There are two types of volatility used in securities analysis: **historical** and **implied** volatility. One measures historical price movements while the other indicates the potential level of future volatility an asset is implying.

### Historical Volatility

**Historical volatility** refers to the price fluctuations exhibited by the underlying asset (such as stock) over time. It is thus a standard deviation calculation. For our purposes, it is the amount – expressed as a percentage – a stock price has actually moved over time, usually 10 days to 30 days, since recent price volatility is far more important for covered calls than for longer periods. A stock’s historical volatility is also known as ** statistical volatility** (SV or HV); the terms are used interchangeably. A stock with an SV of 10% has very low volatility; 35% is considered not very volatile; 80% would be quite volatile.

As I write this, the S&P 500 (SPY) has a 30-day volatility of 31% and a 10-day volatility of 25%. The comparable volatilities for the Nasdaq Composite Index (QQQ) are 31.5% and 24%. In both cases, volatility recently has been dropping.

The stock’s volatility can help us forecast short-term price ranges and can also help us determine the relative value for an option price. The option premiums of a stock with low SV normally will have low time value, and vice-versa. An option’s premium will be influenced by the likelihood that, in the eyes of market participants, the underlying asset will move above or below the various strike prices. Generally, higher historical volatility means higher option premiums, and lower volatility means lower premiums.

When looking at a stock chart, we must take into account not only the visuals of price action, but also the price’s interaction with the 50-day moving average, and the stock’s daily price range. A chart may not *seem* particularly volatile at a glance and yet be quite volatile.

The chart below for South American steel-maker Gerdau (GGB) illustrates this point. Though the price action appears to be in a tight range, the stock’s 30-day volatility exceeds 70%. Each daily price bar seems small, but a $0.40 – $0.80 daily move is significant for a stock in this price range. A $4 move up (down) would be 200% (50%) of recent price!

Note that in the previous 30 days, Gerdau had moved from roughly $6.50 to $8.84, an increase of more than 35%: a big move for a month.

**Figure 5.10**

By contrast, biotech company Cephalon’s (CEPH) chart looks wickedly volatile. But it isn’t all that volatile, actually. The 30-day SV is only 22%, lower than either the SPX or Nasdaq for the same period. The reason is that the last month’s price action varied within a range of only $7.18, about 11% of price (Gerdau moved 35% in the same period), and daily price bars tended not to be huge.

However, its 30-day volatility a month ago, which included the larger 60-day price range, was over 48%. Though a large price movement, it occurred over two months. As we can see, the measurement period has a great effect on volatility.

**Figure 5.11**

If Cephalon’s 48% volatility two months ago seems high, it is not terribly high for a stock appearing at or near the top of a list of the highest covered call returns. Nor is it very high for this time period. Volatility in February 2009 was of course much higher, as it was for every other stock on earth. And the current 22% volatility is quite comfortable.

Option premiums on a stock can become far higher than is warranted by historical volatility, however. When this occurs we say that the abnormally high premium ** implies** an impending higher volatility in the stock.

### Implied Volatility

**Implied volatilit**y (IV) refers to the market’s perception of how volatile a stock likely will be in the future. Covered call writers must grasp IV in order to truly understand the best ways to use stock options, and it can play an important role in constructing covered call writes.

Recall our discussion of the Black-Scholes formula for determining the “fair” price of an option. By using a number of known inputs (*stock price, strike price, stock volatility, risk-free interest rate, time to expiration, dividends*), the formula allows us to calculate the theoretical fair price of an option. However, since we already know the actual price of listed options, we can solve the Black-Scholes formula for volatility instead of fair price.

Doing so tells us what level of stock volatility would be necessary to produce the current option price. The volatility so calculated is the *implied volatility*. For example, if a stock’s volatility is 35% and the fair price of the ATM call would be $2.00, a premium of $3.00 is (at least theoretically) over priced. More to the point, it implies volatility in the stock well in excess of the actual 35%. Note that when we refer to premium in the context of implied volatility, we are speaking only of the *time value *portion of the premium.

A stock whose volatility is 35% might for example be expected, in a perfect world, to always produce option prices that are fair, that is, in-line with 35% volatility. And that sometimes is the case. But often we see that option prices are high enough to imply volatilities far higher than the stock’s actual volatility; and in these cases, we say the option is overpriced or overvalued. Suppose the stock currently has a historical volatility of 35%, but the option price implies a volatility of 60%? In this case, the option is said to be overpriced.

This is so fundamental to understanding options, it bears emphasis. If options were always “fairly” priced, then we would expect the option price to always imply a level of stock volatility that is more or less in-line with historical volatility.

**Example:** Two stocks each are priced at $25, and both have current-month $25 puts available. One put’s asked price is **$1.20**, the other **$2.20**. Being ATM options, the premium is all time value. In weighing the two puts, once is nearly double the price of the other, because the more expensive put has $1.00 more time value premium than the cheaper: *implied volatility at work.*

IV can be **lower** than historical, approximately the **same** (in line with) as historical, or **higher** than historical volatility. A stock with a historical volatility of 80% might have options implying volatility of 80%, in which case IV – though admittedly high – is nonetheless in line with historical volatility. But what if the options imply 80% volatility when historical volatility is only 30%? In Black-Scholes terms, the options would be considered highly overpriced.

This is a key point: knowing that implied volatility is “high” is not the whole story. The question for call writers is: how does the implied volatility compare to historical volatility?

An overpriced option implies a likelihood of the stock price moving. And the more “overpriced” the option, the more volatility is said to be implied. This mechanism is easily understandable in light of human nature. It works like this:

- Wall Street and other traders make money when security prices move.
- For this reason, options are more desirable on stocks expected to become volatile.
- Traders will pay more for options on stocks expected to become volatile (to move).
- The willingness to overpay – sheer demand – leads to overpriced options.

▪ This “*overpriced*” state implies higher volatility in the stock.

In other words, a higher-than-historical level of IV really is telegraphing the fact that the market thinks/hopes that the stock is about to move and, accordingly, is paying more for the option. While many options are bought to *hedge* short positions, a large percentage of them are bought to speculate on the underlying stock’s movement. In a very real sense, then, high IV acts as a **speculation tax** on traders; this is no more than market forces in operation.

It is important to note that higher-than-normal IV *does not* mean that the stock is about to make a large move, only that the market thinks it ** might**. IV can be seen as a measurement of potential reward and risk. I am careful to say “potential” risk, because based on my experience, the majority of stocks with high IV don’t move all that much; and not necessarily in the direction anticipated. That is, IV is an

*implication*, not a promise.

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