Understanding Volatility and its different estimation methods.

1. Knowledge Series: Understanding Volatility
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2. Knowledge Series: Understanding Volatility
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Introduction:
Volatility measures variation in price of a commodity over a period of time. Generally
represented as a % figure, it is estimated on percentage or logarithmic returns and not on the
absolute Prices (due to the stationary nature of returns). Volatility can be understood as the
spread in the return series around the mean return - the larger the spread the higher the
Volatility. Two Commodities with different volatilities may have the same average return, but
the one with higher volatility will have larger price movements (or returns) and there by having
higher uncertainty.
Figure 1: Illustrating volatility as the spread around the mean
Standard Deviation is the simplest way of measuring Volatility:
=
∑ ( − ̅)
( − 1)
(1)
As can be seen from the formula, this is a measure of the spread of , , … . around ̅ which
is the average . It must also be noted that Volatility does not represent the direction of price
movements; rather, it only represents the range in which the next price outcome will be, with a
certain probability.

3. Knowledge Series: Understanding Volatility
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A commodity with CMP (Current Market Price) of 1000 $/MT with 1-day Volatility estimate of
10% suggests that there is 68% probability that tomorrow’s price is in the range 900 $/MT –
1100 $/MT, assuming the price returns are normally distributed and have a zero average return.
A Common Misconception:
There is also a common misconception that consistent uptrend in prices leads to higher
Volatility. Price uptrend does not necessarily mean higher Volatility, in fact a consistent uptrend
means similar daily returns i.e., lower Volatility. The same is depicted in the following figure.
Figure 2: Price trend and time-varying Volatility plot
Application:
Market Risk or Price uncertainty arises from Volatility. Daily Volatility or 1-day Volatility is a good
measure of Price Risk associated with a Commodity. Better risk measures like VaR and Expected
Shortfall that have evolved over time have made decision making more objective and quicker.
However, calculating Volatility has become inevitable considering that VaR, Expected Shortfall
and Derivative Pricing etc. need Volatility as a key input. For forecasting Historic Volatility, one
needs to have a time series of past market price. Prices of some commodities are available on a

4. Knowledge Series: Understanding Volatility
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daily basis whereas others are available on a weekly, fortnightly or monthly basis. If daily Prices
are used for computing, it gives a 1-day estimate or Daily Volatility. Similarly if weekly prices are
used, what we compute is a weekly estimate of Volatility.
Scaling Volatility:
One may roughly approximate a Volatility estimate by scaling it with the square root of time
assuming that the price returns were independent.
ℎ = 1 × √ℎ (2)
1 =
ℎ
√ℎ
(3)
However, it is to be noted that square root of time scaling assumes independent price moves
and constant volatility. If this assumption doesn’t hold good, the resultant volatility may be over
or underestimated or be inaccurate.
Estimation Methods:
Apart from Standard Deviation which computes average deviation from mean, there is a time-
varying volatility i.e., an estimate that changes with the latest price movements (returns). This
approach proves helpful especially when the time series exhibit Volatility Clustering. When
there are periods of higher returns and periods of relatively lower returns, such time series is
said to exhibit Volatility Clustering. Since Unconditional Volatility averages out all deviations
from mean, it does not incorporate clustering phenomenon. Here we’ll see two methods of
time-varying volatility along with the unconditional volatility (or standard deviation).
Unconditional Volatility / Standard Deviation
This is the simplest way of computing Volatility and shows average deviation from mean. A low
standard deviation indicates that the returns tended to be close to the mean; on the other hand
a high standard deviation indicates that they were spread out over a larger range.
=
∑ ( − )
− 1
(4)

5. Knowledge Series: Understanding Volatility
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represents the returns of the commodity, is the average return and is the number of
returns.
Conditional Volatility (EWMA)
EWMA stands for Exponentially Weighted Moving Average. As the name suggests, this method
estimates time-varying volatility by giving varying weights to past returns. The latest return gets
the highest weight and the weight given to the older returns reduces exponentially thereafter.
= × + (1 − ) × ( − ) (5)
∈ [0,1] is the decay factor with a standard value of 0.94 and can be approximated as
unconditional volatility.
Conditional Volatility (GARCH)
Unlike the EWMA approach, this approach lets the commodity returns data itself determines the
weights to be given to the past information while forecasting Volatility. GARCH is the generalised
version of ARCH (Autoregressive Conditional heteroskedasticity) model which was introduced by
Bollerslev (1986). The standard GARCH (1, 1) model for forecasting volatility is,
= + + (6)
where > 0, α > 0, β > 0 are the weights to be estimated and + α + β =1.
The variables , α, β are to be estimated using the maximum likelihood function.
Understanding GARCH (1, 1) equation: The first number in parenthesis represents the no. of
autoregressive lags and second represents the no. of moving average lags .
About the Author: Santoshi Ippili
Santoshi has worked extensively in the Commodity Risk Management Domain for over 8 years and
has been instrumental in developing and implementing risk management software solutions for
several Fortune 2000 companies. She holds a post-graduate degree in Finance from BITS Pilani. At
RES, she is responsible for research and business analysis of the latest tools and techniques in Risk
Management and bringing them in a structured way into the product. She can be reached
on santoshi@riskedgesolutions.com.

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