterfall calcs
- hedge fund fees
- fees and behavior
- return math
- irr
- irr problems
- modified irr
- other measures
- j curve
- notional principal
- return distributions
- moments
- covariance correlation
- beta autocorrelation
- std dev variance
- normality testing
- market efficiency
- time value
- forward rates
- binomial trees
- single-factor default-free bond models
- reduced-form modeling credit risk
- single-factor equity pricing models
- single factor models
- hypothesis testing
- sampling problems
- forwards vs futures
- forward foundations
- forwards on rates
- carry forwards
- managing long short
- option exposures
- rate options
- option pricing
- risk measures
- var
- benchmarking
- ratio measures
- risk adjusted
- estimating alpha
- pricing data
- appraisals smoothing
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