Understanding Nifty Volatility

Definition

Volatility (σ) is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices. There are different ways of calculating volatility. At StockViz, we use Yang Zhang Volatility.

σ is one of the biggest contributor of option premiums. Understanding its true nature will help you trade it better.

Volatility spikes

Observe the volatility spikes since 2005. Even though the average is around 0.3, its not uncommon to have huge swings.

nifty-volatility

Fat tails abound

nifty-volatility-10-histogram

nifty-volatility-20-histogram

nifty-volatility-30-histogram

nifty-volatility-50-histogram

Trading strategy

Always try to be on the long-side of volatility. It might be tempting, while trading options, to try and clip the carry on θ-decay. But you should always be aware of the fat-tails of volatility that can crush many months of carry P&L overnight.

Short Straddle

Introduction

While discussing the subject of the Long Straddle, we touched upon three things:

  1. Most of the obvious uncertainties are priced in. So you better have a unique point of view.
  2. Time is not your friend.
  3. The lack of liquidity means that you are forced to put this trade on closer to expiry and that is exactly the time when θ-decay is at its highest.

What if you invert the trade? This is exactly what the short straddle is made of. You can enter this trade soon after an widely anticipated event occurs and implied-volatility is at its highest.

Construction

This strategy consists of selling a call option and a put option with the same strike price and expiration.

NIFTY 6750 short straddle

The θ-decay now works for you. Sell ATM nearest-expiration options, collect the carry and laugh all the way to the bank, right?

NIFTY 6750 short straddle payoff
NIFTY 6750 short straddle pl

Not so fast! If the NIFTY breaks-out above 6836.50 or below 6663.50, then you are exposed to ∞ loss. It is up to you to figure out if the Rs. 4325.00 you are getting is enough compensation for insuring against the likelihood of that breakout.

Exiting the trade

Time is your friend and volatility is your enemy. When you sell insurance of this kind, you are exposed to external events that may not have anticipated and that occur outside of market hours. If you see volatility creep up, its best to exit this trade, even if at a loss.

Long Straddle

Introduction

If you are sure that the underlying stock/index is going to move strongly before expiration, then this is the option strategy for you. The move can be in any direction, as long as its violent. For example, you might be expecting an important court ruling, the outcome of which will be either very good news or very bad news for the underlying.

Remember that most of the obvious uncertainties are priced in. So you better have a unique point of view.

Construction

This strategy consists of buying a call option and a put option with the same strike price and expiration, making it relatively expensive.

With the NIFTY trading at ~6780, you can either buy the 6750 straddle or the 6800 straddle. Let’s walk through each trade.

May Nifty 6750 long straddle

nifty 6750 long straddle

Note the θ (-742.73) on the ITM call. Its a lot of time-decay if you are wrong. The model says that the market prices are too disjointed from the model price. Besides, the break-evens are 6161.00 and 7339.00 which means that you have to be absolutely convinced that something big is going to happen.

nifty 6750 long straddle payoff
nifty 6750 long straddle p&l

May Nifty 6800 long straddle

nifty 6800 long straddle

The θ situation has improved somewhat and the break-evens – 6217.20 and 7382.80 – look better. The trade costs Rs.29,140/- to put on and that caps your max-loss.

nifty 6800 long straddle payoff
nifty 6800 long straddle pl

Exiting the trade

Time is not your friend here. You can either exit the trade right before the event occurs – when implied volatility is at its highest or soon after the event (irrespective of the magnitude of the movement.)

The lack of liquidity means that you are forced to put this trade on closer to expiry and that is exactly the time when θ-decay is at its highest.

Weekly Recap: Options

Equities

world equity markets 2014-04-11.2014-04-18

It was a short week that saw a very volatile Nifty end flat (-0.14% in USD terms.) Here’s how the rest of the world markets fared:

Major
DAX(DEU) +0.99%
CAC(FRA) +1.50%
UKX(GBR) +0.97%
NKY(JPN) +3.28%
SPX(USA) +2.38%
MINTs
JCI(IDN) +1.67%
INMEX(MEX) +2.20%
NGSEINDX(NGA) +0.62%
XU030(TUR) +1.33%
BRICS
IBOV(BRA) -0.88%
SHCOMP(CHN) -1.49%
NIFTY(IND) +0.05%
INDEXCF(RUS) -2.40%
TOP40(ZAF) +0.76%

Commodities

Energy
Brent Crude Oil +1.87%
Ethanol -7.56%
Heating Oil +2.35%
Natural Gas +2.16%
RBOB Gasoline +1.11%
WTI Crude Oil +0.65%
Metals
Copper +0.33%
Gold 100oz -1.88%
Palladium -1.08%
Platinum -2.98%
Silver 5000oz -2.00%

Currencies

USDEUR:+0.42% USDJPY:+0.69%

MINTs
USDIDR(IDN) +0.09%
USDMXN(MEX) +0.08%
USDNGN(NGA) +0.91%
USDTRY(TUR) +0.38%
BRICS
USDBRL(BRA) +1.56%
USDCNY(CHN) +0.13%
USDINR(IND) +0.19%
USDRUB(RUS) +0.05%
USDZAR(ZAF) -0.02%
Agricultural
Cattle -0.55%
Cocoa -0.27%
Coffee (Arabica) +0.25%
Coffee (Robusta) -0.94%
Corn -0.85%
Cotton +1.35%
Feeder Cattle -0.74%
Lean Hogs -1.46%
Lumber -0.82%
Orange Juice +0.27%
Soybean Meal +3.49%
Soybeans +3.64%
Sugar #11 -0.83%
Wheat +4.66%
White Sugar +6.50%

Nifty Heatmap

CNX NIFTY heatmap 2014-04-11.2014-04-17

Index returns

index performance 2014-04-11.2014-04-17

Top winners and losers

RECLTD +3.50%
CROMPGREAV +7.67%
MCDOWELL-N +11.58%
DLF -9.44%
BANKINDIA -6.21%
YESBANK -5.89%
Banks saw some profit taking, USL was lifted by Diageo’s open offer.

ETFs

INFRABEES +16.16%
GOLDBEES +1.26%
NIFTYBEES +0.05%
BANKBEES -0.26%
JUNIORBEES -2.43%
PSUBNKBEES -4.54%
Infrastructure was back with a bang.

Investment Theme Performance

High beta tumbled and is Consistent10 has turned in 2x NIFTY returns since its inception!

consistent10 theme performance

Sector performance

sector performance 2014-04-11.2014-04-17

Yield Curve

yield Curve 2014-04-11.2014-04-17

Weekend Reading

We have started a series of posts that introduces options. We discuss the intuition behind the math and quant models, greeks and strategies with a ton of charts and original content. If you have read about options before or have a vague idea of what they are, then this is a good take-off point.

Options Trading Guide

The most important assumption

Prices and Returns

Prices don’t follow a statistical distribution (they are not ‘stationary’.) There is no obvious mean price and it doesn’t make sense to talk about the standard deviation of the price. Working with such non-stationary timeseries is a hassle.

NIFTY 2005-2014

But returns, on the other hand, are distributed somewhat like a normal (Gaussian) distribution.

nifty-histogram

And there doesn’t seem to be any auto-correlation between consecutive returns.

nifty-autocorrelation

If returns are normally distributed, then how are prices distributed? It turns out that the logarithm of the price is normally distributed. Why? Because

returns(t) = log(price(t)/price(t-1))

Now statisticians can magically transform a random time-series (prices) into something that is normally distributed (returns) and work with that instead. Almost all asset pricing models that you will come across in literature has this basic assumption at heart.

Fat tails

The assumption that returns are normally distributed allow mathematically precise models to be constructed. However, they are not very accurate.

In the normal distribution, events that deviate from the mean by five or more standard deviations (“5-sigma events”) have lower probability, thus meaning that in the normal distribution rare events can happen but are likely to be more mild in comparison to fat-tailed distributions. On the other hand, fat-tailed distributions have “undefined sigma” (more technically, the variance is not bounded).

For example, the Black–Scholes model of option pricing is based on a normal distribution. If the distribution is actually a fat-tailed one, then the model will under-price options that are far out of the money, since a 5- or 7-sigma event is much more likely than the normal distribution would predict.

Precision vs Accuracy

When you build models, the precision that they provide may lull you into a false sense of security. You maybe able to compute risk right down to the 8th decimal point. However, it is important to remember that the assumptions on which these models are build don’t led themselves to accuracy. At best, these models are guides to good behavior, and nothing more.

accuracy vs precision

Sources:
Fat-tailed distribution