Description
It explains A comprehensive document on India VIX index for risks.
Is India VIX A Good Forecast Of The Market Risk ?
Submitted By : Madhav Kumar Sharma
IS INDIA VIX A GOOD FORECAST OF MARKET RISK ?
Risk, as can be defined in finance, refers to the likelihood that we will receive a return on an investment that is different from the return we expected to make. Thus, risk includes not only the bad outcomes, i.e., returns that are lower than expected, but also good outcomes, i.e., returns that are higher than expected. The former is referred to as downside risk and the latter is upside risk; but we consider both when measuring risk. Although actual returns may differ from expected returns due to a variety of reasons, we can group the reasons into two categories: • • Firm-specific risks or Unsystematic risks or Diversifiable Risks Market-wide risks or Systematic risks or Non – Diversifiable risks
The risks that arise from firm-specific actions affect one or a few investments, while the risk arising from market-wide reasons affect many or all investments. Some risk may affect only one or a few firms and it is this risk that we categorize as firmspecific risk. Within these we would consider a wide range of risks, like the risk that a firm may have misjudged the demand for a product from its customers; we call this project risk. The risk could also arise from competitors proving to be stronger or weaker than anticipated; we call this competitive risk. There is other risk that is much more pervasive and affects all investments. For instance, when interest rates increase, all investments are negatively affected, although to different degrees. We term this risk market risk. Diversification reduces an investor’s exposure to Firm specific risks and he is rewarded only for bearing the market risks or the non diversifiable risks. Volatility Index is a measure of market’s expectation of volatility over the near term. Volatility Index is a measure, of the amount by which an underlying Index is expected to fluctuate, in the near term, calculated as annualized volatility, denoted in percentage e.g. 20%, based on the order book of the underlying index options. India VIX is a volatility index based on the Nifty 50 Index Option prices. From the best bid ask Prices of near term Nifty 50 Options contracts , a volatility
figure (%) is calculated which indicates the expected market volatility over the next 30 calendar days. Higher the implied volatility higher the India VIX value and vice versa. The VIX is often referred to as a "fear gauge" because it is anti correlated with market performance: i.e. when the Index goes up the implied volatility goes down, and vice versa. To characterize the probability distribution with a single volatility value, it is fitted to a Gaussian. Historically, the outlier events are much more likely than implied by a log normal distribution. Deep out of the money options are included in the VIX computation as long as there are nonzero bids and no intervening zero bids at more probable strikes. This only goes out about 2 sigma into the tail, so the distortion from mispricing of rare events is small. So, though the tail risks are not included in VIX forecasts, the effect of ignoring it is minimal. The VIX methodology involves calculating an estimate of "fair variance" for near-term and nextterm options, weighting these two values to construct a constant 30-day variance, and then taking the square root to produce a value for VIX. The main attraction of VIX index is that it mitigates many of the problems which lead to biased implied volatility estimate. Volatility index calculation requires two pairs of options that are used from each series. Each pair consists of one call and one put with the same strike. In total, eight options must be used. The implementation of the method assumes a very liquid market. But the value of the VIX does not always present a true sentiment of the market as it is dependent on the liquidity of the index option contracts in the mid month contracts. Unfortunately liquidity in index options beyond the current series is very less. Hence the spread across bid and offers for such far month contracts tends to be huge. This then affects the calculation of VIX thus making it erratic at times. By dividing the VIX with the PCR (put-call ratio) of near month contracts the anomaly is cured to a great extend. Another problem associated with India VIX is that there are no tradable products based on India VIX. The derivative contracts on Volatility Indices allow investors to trade ‘volatility’. Volatility is one among the various factors that affect the options prices. Many market participants have been calling for tradable products which they would find it useful in hedging their portfolios.
India VIX calculation methodology India VIX is calculated using the methodology adopted by CBOE currently for computing VIX on S&P 500 options. This method does not use any option pricing model such as Black and Scholes to calculate the VIX. Simply put, it derives the implied or expected volatility from the near and mid month options bid and offer prices of the Nifty 50 index options. From the options bid and offer prices an indicator can be derived as to what is the volatility the investors are expecting in the market. This volatility figure, denoted in percentage, is the India VIX value. The actual computation methodology is given below. The generalized formula used in the India VIX calculation is:
Select call options that have strike prices greater than K0 and a non-zero bid price. Select put options that have strike prices less than K0 and a non-zero bid price where K0 is the strike price
immediately below the forward index level. Finally we select both the put and call with strike price K0. K denotes the strike price and T denotes the days to maturity. Strike prices are assumed to be of the order such that K(j+1) > K(j) K0 is the first strike below the forward index level , F K(i) is the strike price of the ith out-of-the-money option; a call if K(i) > K(0) and a put if K(i) < K(0); both put and call if K(i) = K(0). The INDIA VIX generally uses put and call options in the two nearest-month expiration in order to bracket a 30-day calendar period. In the calculation of VIX restriction is imposed on the two maturities such that T(2) >= 22 >= T(1) >= 8 To reduce biases in computing the volatility indexes, the prices of second nearby options to replace nearby options with 8 days to expire is used. Volatility index isolates expected volatility from other factors affecting options prices, such as changes in the underlying price, dividends, interest rates, time to expiration. The volatility index offers a way for investors to buy and sell option volatility directly, without having to deal with other risk factors that would have an impact on the value of an index option position. Standard deviation method can measure the standard deviation between equity returns with respect to the equity index. Exponential GARCH (eGARCH) model which is asymmetric GARCH can be used to measure risk for equities as it is less likely to breach non-negativity constraints Conclusions: As discussed above, the Indian VIX does not tell about the prices but the Risks associated with the stocks. In an upside market VIX is low while in a downside or bearish run VIX tends to be high. If the value of India VIX is above 50 the market is perceived to be dangerous while a value above 30 indicates a fragile market. In this way VIX has a contrarian relation with the market.
But a closer look in the way VIX is constructed and the basic assumptions reveal a few interesting facts. As discussed, the assumption of high liquidity is not very reliable and the lack of availability of tradable products on Volatility makes Indian VIX a limited tool as far as application is concerned. Thus VIX standalone cannot be used as an effective indicator to gauge market volatility. An improvised version of VIX coupled with put call ratio (volumes) is a much more formidable tool to judge volatility in the market. Smart Money Ratio (SMR) is better than VIX. SMR can be mathematical ratio of India VIX to the near month put-call ratio (PCR). .
References:
1. www.nseindia.com
2. “ Options, Futures & Other Derivatives” By John Hull
3.http://www.cboe.com/micro/IndexSites.aspx
4. “VIX Whitepaper” by Chicago Board Option Exchange (CBOE) 5. “VIX Thoughts” on “Info processing” ,Blog of Prof. Steve Hsu 6.http://www.nseindia.com/content/vix/India_VIX_comp_meth.pdf
doc_934633884.doc
It explains A comprehensive document on India VIX index for risks.
Is India VIX A Good Forecast Of The Market Risk ?
Submitted By : Madhav Kumar Sharma
IS INDIA VIX A GOOD FORECAST OF MARKET RISK ?
Risk, as can be defined in finance, refers to the likelihood that we will receive a return on an investment that is different from the return we expected to make. Thus, risk includes not only the bad outcomes, i.e., returns that are lower than expected, but also good outcomes, i.e., returns that are higher than expected. The former is referred to as downside risk and the latter is upside risk; but we consider both when measuring risk. Although actual returns may differ from expected returns due to a variety of reasons, we can group the reasons into two categories: • • Firm-specific risks or Unsystematic risks or Diversifiable Risks Market-wide risks or Systematic risks or Non – Diversifiable risks
The risks that arise from firm-specific actions affect one or a few investments, while the risk arising from market-wide reasons affect many or all investments. Some risk may affect only one or a few firms and it is this risk that we categorize as firmspecific risk. Within these we would consider a wide range of risks, like the risk that a firm may have misjudged the demand for a product from its customers; we call this project risk. The risk could also arise from competitors proving to be stronger or weaker than anticipated; we call this competitive risk. There is other risk that is much more pervasive and affects all investments. For instance, when interest rates increase, all investments are negatively affected, although to different degrees. We term this risk market risk. Diversification reduces an investor’s exposure to Firm specific risks and he is rewarded only for bearing the market risks or the non diversifiable risks. Volatility Index is a measure of market’s expectation of volatility over the near term. Volatility Index is a measure, of the amount by which an underlying Index is expected to fluctuate, in the near term, calculated as annualized volatility, denoted in percentage e.g. 20%, based on the order book of the underlying index options. India VIX is a volatility index based on the Nifty 50 Index Option prices. From the best bid ask Prices of near term Nifty 50 Options contracts , a volatility
figure (%) is calculated which indicates the expected market volatility over the next 30 calendar days. Higher the implied volatility higher the India VIX value and vice versa. The VIX is often referred to as a "fear gauge" because it is anti correlated with market performance: i.e. when the Index goes up the implied volatility goes down, and vice versa. To characterize the probability distribution with a single volatility value, it is fitted to a Gaussian. Historically, the outlier events are much more likely than implied by a log normal distribution. Deep out of the money options are included in the VIX computation as long as there are nonzero bids and no intervening zero bids at more probable strikes. This only goes out about 2 sigma into the tail, so the distortion from mispricing of rare events is small. So, though the tail risks are not included in VIX forecasts, the effect of ignoring it is minimal. The VIX methodology involves calculating an estimate of "fair variance" for near-term and nextterm options, weighting these two values to construct a constant 30-day variance, and then taking the square root to produce a value for VIX. The main attraction of VIX index is that it mitigates many of the problems which lead to biased implied volatility estimate. Volatility index calculation requires two pairs of options that are used from each series. Each pair consists of one call and one put with the same strike. In total, eight options must be used. The implementation of the method assumes a very liquid market. But the value of the VIX does not always present a true sentiment of the market as it is dependent on the liquidity of the index option contracts in the mid month contracts. Unfortunately liquidity in index options beyond the current series is very less. Hence the spread across bid and offers for such far month contracts tends to be huge. This then affects the calculation of VIX thus making it erratic at times. By dividing the VIX with the PCR (put-call ratio) of near month contracts the anomaly is cured to a great extend. Another problem associated with India VIX is that there are no tradable products based on India VIX. The derivative contracts on Volatility Indices allow investors to trade ‘volatility’. Volatility is one among the various factors that affect the options prices. Many market participants have been calling for tradable products which they would find it useful in hedging their portfolios.
India VIX calculation methodology India VIX is calculated using the methodology adopted by CBOE currently for computing VIX on S&P 500 options. This method does not use any option pricing model such as Black and Scholes to calculate the VIX. Simply put, it derives the implied or expected volatility from the near and mid month options bid and offer prices of the Nifty 50 index options. From the options bid and offer prices an indicator can be derived as to what is the volatility the investors are expecting in the market. This volatility figure, denoted in percentage, is the India VIX value. The actual computation methodology is given below. The generalized formula used in the India VIX calculation is:
Select call options that have strike prices greater than K0 and a non-zero bid price. Select put options that have strike prices less than K0 and a non-zero bid price where K0 is the strike price
immediately below the forward index level. Finally we select both the put and call with strike price K0. K denotes the strike price and T denotes the days to maturity. Strike prices are assumed to be of the order such that K(j+1) > K(j) K0 is the first strike below the forward index level , F K(i) is the strike price of the ith out-of-the-money option; a call if K(i) > K(0) and a put if K(i) < K(0); both put and call if K(i) = K(0). The INDIA VIX generally uses put and call options in the two nearest-month expiration in order to bracket a 30-day calendar period. In the calculation of VIX restriction is imposed on the two maturities such that T(2) >= 22 >= T(1) >= 8 To reduce biases in computing the volatility indexes, the prices of second nearby options to replace nearby options with 8 days to expire is used. Volatility index isolates expected volatility from other factors affecting options prices, such as changes in the underlying price, dividends, interest rates, time to expiration. The volatility index offers a way for investors to buy and sell option volatility directly, without having to deal with other risk factors that would have an impact on the value of an index option position. Standard deviation method can measure the standard deviation between equity returns with respect to the equity index. Exponential GARCH (eGARCH) model which is asymmetric GARCH can be used to measure risk for equities as it is less likely to breach non-negativity constraints Conclusions: As discussed above, the Indian VIX does not tell about the prices but the Risks associated with the stocks. In an upside market VIX is low while in a downside or bearish run VIX tends to be high. If the value of India VIX is above 50 the market is perceived to be dangerous while a value above 30 indicates a fragile market. In this way VIX has a contrarian relation with the market.
But a closer look in the way VIX is constructed and the basic assumptions reveal a few interesting facts. As discussed, the assumption of high liquidity is not very reliable and the lack of availability of tradable products on Volatility makes Indian VIX a limited tool as far as application is concerned. Thus VIX standalone cannot be used as an effective indicator to gauge market volatility. An improvised version of VIX coupled with put call ratio (volumes) is a much more formidable tool to judge volatility in the market. Smart Money Ratio (SMR) is better than VIX. SMR can be mathematical ratio of India VIX to the near month put-call ratio (PCR). .
References:
1. www.nseindia.com
2. “ Options, Futures & Other Derivatives” By John Hull
3.http://www.cboe.com/micro/IndexSites.aspx
4. “VIX Whitepaper” by Chicago Board Option Exchange (CBOE) 5. “VIX Thoughts” on “Info processing” ,Blog of Prof. Steve Hsu 6.http://www.nseindia.com/content/vix/India_VIX_comp_meth.pdf
doc_934633884.doc