Added VIX > VIX3M Backwardation Signal
CONTANGO
Definition: A market condition where longer-term futures or volatility indices trade at higher levels than shorter-term ones, reflecting an upward-sloping term structure.
VIX9D < Spot VIX < VIX3M < VIX6M < VIX1Y during stable markets.
Contango occurs in a normal, calm market. Volatility expectations increase with time due to uncertainty, so longer-term indices (e.g., VIX1Y) are higher than shorter-term ones (e.g., Spot VIX).
Implication: Indicates stability or low immediate fear, with higher costs for hedging further out.
BACKWARDATION
Definition: A market condition where shorter-term futures or volatility indices are higher than longer-term ones, reflecting a downward-sloping term structure.
Spot VIX > VIX3M > VIX6M > VIX1Y during periods of heightened uncertainty or panic, or even VIX9D > Spot VIX in extreme short-term panic.
Backwardation occurs during periods of heightened near-term uncertainty or panic, where immediate volatility (e.g., Spot VIX) spikes above longer-term expectations (e.g., VIX6M).
Implication: Often a contrarian buy signal for equities, as extreme near-term fear may signal a market bottom.
VIX CALCULATIONS
The CBOE VIX indices measure annualized implied volatility based on S&P 500 (SPX) option prices. Here’s how it’s calculated step-by-step:
Step 1: Gather Option Prices. Collect the prices of out-of-the-money (OTM) SPX put and call options for a specific expiration period.
• Puts with strike prices below the current SPX forward price.
• Calls with strike prices above the current SPX forward price.
Step 2: Determine Key Variables
• T: Time to expiration in years (e.g., 30 days / 365 = 0.0822 years for Spot VIX).
• F: Forward SPX price, derived from the strike price where the put and call prices are closest in value.
• K0: The strike price just below F (the "at-the-money" reference point).
• Ki: Each option’s strike price in the basket.
• ΔKi: The difference between consecutive strike prices (e.g., if strikes are 4000 and 4010, ΔKi = 10).
• R: Risk-free interest rate (e.g., based on U.S. Treasury yields for the expiration period).
• Q(Ki): Midpoint price of the option at strike Ki.
Step 3: Calculate Variance Contribution
For each option (put or call), compute its contribution to variance:
Contribution = (ΔKi / Ki^2) * e^(R * T) * Q(Ki)
Where:
• ΔKi / Ki^2: Weights the option by its strike price (lower strikes contribute more).
• e^(R * T): Adjusts for the time value of money using the risk-free rate.
• Q(Ki): The option’s price.
Sum these contributions across all OTM puts and calls:
Sum = (2 / T) * [Sum of all (ΔKi / Ki^2) * e^(R * T) * Q(Ki)]
Step 4: Adjust for Forward Price
Calculate a correction term based on the difference between the forward price and the at-the-money strike:
Correction = (1 / T) * [(F / K0) - 1]^2
Subtract this from the sum:
Variance = Sum - Correction
Or, fully written:
Variance = (2 / T) * [Sum of (ΔKi / Ki^2) * e^(R * T) * Q(Ki)] - (1 / T) * [(F / K0) - 1]^2
Step 5: Convert to Volatility
Take the square root of the variance and annualize it:
VIX = 100 * SquareRoot(Variance)
This gives the VIX value as an annualized percentage.
Interpolation (When Needed)
If the target horizon (e.g., 30 days) doesn’t match an exact option expiration:
Calculate variance for two nearby expirations (e.g., 23 days and 37 days).
Interpolate linearly:
Variance_30days = w1 * Variance_23days + w2 * Variance_37days
Where:
• w1 and w2 are weights based on days (e.g., w1 = (37-30)/(37-23), w2 = (30-23)/(37-23)).
Then apply Step 5 to the interpolated variance.
Spot VIX (30-day VIX):
• Definition: The Spot VIX, officially the CBOE Volatility Index (VIX), measures the market’s expectation of 30-day implied volatility of the S&P 500.
• Options: Derived from near-term and next-term SPX options (e.g., 23-day and 37-day expirations) to interpolate a constant 30-day horizon.
• T: 30 days / 365 = 0.0822 years.
VIX3M (3-month Volatility Index):
• Definition: Measures the expected 3-month (approximately 90-day) implied volatility of the S&P 500.
• Options: Derived from SPX options expiring around 90 days (e.g., 85-day and 95-day, interpolated if needed).
• T: 90 days / 365 = 0.2466 years.
VIX6M (6-month Volatility Index):
• Definition: Measures the expected 6-month (approximately 180-day) implied volatility of the S&P 500.
• Options: Derived from SPX options expiring around 180 days (e.g., 175-day and 185-day, interpolated if needed).
• T: 180 days / 365 = 0.4932 years.