Section 6 – Chapter 1 - Extrapolating Price from Volatility

Chapter 1 - Extrapolating Price from Volatility
Section 6 – Volatility Analysis
Presented By :
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Agenda
 State what the VIX measures
 State how the VIX expresses that
measurement
 Calculate expected volatility and price
ranges for various look-ahead periods
using VIX
 Express a limitation of VIX-based forecasts

📊 Key Takeaways : estimating future prices with the VIX
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1. VIX as a Market Sentiment Indicator: The VIX, often called the “fear index,” measures
implied volatility in the S&P 500 index options. A higher VIX suggests greater market
uncertainty or risk, while a lower VIX indicates a more stable or calm market.
2. VIX and Price Estimation: By observing the VIX, traders attempt to gauge potential
price movements of the underlying assets (like stocks or indexes). In general, a high VIX
signals that future price movements may be more volatile (up or down), while a low VIX
suggests the opposite.
3. VIX Futures: Futures contracts based on the VIX can be used to predict market
volatility. By examining the shape of the VIX futures curve (normal or inverted), one can
anticipate whether market participants are expecting rising or falling volatility.

📊 Key Takeaways : estimating future prices with the VIX
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4. Implied vs. Historical Volatility: VIX is a measure of implied volatility,
which is forward-looking, while historical volatility reflects past price
movements. Using the VIX alongside historical data can give more precise
predictions of future price ranges.
5. VIX as a Risk Management Tool: Traders and investors use VIX to hedge
risk. For example, a high VIX reading might encourage risk-off behavior (e.g.,
selling stocks or buying safe-haven assets like gold).

📊 Cheat Sheet for Estimating Future Prices with VIX
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VIX High (>30): Expect significant volatility in the near future. Traders might
anticipate big price swings in either direction, which can provide opportunities
for short-term trades or hedging.
VIX Moderate (20-30): Moderate market volatility expected. Price movements
are more likely to stay within a defined range, offering less risk for long-term
investors.
VIX Low (<20): Low volatility, suggesting stable market conditions. Prices
might not change dramatically, presenting a more predictable environment for
longer-term investments.

📊 Cheat Sheet for Estimating Future Prices with VIX
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• VIX Spike (Sharp Increase): If there is a sudden spike in the VIX,
it can signal an impending sharp price correction or crash.
• VIX Drop (Sharp Decrease): A rapid decrease in VIX may signal
investor complacency, potentially leading to an overbought market.

📊 Interpretation: Case Study – Estimating Future Prices Using VIX
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Interpretation: Case Study – Estimating Future Prices Using VIX
Let’s take a hypothetical case study where the VIX is currently at 35, indicating higher market
volatility:
Current VIX Analysis: The VIX is above 30, indicating heightened uncertainty. This suggests that the market
could see large price swings in the short term. If you're looking at a stock or an index, such as the S&P 500,
you may expect volatility in the next few days or weeks.
Estimating Future Price Range:
Lower Bound (Bearish Case): Assume the underlying stock index is trading at $4,000, and we expect
volatility to increase by 5%. This means a potential drop of $200 (5% of $4,000). In this case, the index
could fall to $3,800.
Upper Bound (Bullish Case): Similarly, a 5% upward move would push the price to $4,200.

📊 Interpretation: Case Study – Estimating Future Prices Using VIX
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Trading Strategy: Given the higher VIX, an investor might use options to hedge against
price movements. If anticipating a bearish trend, a trader could buy put options.
Alternatively, they might choose to hold cash and wait for volatility to stabilize before
making new investments.
VIX Futures Curve: If the VIX futures curve is upward sloping (contango), this indicates
that volatility is expected to rise over time. Conversely, if the curve is downward sloping
(backwardation), the market expects volatility to decrease, which could indicate
potential price stability in the future.

📊 Limitations of VIX-Based Forecasts
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1. VIX Reflects Implied, Not Realized Volatility: The VIX represents implied volatility
derived from the S&P 500 options market, meaning it reflects what traders expect future
volatility to be, not what has already occurred. As a result, it may not always accurately
forecast actual market moves or volatility.
2. Doesn’t Predict Direction: While the VIX gives insights into the level of volatility, it
doesn't predict whether the market will move up or down. A high VIX might indicate large
price swings, but it does not specify the direction of those movements.
3. Short-Term Focus: VIX is primarily a short-term indicator, often used to predict
volatility in the next 30 days. It is not a reliable tool for predicting long-term trends or price
movements.

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4. Lag Between VIX and Market Reactions: The VIX may not always move in sync with
actual market events or reactions. For example, a sudden news event or geopolitical crisis
can lead to volatility that is not immediately reflected in the VIX.
5. Market Manipulation Risk: As the VIX is derived from option prices, it can be
affected by market manipulation, especially in low-volume environments, which could
distort volatility predictions.
6. Cannot Account for Fundamental Changes: VIX does not incorporate fundamental
analysis. Major economic events (e.g., changes in interest rates, earnings reports,
geopolitical conflicts) can influence the market in ways that VIX cannot anticipate.

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7.VIX Only Measures Equity Market Volatility: The VIX is tied to the S&P 500 index, and as
such, it does not capture volatility in other asset classes (e.g., bonds, commodities, or
cryptocurrencies). A drop in the VIX doesn't necessarily correlate with lower volatility in
other markets.
8.VIX Mean Reversion: The VIX often shows mean-reverting behavior, where it spikes
during periods of high uncertainty but generally falls back to lower levels. This pattern can
mislead investors into thinking that volatility will always return to "normal" levels after a
crisis.

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 Longer tails mean more outliers.
This speaks to the need for
effective risk management. Also,
the more “peaked” or taller shape
of the S&P 500 return distribution
implies that VIX sometimes
underestimates upside and
downside price movement in the
S&P 500.
 This tendency of underestimating
forward returns in the S&P 500
illuminates its limitation.

📊 Cheat Sheet: Limitations of VIX-Based Forecasts
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Implied vs. Realized Volatility:
Implied (VIX) reflects expectations; Realized reflects actual outcomes.
VIX is forward-looking, so it may not always correlate with future realized volatility.
Does Not Predict Market Direction:
High VIX = High volatility, but not necessarily a market crash or rally.
Directionality needs additional analysis (e.g., news, technical patterns).
Short-Term Forecasting:
VIX predicts volatility in the next 30 days but not over the long term.
Longer-term predictions require broader analysis beyond the VIX.

📊 Cheat Sheet: Limitations of VIX-Based Forecasts
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Lagging Indicator:
VIX reacts to market moves and doesn't always lead them.
Sudden events might spike volatility before the VIX catches up.
Fundamental Analysis is Ignored:
The VIX doesn’t account for economic fundamentals, earnings, or corporate health.
Major changes in the underlying economy may not be reflected in the VIX.
Non-Equity Volatility:
The VIX is tied to equity markets and may not predict volatility in other asset classes.
Mean Reversion:
The VIX tends to revert to historical averages after spikes, which could mislead short-term
forecasts.

📊 Interpretation: Case Study – Limitations of VIX-Based Forecasts
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Let’s consider a case study where a trader is using the VIX to forecast future market
moves following a geopolitical crisis:
Scenario:
A geopolitical crisis causes tensions in a major economy, leading to an initial spike in
the VIX, which rises to 45 from a baseline of around 20.
• VIX Interpretation: The spike to 45 suggests heightened uncertainty and suggests
increased volatility in the short term. Traders might expect significant price swings in
the S&P 500.

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Limitations of the VIX in this Case:
No Directional Guidance: The rise in the VIX suggests volatility, but it doesn’t indicate whether the market will
move higher or lower. The market could fall as investors sell off in response to the crisis, or it could rally if the
crisis is resolved or mitigated quickly.
Not Reflecting Longer-Term Impact: The VIX only gives a snapshot of the next 30 days. If the geopolitical crisis
persists for months, the VIX will gradually revert to its mean, even if the crisis' long-term impact continues. This
could create a misleading sense of stability.
External Factors Not Accounted For: The VIX will not reflect other critical factors such as changes in economic
policy, corporate earnings, or central bank actions. If the crisis prompts a central bank intervention, the market
might stabilize, and the VIX may not show this shift in sentiment.
Lagging Indicator: The VIX might not immediately spike in response to a new crisis, especially if it is unexpected
or not yet fully priced into the options market. There might be a lag in how quickly the VIX reacts.

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Trading Implications:
• Short-Term Hedging: An investor might use the VIX to hedge against volatility by
buying options or using volatility products like VIX futures or ETFs. However, they
need to understand that the VIX will not always predict the direction or long-term
effects of market movements.
• Risk of Misleading Signals: Relying solely on the VIX for forecasting might
mislead the investor, especially in cases of geopolitical uncertainty where external
factors (like policy changes) significantly impact market sentiment.

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Conclusion:
 While the VIX is a valuable tool for gauging expected market volatility, its limitations need to be carefully
considered. It’s a short-term measure of implied volatility and doesn’t predict market direction or take into
account economic fundamentals. Investors and traders should supplement VIX-based forecasts with other tools
and analysis methods to get a more comprehensive view of future market behavior.
 Yes, estimates of quarterly, monthly, weekly, and daily standard deviations of prices can be derived from the
daily values of the VIX, but this requires making some assumptions based on the relationship between VIX and
expected volatility.
 The VIX gives the annualized implied volatility for the S&P 500 options market, which is the standard deviation
of the underlying index over the next 30 days, expressed on an annualized basis. Here’s how we can derive the
standard deviations for different time periods (quarterly, monthly, weekly, and daily) from the VIX.

📊 Key Formula: Expected Price Range
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Practical Example :
Current S&P 500 Price: 5000
VIX Level: 20
Key Takeaways
Higher VIX → Larger Expected Moves
(Greater Uncertainty)
Lower VIX → Smaller Expected Moves
(Lower Volatility)
Ranges are Approximate: This is a
statistical estimate, not a guarantee.

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At the end of the first quarter of 2024, VIX, which is usually expressed as a percentage,
was 13.01%. We can now estimate volatility, in this case standard deviation, for different
periods of time using the following formulas:

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where σ (sigma) = annualized volatility, assuming 252 trading days in a year
Monthly volatility is calculated by dividing 13.01%, the current VIX reading, by 3.46 or the square
root of 12.
This predicts a 68.2% (one standard deviation or sigma) probability of prices being between +3.76%
and −3.76% from the current price in 30 days’ time. Using the SPX closing price of 5,254.35 on
March 28, 2024 from Figure 6.1.1, we can now calculate the implied or expected price range over
the same 30 days.
Implied 30-day price move = current SPX index value × VIX monthly volatility
Implied 30-day move = 5,254.35 × (3.76% / 100)
Implied 30-day move = +/− 197.56
Finally, add and subtract the value of the implied 30-day move to conclude, with a 68.2% probability over
the next 30 days, the options market is expecting SPX to trade between 5,451.91 and 5,056.76.

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The standard deviation calculated from implied volatility also gives market participants an
opportunity to estimate daily and weekly trading ranges.
Daily volatility is calculated by dividing 13.01%, the current VIX reading, by 15.87 or the square root
of 252.
This predicts a 68.2% (one standard deviation or sigma) probability of prices being between +0.82% and
-0.82% from the current price in one day’s time.
Now calculate the implied 30-day move in SPX and add and subtract that from the current price.
Implied single-day move ≈ SPX index value × VIX daily volatility
Implied single-day move ≈ 5,254.35 × (0.82% / 100)
Implied 30-day move ≈ +/− 43.09
Using the SPX closing price of 5,254.35 on March 28, 2024 from Figure 6.1.1, the options market expects
price to trade in the range of 5,297.44 and 5,211.26, with a 68.2% probability over the next day.

Next Chapter 2 - Volatility Risk Premium
Section 6 - Volatility Analysis
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Section 6 – Chapter 1 - Extrapolating Price from Volatility

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