Implied and historical volatility ploted on a graph

Volatility

Volatility is a measure of a financial instrument’s unpredictable change over a proposed time interval; in other words, a financial instrument’s standard deviation measure of continuously compounded variance between returns in a given time interval. Commonly, the higher the volatility, the riskier is the financial instrument.

The trader evaluates his or her alternative available investments by the expected risk-return trade-offs. He or she will choose the financial instruments based on the perception of higher risk, which will require a higher rate of return.

Some financial instruments are considered highly volatile and some are less, for example, bonds are less volatile (in nominal values) than stocks.

Bonds’ volatility depends on the issuer and the time to maturity.
Issuers with lower ratings will lead to a relatively higher volatility in any time interval; WMT (the world largest retailer) or 10-year corporate bonds will be less volatile then AMD, a global semiconductor company.

The US Government Treasury security rating is lower than any issued corporate bond and has several maturities. Treasury bills mature in one year or less, Treasury notes mature in two to ten years, and the T-Bond (Long-Bond) commonly issued with a maturity of thirty years.

Time in interest rate are the volatility factors for bonds’ face value; to simplify, every bond valued by its yields (gain an amount as a return on an investment), let us say a 2-year T-bill, will yield 5% a year to maturity, 5% a year each year, and a 10% return in 2 years.

To simplify (we will not calculate the compounded rate of return), the calculation for a T-bill not paying a coupon periodically, it would have been issued below the par value by 10%. If the par value is 100 then this T-bill face value should be 90 at this point in time.

Now, what will be the new face value if the Federal Reserve lowers interest rates by 75 base points? The yield will reduce from 5% a year to 4.25% a year, and the total difference will be 0.75 X 2 =1.5%. The new face value after the rate cut declaration will be 90 + 1.5 = 91.5, a change of 1.7% in face value (1.5/90). What will happen if it was an 8-year 5% T-bill? The face value would have been $40.00 (8X5) and the change in face value would be more volatile 8 X 0.75 = 6%, a change of 6 / 40 = 15%.

Exchange-Traded Funds
To trade these instruments using derivatives, you need to understand thoroughly an interest rate’s time to maturity, convexity and concavity (the rate of face value change to the change in the core interest rate and time to maturity) characteristics, and way to exploit the changes.
Exchange-traded funds (EFTs) are investment vehicles traded on stock exchanges. They hold securities such as stocks or bonds and trade at approximate net security value of the underlying securities over the course of the trading day; they track major indexes, sectors, economies (countries) and regions (group of countries). The volatility of ETFs could vary from solid bonds ETFs and pharmaceutical defensive ETFs to a relatively aggressive segment such as commodities, biotechnology, and other small-cap companies’ ETFs.

Because of its diversification, an ETF is less volatile than its component-traded stock; therefore, if a trader considered a certain strategy, the trader should decide whether an ETF or a stock is appropriate.
Analyzing a stock’s volatility (risk), the trader should consider whether he or she wants a defensive stock such as WMT; a well-diversified retailer, its stock’s volatility varies at the 20%-a-year level.

Another stock from a relatively defensive sectorthe healthcare sectorJohnson & Johnson (JNJ) is well diversified and has more than 250 operating companies. Volatility varies at the 15%-a-year level, versus a relatively volatile stock such as AAPL. In the general high-tech sector is a company that sells computers, cell phones, and a variety of computerized gadgets, due to competition and subject to changes in consumer fashion and economy, the stock is traded in a more volatile manner and its volatility varies at the 40%-a-year level.

Commodities
Most agricultural commodities are subject to seasonal changes. Other commodities, such as copper, are universal, and fluctuate based on global supply and demand. Because commodities are futures contracts and their multiplier factor is very high, even a small price change can lead to losses. For example, one oil future, CL, represents 1,000 barrels; thus a one-dollar change in price equals $1,000. Historically, there were times when these futures traded with as much volatility as 6 to 10 dollars a day.

Historical Volatility (HV)
Historical volatility is the standard deviation of price changes over a given number of trading days. To annualize the volatility level multiply by a factor of 260 trading days. A volatile market therefore has a larger standard deviation and thus a higher historical volatility value.

To calculate historical volatility, the first step is to calculate log normal of every day’s change from the day before; for example, if yesterday's price was $42.35 and today's price is $41.88, log normal is 41.88/42.35 = 98.8%, or -1.11%. This calculation goes along the given time; to calculate the volatility, by calculating the Standard Deviation of the last 30 days multiply by (year) 2, volatility plotted for every lognormal day from the 30th day and so forth. This why plotting a graph will show the changes along the passage of time.

Symbol; QQQQ's historical data collected from Nov05h 2005 to May06 2006.
Dotted Line; 6 months plotted graph and 30 days Historical Volatility Solid line.

Studying the historical volatility plotted graph above, higher values mean the underlying security prices changed sharply regardless of its direction. Small price changes, financial instrument converges, as a consequence there is a decline in the historical volatility reading. You will discover that in volatile times from the start of the graph up until the start of January 2006, the solid line shows constant increase in values because of market actual volatility.  After that date until end of March 2006, values decreased because relative price fluctuations dropped continuously.

As the time got closer to the end of this time interval, you see one more time rapidly increasing values (solid line).

Historical volatility is in use as a tool by traders who quantify a market’s volatility and estimate how far the market can change and thus make price projections and place orders according to these estimates.
For example, a financial instrument trades at a price range of $42.00 and its annualized historical volatility trades at range of 20%. Over a month, its price increased to $49.50, about an 18% gain. This goes without saying that this financial instrument has reached its annualized historical volatility in one-twelfth of the time and it is probable that it will tend to lower its prices to the mean.    

Mean-convergence theory states that in general, random prices have cohesiveness to the mean (the average price activity in a given period of time, common time for calculation is 30-day moving average). Therefore, placing a sort of short-to-neutral strategy will more probably succeed than a long bullish strategy.

A financial instrument’s historical volatility may act in a periodic manner from various causes.

The periodic volatility of stocks stems from quarterly and yearly statements. Every quarter a company has to disclose its activity with an unaudited quarterly report (quarterly report is only on best efforts).  Every company has its unique fiscal year, and at every end of the fiscal year the company must issue an audited report (most companies’ fiscal year is the calendar year). Stocks’ volatility has its implications from the fundamental pricing models based on the reports.

Usually a week or two before the report publication, prices tend to converge by the market participants (market participants wait for the earnings report). At the time of publication, prices tend to be volatile and relatively higher than before the announcement. Yearly statements often provoke higher volatility because these reports are signed by an external auditor and companies often cannot hide any more deteriorations. Most companies guide the market to the end-of-year prospects and its implications. Certain stocks, ETFs, and indexes are affected by economy publications, such as interest rates. For example, if a company’s main commodity to maintain its business is leveraged money transactions, its profitability will be affected by the change in interest rates publications (every month).

For car leasing and renting companies, which base their activities on interest rate spreads and borrow with the interest rate and lease by adding to the spread, a change in the interest rate can affect profitability. Therefore, before any interest rate announcement, their stocks’ volatility may rise.