🟣 Implied Volatility: Calculate the Price Range of a Stock

• 06-11-2024
• JOY MUKHERJEE
• JOY MUKHERJEE

How can I understand how far a stock is likely to move?

The statistical distribution of prices :: Normal distribution & Log-normal distribution

Normal Distribution gives equal chance of prices occurring either above or below the Mean (which is shown here as 0). We are going to use normal distribution for simplicity’s sake.

If a price distribution is considered Normal, 68.20% of the time, you will be within 1 standard deviation. Mostly, stock exhibits a normal distribution/bell-curve. A normal distribution of data means most numbers in a data set are close to the average, or mean value, and relatively few examples are at either extreme. In layman’s terms, stocks trade near the current price and rarely make an extreme move.

Implied volatility (IV) is one of the most important concepts for options traders to understand for two reasons. First, it shows how volatile the market might be in the future. Second, implied volatility can help you calculate probability.

With an option’s IV, you can calculate an expected range – the high and low of the stock by expiration. Implied volatility tells you whether the market agrees with your outlook, which helps you measure a trade’s risk and potential reward.

The historic volatility (HV) is the movement that did occur. The implied volatility (IV) is the movement that is expected to occur in the future. When we are estimating future prices, we use the implied volatility only.

Let’s assume a stock trades at Rs.50 with an implied volatility of 20% for the ATM options.

·         One standard deviation move = Rs.50 x 20% = Rs.10

The first standard deviation is Rs.10 above and below the stock’s current price, which means its normal expected range is between Rs.40 and Rs.60. Standard statistical formulas imply the stock will stay within this range 68% of the time (see Figure 1).

All volatilities are quoted on an annualized basis (unless stated otherwise), which means the market thinks the stock would most likely neither be below Rs.40 or above Rs.60 at the end of one year. Statistics also tell us the stock would remain between Rs.30 and Rs.70 – two standard deviations — 95% of the time.

ü Standard deviation for specific time periods   

Since we don’t trade one-year options contracts, we must break down the first standard deviation range so that it can fit our desired time period, The formula is:

1 standard deviation = Stock Price x Implied Volatility x (Square Root of [days to expiration (22) / 256])

(Note: it’s usually considered more accurate to use the number of trading days until expiration instead of calendar days. Therefore remember to use 252 – the total number of trading days in a year. As a short cut, many traders will use 16, since it is a whole number when solving for the square root of 256.)

Quick Trick for 50% Probability Trade

Now, you can just use an options chain to get an estimate of where the stock could move... Find the price of the ATM straddle and the nearest OTM strangle and add them together and divide by two. That is about equal to the 50% probability movement.

IV can help you to determine the likelihood of a stock reaching a specific price by a certain time period. That can be crucial information when you’re choosing specific options contracts to trade.