In the first part

of this series we defined volatility and looked at its characteristics, such as its cyclical nature, its persistency and its tendency to revert to the mean. We used a simple calculation called average true range to demonstrate these inherent features.

In this second installment, we will look a historical volatility, a more mathematically complex but useful way of measuring volatility. Weâ€™ll show how you can use it to find (or avoid) volatile stocks, determine risk, set practical stops and forecast where the market has the potential to trade.

**Historical volatility defined**

Historical Volatility (HV) is the standard deviation of day-to-day price change expressed as an annual percentage.^{1 } Whew! Essentially, all that means is that historical volatility is a measurement of how much prices fluctuate over time. Suppose a stock or commodity is trading at $100 and its historical volatility is 10%. At the end of the year the market will *likely*^{2} (statistically a 66% chance, see appendix if you are interested in the math) be trading somewhere between $90 ($100 â€” 10%) and $110 ($100 + 10%). Markets with a high HV tend to offer more opportunity yet are more risky than those with a low HV and vice versa. By the way, as with all indicators, I strongly urge you have the computer do the work for you. Also, itâ€™s more important to understand how to read and use the indicator than it is to understand the formula itself.

**A tale of two markets**

Letâ€™s look at two completely different markets in terms of their volatility. Orange Juice is a volatile market due to its nature (and mother nature). Itâ€™s a crop thatâ€™s extremely effected by weather conditions (i.e., freezes) and reports (note: the movie *Trading Places* does a good job of describing why orange juice is volatile).

On the other hand, the Canadian dollar is fairly stable. Obviously, the currency does fluctuate over time, but much less than a market like orange juice. Therefore, the volatility (HV) of orange juice futures tends to run between 30% and 40% (or higher) whereas the volatility on the Canadian dollar tends to run around 6% to 8%. So, you could expect the Canadian Dollar to fluctuate around 6% to 8% annually and orange juice to fluctuate around 30% to 40% annually. The same analogy can be applied to a government-regulated utility stock which tends to fluctuate 10% or less during a year versus a high-flying technology stock than can move as much as 30% or more in one day.

**Finding (or avoiding) volatile markets**

HV is one of the best indicators for determining volatility. If you are a day trader whose profits are limited to the amount a stock can move during the trading day, then you probably want to seek out more volatile markets. On the other hand, if you take a longer-term view, you might want to avoid the more volatile markets because of their additional risk. At TradingMarkets.com we have found that a 50-Day HV reading is useful for gauging the volatility of a market. (This is what is used on the Trading Where The Action Is List and the Futures Volatility Ranking lists. These lists rank the most volatile markets, from highest to lowest based on their 50-day HV readings).

**Why Johnny Gets Stopped**

Johnny has carefully studied all the entry techniques and momentum trading. With all this knowledge, he finds the hottest stocks in the hottest sectors and buys precisely where his studies indicate. He plans to hold on for a few days and dreams of the large moves heâ€™ll capture. He puts in a tight stop and waits. However, to his dismay, heâ€™s constantly stopped out, losing time after time.

Why? Because Johnny failed to study the volatility of the stocks that he was trading. The â€œnoiseâ€ alone on his stocks is far greater than his stop placement points, thereby almost guaranteeing him a loss.

**Know Thy Volatility: Using HV to Set Stops**

To help ensure (but not guarantee, of course) that you do not get stopped out when position trading, HV can be used to determine where practically they should be placed. Connors has shown^{3} that by taking the HV and factoring in the number of days you intend on holding a position, a realistic placement of stops can be achieved. Letâ€™s apply this method of stop placement to a volatile stock

Figure 1. Metricom (MCOM), daily. Using historical volatility to define likely trading ranges and stop levels. |

Suppose you wanted to trade Metricom [MCOM>MCOM], a stock with an extremely high historical volatility rating of 145% on 7/21/99. Also, suppose you intend to hold the position for at least five days. If we reduce the volatility down to the holding period (five days), it suggests that the stock has the potential (a two-thirds chance) to trade as high as 42 5/8 and as low as 28 3/8. Therefore, in order to reduce the likelihood of getting stopped out, you would have to set your stops *outside* of 28 3/8 for longs (a) and 42 5/8 (b) for shorts.

In trading, thereâ€™s always the flip side. Some may argue for tighter stops even on volatile stocks, knowing that the majority of the time they will be stopped out but the occasional winner will make up for the losses. However, regardless of your trading style or beliefs, you canâ€™t ignore the fact that more volatile markets have the potential for larger swings and increased risk.

**Forecasting Price Ranges Using HV**

The same method used to set stops can also be used when planning options trades. For instance, according to above method of setting stops (and referring to the chart), the stock has the potential (a 66% chance) that it could trade to (a) or (b). One could then analyze the premium of the option to determine if the option has the chance to be worth more than the current cost based on the potential of the market. Obviously, thereâ€™s a lot more to option trading than the above, and I would strongly urge you not to make decisions on trading options purely on HV. The point here is to show where the stock has the potential to go based on volatility.

**Summary**

Historical Volatility is a measurement of how much prices of a market fluctuate over time. Markets with a higher HV generally will fluctuate more than those with lower HV. Day traders, whose profits are limited to the amount a market can move during the day, may seek out more volatile markets. Longer-term traders may want to avoid the more volatile markets in an effort to reduce risk. Because HV is a measurement of how much prices fluctuate, it can also be used to set realistic stops. By the same token, these levels could also be used when planning options trades.

**Looking Ahead**

In our final installment on volatility, we will expand upon the concepts introduced in the first article (cyclical nature, reversion to the mean, and so on) through the use of historical volatility. Weâ€™ll look at various HV lengths and how the ratio of short-term HV divided by long-term HV can be used to find markets that are likely to experience an explosive move and those in which the move may have exhausted itself. Weâ€™ll also look at combining technical analysis with volatility to help determine directional movements out of low-volatility situations.

**Appendix**

*Calculating Historical Volatility*

As with any indicator, I strongly urge you to purchase software with the indicators already programmed and would never suggests anyone attempt this by hand. With that said:

Let *Length* = length of volatility to be calculated and *ln* = natural logarithm

Historical Volatility(length) =

standard deviation(ln(close/yesterdayâ€™s close),length) * 100 * square root (256).

In English:

- Divide todayâ€™s close by yesterdayâ€™s close.
- Take the natural log of #1.
- Take the standard deviation of #2 for length desired (the number of trading days, i.e. 50)
- Multiply #3 by 100.
- Multiply #4 by the square root of the number of trading days in 1 year (around 256).

*HV is based on a one-standard deviation move*

For those familiar with the bell curve and standard deviations, statistically, this suggests that approximately 66% the market should trade within these ranges. If you double the HV, which gives you two standard deviations, then this gives you a statistical probability that 95% of the time the market will trade within this range. A three standard deviation (3 * HV) would suggest that the market would trade within that range 99.7% of the time.

Keep in mind, however, that these calculations assume a normal distribution and are based on present volatility (volatility is constantly changing). Natenberg said it best in *Option Volatility and Pricing Strategies*: â€œ(You) shouldnâ€™t confuse unlikely with impossible.â€

*Using HV to set protective stops*

In *Connors on Advanced Trading Strategies*, Larry Connors shows that historical volatility can be used to determine where stops should be placed. Calculation of these stop points are as follows:

- Divide 260 trading days by the number of days you intend to hold the position.
- Take the square root of #1.
- Divide the historical volatility by #2.
- Take the stock price and add (for shorts) and subtract (for longs) #3 from it.

**Footnotes**

- Connors On Advanced Trading Strategies,Laurence A. Connors. See the appendix for the formula for HV.
- Trading Connors’ VIX Reversals, Larry Connors.
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