2002issue C021-7
Set mixed-book share counts from one portfolio loss bound
A single-name long-stock sizing rule does not extend unchanged to a book with several names and both long and short positions. Portfolio Value at Risk turns recent return statistics into one loss bound at a chosen confidence level. Pairwise correlations keep that bound from being a simple sum of standalone risks, and Mean-variance optimization then reallocates share counts under a stated Portfolio risk budget.
- A sizing rule built for one long stock does not extend unchanged to a book that holds several names and both long and short positions.
- Portfolio Value at Risk is the largest loss, in money or percent of portfolio value, that can occur over a fixed horizon at a chosen confidence level.
- Pairwise correlations of percentage price changes can be far from one, so a joint risk figure must use those coefficients instead of adding standalone position risks.
- Mean-variance optimization can reallocate share counts across the same names so successively lower Value at Risk is paired with lower expected return.
A single-name rule is not a book rule
A single-name long-stock sizing rule does not extend unchanged to books that hold several names and both long and short positions.
One loss bound for the whole book
Portfolio Value at Risk is defined as the largest loss, in money or percent of portfolio value, that can occur over a fixed horizon at a chosen confidence level.
Weekly portfolio Value at Risk is computed as portfolio mean minus a chosen number of standard deviations times portfolio volatility, with the mean taken as a position-weighted average of the components.
A weekly horizon can be estimated either by scaling daily mean and volatility or by measuring those statistics on weekly data, using the sample judged most representative of the coming week.
Do not add standalone position risks
In the worked five-name long-short book, a 21-day lookback of log returns produced individual position Value at Risk figures that summed to an undiversified total of -201107.
Pairwise correlations of percentage price changes can be far from one, so a joint risk figure must use those coefficients rather than adding standalone position risks.
Reallocate shares under the bound
Mean-variance optimization can reallocate share counts across the same names to produce an efficient frontier of portfolios that pair successively lower Value at Risk levels with lower expected return.
The construction step assumes that the stated return views are correct and that volatilities and correlations stay constant over the chosen horizon.
The same steps apply to funds
The same Value at Risk and correlation machinery can be applied when the holdings are funds rather than individual stocks, using historical return records and a stated confidence-level loss bound.
All readings on this track · 6 readings
- 1990Score drawdown depth and duration as a pain budget
- 1993Comfort before capital: walk the tape before you size
- 1994Set the portfolio risk budget before you size
- 2001Evaluate portfolio survival with value-at-risk, budgets, and scenarios
- 2002Set mixed-book share counts from one portfolio loss bound
- 2010Treat the pairs book as one risk budget before adding a layer