Curriculum·S211 Portfolio Analytics and Performance Measurement·about 42 min
Risk-adjusted measures
By the end of this lesson you can
- →Compute a Sharpe ratio and the confidence interval around it from the same data
- →Explain why a short sample makes the point estimate uninformative regardless of its value
- →Identify the return shapes on which volatility-based measures systematically understate risk
- →Choose the measures that remain usable at individual sample sizes
Sophomore · enrolled learners
This lesson opens with Long-Term Capital Management, 1998.
- What happened
- LTCM reported after-fee returns of about 21 percent in its first year of trading, 43 percent in its second and 41 percent in its third, with low reported volatility, from a book of convergence trades run at very high leverage. In 1998, following the Asian and Russian crises, it lost about $4.6B in under four months. Leverage was roughly 50 to 1 at the end of August 1998, and by mid-September capital had fallen to around $600M against balance sheet assets still exceeding $100B, an effective ratio near 167 to 1. The Federal Reserve Bank of New York convened a recapitalisation by fourteen counterparties in late September.
- The decision point
- Every risk-adjusted measure computed on that return series was computed correctly. The failure was not arithmetic. A volatility-based measure estimates risk from the dispersion of returns that have already happened, and the strategy's whole design was to produce small, steady, positive returns until a specific and rare condition arrived. So the measure described the quiet period accurately and said nothing about the distribution the portfolio was actually drawn from, and the estimate rested on a handful of annual observations.
- Recorded loss
- $4,600,000,000
What you will be able to answer
- →What does a Sharpe ratio actually measure?
- →How precise is a Sharpe estimated from twelve monthly returns?
- →On which return shape does volatility understate risk most?
- →What is usable at individual sample sizes?
Orientation and Year One are open: anyone can read them without an account. From Year Two onward the lessons are for enrolled learners, because progress through the later years only means anything if it is tracked against a record.
It is free. We do not sell the list and there is nothing to buy at the end of it.
Sources and review
- https://www.federalreservehistory.org/essays/ltcm-near-failure
- https://www.aeaweb.org/articles?id=10.1257%2Fjep.13.2.189
- https://www.cftc.gov/sites/default/files/tm/tmhedgefundreport.htm
- https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2460551
Confidence high·Volatility low·Reviewed 2026-08-06·Owner unassigned
Contested
The Sharpe ratio computed in the worked example is derived here from the three reported annual return figures as an illustration. It is not a figure LTCM published, and three annual observations is precisely the sample size the lesson argues is unusable. That is the point of the exercise and it is labeled as such.
The standard error formula used is the asymptotic result for independent, identically distributed returns. Real return series are neither, and both violations tend to make the true uncertainty larger rather than smaller, so the intervals shown are optimistic.