Knowledge series understanding volatility

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:

푆퐷 =∑ (푥 − 푥̅)

(푛 − 1) (1)

As can be seen from the formula, this is a measure of the spread of 푥 , 푥 , … . 푥 around 푥̅ which

is the average푥. 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.



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



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.

ℎ푑푎푦푉표푙푎푡푖푙푖푡푦 = 1푑푎푦푉표푙푎푡푖푙푖푡푦× √ℎ (2)

1푑푎푦푉표푙푎푡푖푙푖푡푦 =ℎ푑푎푦푉표푙푎푡푖푙푖푡푦

√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.

휎 =∑ (푟 − 휇)

푇 − 1 (4)



푟 represents the returns of the commodity, 휇 is the average return and 푇 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.

휎 = 휆 × 휎 + (1 − 휆) × (푟 − 휇) (5)

휆 ∈ [0,1] is the decay factor with a standard value of 0.94 and 휎 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,

휎 = 휔 + 훼휀 + 훽휎 (6)

where 휔 > 0,α > 0,β > 0 are the weights to be estimated and 휔 + α+ β =1.

Thevariables휔,α,βare to be estimated using the maximum likelihood function.

Understanding GARCH (1, 1) equation: The first number in parenthesis represents the no. of

autoregressive lags 훼휀 and second represents the no. of moving average lags 훽휎 .

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 [email protected].



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Knowledge series understanding volatility