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 dampens every statistic the fund reports. The question on exam day is whether you can spot the illusion.
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. Semistandard deviation (sometimes called semideviation) is the square root of semivariance. Note that the denominator T can be the total number of observations (the standard statistical choice) or the number of below-mean observations (which scales better against standard deviation).
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. The exam tests which is which.
- 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. 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. With zero correlation the answer is $141,421, and with perfect negative correlation it is $0.
Bottom line
- Seven loss-side measures: semivariance, semistandard deviation, semivolatility, shortfall risk (a probability), target semivariance, TSSD (downside deviation), and tracking error; semivariance uses the mean, target measures use a chosen target
- Parametric VaR = Z × σ × √Days × Value, with Z = 2.33 (99%) and 1.65 (95%); risk scales with √Days, so a 10-day VaR = √10 × one-day VaR
- Portfolio VaR depends on correlation: sum (ρ=+1), √(sum of squares) (ρ=0), zero (ρ=−1)
- Sharpe (σ_p), Sortino (TSSD), Treynor (β_p), Information (tracking error), and RoVaR (VaR) each swap denominators; Sharpe has 5 named properties, Treynor 4
Exam shortcut
When a question gives downside risk, match the threshold to the measure: mean → semivariance/semistandard deviation/semivolatility; investor target → target semivariance/TSSD; probability of falling short → shortfall risk; benchmark → tracking error. For parametric VaR, always write Z × σ × √Days × Value. Plug 2.33 for 99% and 1.65 for 95%. For ten days from one day, multiply by √10 ≈ 3.16.
The full lesson (about 5,642 words, 38 min read) adds 2 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- defining alts
- blurred lines
- history us
- history asia
- risk return characteristics
- goals
- 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
- arbitrage
- binomial trees
- single factor models
- hypothesis testing
- sampling problems
- forwards vs futures
- forward foundations
- forwards on rates
- carry forwards
- managing long short
- option exposures
- rate options
- rate swaps
- option pricing
- risk measures
- var
- benchmarking
- ratio measures
- risk adjusted
- pricing data
- appraisals smoothing
- alpha beta overview
- estimating alpha
- return attribution
- statistical issues
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