2012issue C1077-78
Equity-curve bands as a critique of value at risk
Value at risk is presented as a typical-day dollar bound, not a ruin measure. The archive rebuilds the same two-standard-deviation envelope as a lower Bollinger Band on a four-week channel breakout equity curve and sets individual survival on position size.
- Value at risk is formed as portfolio value times a normal left-tail return and is presented as a dollar loss bound for typical days, not for the extreme days that can dominate a year.
- Under its own normal assumption a two-standard-deviation bound is expected to be breached about once every 44 trading days, while clustered many-standard-deviation selloffs are used to argue that large down days arrive far more often than that model implies.
- A lower Bollinger Band on the equity curve of a four-week channel breakout, with a 20-week lookback, takes the loss figure from realized system equity rather than from a theoretical return distribution.
- Position size is the primary individual control on risk of ruin: risking about 5% of capital per trade is presented as a rule under which roughly 130 consecutive losses would be required to lose 99% of starting capital.
A typical-day dollar bound
Value at risk is formed as portfolio value times a normal left-tail return. That return is the mean plus a z-multiple of return standard deviation, then scaled by portfolio value. The result is presented as a dollar loss bound for typical days, not for the extreme days that can dominate a year.
Under its own normal assumption, a two-standard-deviation value-at-risk bound is expected to be breached about once every 44 trading days. Account moves larger than the bound are treated as frequent rather than exceptional.
Internal inconsistency and clustered tails
Two value-at-risk models applied to the same concentrated hedge produced dollar estimates of 67 million and 129 million. That gap is used to show that the metric can be internally inconsistent and inadequate as a risk definition.
Clustered many-standard-deviation down days, including a sequence described as 25-standard-deviation moves on successive days, are used to argue that selloffs occur far more often than a normal value-at-risk model implies.
A lower band on realized equity
A rough individual equivalent of value at risk is obtained by tracking account equity, taking the standard deviation of those balances over a lookback such as 20 days or weeks, and multiplying that standard deviation by two.
That envelope is implemented as a lower Bollinger Band on the equity curve of a four-week channel breakout traded across a commodity basket, using a 20-week lookback. The loss figure comes from realized system equity rather than from a theoretical return distribution. The object of the measurement is the breakout system's equity path, not its trade list.
Position size and risk of ruin
Individual survival rules set against concentrated institutional books include diversifying across markets, restricting activity to liquid venues, and keeping size small enough that an ordinary adverse move cannot empty the account.
The same 1,000-dollar account that would need about a 50% decline to be wiped out in a fully margined stock position could be wiped out by a 5% move if leveraged 20-to-1 in futures.
Risking about 5% of capital per trade is presented as a sizing rule under which roughly 130 consecutive losses would be required to lose 99% of starting capital, allowing distant or omitted stops so trades have more time to work.
Even traders who view close stops as harmful to backtested profitability are described as placing disaster stops 20% to 25% away from the market to block career-ending losses. Risk of ruin, the chance that a string of ordinary losses ends the account, is the survival problem placed above a typical-day value-at-risk number.