The Hindu Business Line : Managing risk volatility

Volatility is a statistical measurement of the rate of price change of a futures contract, whether it is commodity or security or other underlying instrument. Commodity prices are extremely volatile due to a variety of external factors - macro and micro, domestic and global.

There also exist occasional but violent explosions in commodity prices.

There is no specific pattern or predictability to these price movements. As a result, incomes are subject to unpredictable price "booms and busts" cycles.

Standard deviation is not a well-known concept in our country.

But, it has been successfully applied globally to manage the volatility and effectively manage risk.

Standard deviation

Volatility of the time series of prices at time t-1 can be defined as the standard deviation of the time t return.

For statistical reasons, return is defined as the logarithmic return. (equation 1)

If we assume that returns are conditionally homoskedastic (where standard deviation is constant), equation 1 is exact. However, if they are conditionally heteroskedastic (where conditional/unconditional standard deviation are not constant), we need to clarify the definition.

Does volatility at time t - 1 represent the unconditional standard deviation of the time t log return? Or does it represent the standard deviation of the time t log return conditional on information available at time t - 1?

To emphasize this, we might express equation 1 as equation 2.

Equation 1 indicates that the standard deviation is conditional on information available at time t - 1.

Another issue in defining volatility is that of the unit of time on which it is based, whether it is daily, weekly, monthly or annual volatility.

Volatilities for different units of time are fundamentally different notions. There is no direct relationship between, say a weekly volatility and an annual volatility.

What is VaR?

VaR (Value at Risk) is defined as - "the maximum expected loss (measured in currency units) in an asset's value (or a portfolio) over a given time period and at a given level of confidence (or with a given level of probability), under normal trading conditions."

VaR describes the probability of the market risk of an underlying asset.

Using the historical volatility, e.g. over a rolling 100 trading day's volatility one can come to know that how risky the trading asset had been over the previous 100 days.

Two parameters

VaR has two parameters: the time period we analyze (i. e. the length of time over which we plan to hold the assets in the portfolio) and the confidence level at which we plan to make the estimate.

The typical holding period is 1 day and the popular confidence levels usually are 99 per cent and 95 per cent.

VaR measures how much we could lose, but it also provides an indication of how much money might be put aside as a cushion for days when losses are unexpectedly large.

VaR is not only a risk measurement tool, but also facilitates risk management. The simplest way of VaR calculation is based on historical volatility of normal distribution of asset returns. Here we calculate 99 per cent VaR, based on three sigma limits.

It is better to understand the concepts of standard deviation and VaR and use the same to effectively manage risk and volatility.

(Kailash Gupta is Managing Director of NMCE. He can be reached at comex@icenet.net)

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