A Quantitative Approach to Width Selection Using Standard Deviations
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A purely discretionary approach to credit spread width selection can be prone to emotional biases and inconsistent results. A more robust and objective method is to use a quantitative approach based on standard deviations. This article will outline a framework for using standard deviations to guide the selection of credit spread widths.
The Concept of Standard Deviation in Trading
Standard deviation is a statistical measure of the dispersion of a set of data from its mean. In trading, it is used to measure the volatility of an asset's price. A one-standard-deviation move represents a price change that is within the expected range of price fluctuations for a given period.
A one-standard-deviation move can be calculated using the following formula:
One Standard Deviation Move = Current Price * Implied Volatility * sqrt(Days to Expiration / 365)
This formula provides an estimate of the expected trading range of the underlying asset over the life of the option.
Using Standard Deviations to Select Spread Width
The concept of standard deviation can be used to inform the selection of both the short strike and the spread width.
- Short Strike Selection: A common practice is to place the short strike of a credit spread outside of the one-standard-deviation range. This increases the probability of the option expiring worthless.
- Spread Width Selection: The width of the spread can also be determined based on standard deviations. For example, a trader might choose a spread width that is a certain percentage of the one-standard-deviation move.
Data Table: Standard Deviation and Spread Width
Let's consider a stock trading at $100 with an implied volatility of 30% and 30 days to expiration.
- One Standard Deviation Move: $100 * 0.30 * sqrt(30 / 365) = $8.68
| Spread Width Strategy | Short Strike | Long Strike | Spread Width | Approx. POP |
|---|---|---|---|---|
| 1 SD Short Strike, $2 Width | $91.32 | $89.32 | $2 | 84% |
| 1 SD Short Strike, $5 Width | $91.32 | $86.32 | $5 | 84% |
| 1.5 SD Short Strike, $5 Width | $86.98 | $81.98 | $5 | 93% |
This table illustrates how standard deviations can be used to construct credit spreads with different risk-reward profiles. The 1.5 SD short strike spread has a higher probability of profit, but it also has a lower premium and a higher risk-reward ratio.
The Benefits of a Quantitative Approach
A quantitative approach to spread width selection offers several benefits:
- Objectivity: It removes emotional biases from the decision-making process.
- Consistency: It ensures that the same criteria are applied to every trade.
- Testability: It allows a trader to backtest their strategy to see how it would have performed in the past.
Actionable Example
A professional trader might develop a trading plan that specifies the exact standard deviation levels they will use for their short strikes and spread widths. For example, they might have a rule to sell a bull put spread with the short strike at the 1.25 standard deviation level and a spread width equal to 25% of the one-standard-deviation move.
This level of precision and consistency is a hallmark of a professional trader. By using a quantitative approach, they can transform their trading from a discretionary art to a systematic science.
In conclusion, using standard deviations to guide the selection of credit spread widths is a effective technique that can help to improve the objectivity, consistency, and profitability of a trading strategy. While it requires a bit more effort than a purely discretionary approach, the benefits are well worth it.