In Option Basics - Part 1 we discussed the Option Contract, Assignment and Exercise, and American and European style options. In Option Basics - Part 2 we discussed the components that comprise an option's price and the Greeks. In Option Basics - Part 3 we discussed Intrinsic and Extrinsic value: two components that comprise an option's overall value.

In Part 4 we will be discussing the important topic of Volatility; specifically the differences between Historical and Implied volatilities.

We've all heard of volatility. It is a measure of fluctuation; specifically the fluctuation in price of the underlying. For those who remember statistics from school, the unit of measure is standard deviation (or variance).

There are all types of volatility, but the most common in the financial industry are historical volatility (HV) and implied volatility (IV).

Historical Volatility (HV)
HV is a measure of realized or actual current volatility based on the underlying's price action over a period of time (typically 30 to 90 days), including the most current price. For this reason, HV is considered a backward looking measure.

If the price action follows a Gaussian random walk, then the width of the distribution increases over time reflecting the increased probability that the underlying's price will be further away from its starting point. However, the increase is not linear, but rather increases with the square-root of time (due to the fact that some fluctuations are expected to cancel out each other, so that after double the time the deviation will not be double the distance from zero).

HV is important to investors for the following reasons...

o The wider the swings in an investment's price, the harder emotionally it is to not worry

o When cash flows from selling a security are needed at a specific future date, higher volatility means a greater chance of a shortfall

o Higher volatility of returns while saving for retirement results in a wider distribution of possible final portfolio values

o Higher volatility of return when retired gives withdrawals a larger permanent impact on the portfolio's value

o Price volatility presents opportunities to buy assets cheaply and sell when overpriced

It is important to note that HV does not measure the direction of the underlying's price, just its dispersion. Two underlyings with differing volatilities may have the same expected return, but the underlying with the higher volatility will have wider swings over a given period of time.

For example, a low volatility underlying (5% annually) may have an expected (or average) annual return of 7%. That is, the returns would range from -3% to +17% at 2 standard deviations (2 SDs) with a probability of 95%. A high volatility underlying (20% annually) with the same expected return of 7% would see its returns range from -33% to +47% at 2 SDs (assuming a normal distribution).

Implied Volatility (IV)
IV of an option contract is the expected volatility of the underlying price action over the term of the option which, when entered into an option pricing model (ex: Black-Scholes) yields the theoretical value of the option.

If we consider the markets to be efficient, then the market price of an option should match its theoretical price; therefore (using this assumption), we can derive implied volatility by inserting the market price into the option pricing model.

IV is measuring current expected volatility of the underlying (over the life of the option), which is reflected in the option's price. Because of this, IV is considered a forward-looking and subjective measure. However, don't confuse forward-looking as being predictive (a common mistake), since IV changes continuously as expectations change.

Changes in expectations of the underlying volatility will affect an option's price, and hence its IV. Increases in IV represent increases in the option's price; and decreases in IV represent decreases in the option's price.

Factors that affect expected volatility (and hence IV) are:

o scheduled and unscheduled events (or News) that alter market expectations
o earnings
o rumored mergers
o changes in upper management

In conclusion, historical volatility is a measure of past price action, and therefore is considered backward looking; implied volatility is a measure of current market expectations of volatility (over the life of the option contract), and therefore is considered forward looking. Since IV is constantly changing (even though by small amounts daily), it is a mistake to consider it predictive.

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