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its implied volatility to determine a probability of a stock reaching a certain price, it can be smarter to use a cumulative volatility that combines the prices of many of a stock’s or an index’s options to capture more of those traders’ opinions. One cumulative volatility is the CBOE’s VIX, based on SPX options.

But a similar cumulative volatility is available for individual stocks, exchange-traded funds and other indexes on the tastyworks platform. For instance, it boils down Apple’s 160 put, 100 put and all of Apple’s other options into an overall implied volatility for Apple that captures the cumulative knowledge of every trader in Apple. That’s what makes this style of cumulative volatility reliable for predicting stock or index prices.

Moreover, on the tastyworks plat-

Two-Sigma stock prices

Statisticians consider 95% probability a significant level of confidence and call it a two-Sigma event. They apply the three-Sigma designation to events where their level of confidence reaches 99.7%

Here’s where some major stocks and indexes may land at the end of this year, based on the overall volatilities of their options in the December 2022 expiration and a 95% probability. Apple between $75 and $305 Alphabet between $1,400 and $5,100 S&P 500 between $2,350 and $7,900 Gold between $1,210 and $2,550 Oil between $25 and $150 Bitcoin between $10,000 and $170,000

form, each option expiration has its own overall implied volatility, which enables traders to calculate the probability of a stock hitting a certain price for different times in the future. How that’s done is covered in previous Normal Deviate articles.

Tom Preston, Luckbox contributing editor, is the purveyor of all things probabilitybased and the poster boy for a standard normal deviate.

DO DILIGENCE QUIET FOUNDATION HELPS INVESTORS FIND NEW TRADING OPPORTUNITIES

Essential Market Forecasting Tools

Traders benefit from understanding market trends that repeat over time

By James Blakeway

W

hile the saying “history repeats itself” may seem like a nauseating cliche, it often holds true in economics, finance and trading.

Take the example of positive drift in the stock market, which suggests that an aggregate index of stocks will continue to rally over time. Not every stock will increase in price, but a broad-based index will grow as innovation continues at new and established companies.

Positive drift has generally held true since the advent of indexes such as the Dow Jones Industrial Average in 1882 and the S&P 500 in 1860.

Another idea that tends to repeat itself is that fear is overstated in the markets. Financial assets with liquid options markets have implied volatility values, which can be utilized to estimate the magnitude of future expected movement. An asset should fall within the expected the expected range 68% of the time. But history shows that stock indexes stay within that expected range more often than anticipated.

Take the iShares Russell 2000 exchange-traded fund (ETF) for example. It represents a portfolio of 2,000 small-cap U.S. stocks. Unlike

iShares Russell 2000 ETF bullish trade

This trade has a breakeven price far below the current price.

IWM at $213.38 IVR: 57%

Bullish to neutral Jade Lizard Buy 1 IWM 232.0 Call in February-18’22 (66 DTE) Sell -1 IWM 229.0 Call in February-18’22 (66 DTE) Sell -1 IWM 180.0 Put in February-18’22 (66 DTE)

240

230

220

210

200

190

Downside Breakeven 180 Sep 15 Oct 01 Oct 15 Nov 01 Nov 15 Dec 01 Dec 15

Credit/debit: $3.16 credit Estimated buying power reduction: $2,010

Max profit: $316.0 Max loss: $17,684

Downside breakeven: 176.84 Upside breakeven: No upside risk Max profit zone: Between 180.0 and 229.0

iShares Russell 2000 ETF (IWM) Short 30 Delta Put backtest results

Win rate Average premium collected Average profit per trade

Average profit per day

86% $187.39 $32.73 $0.78 the Dow, S&P 500 and Nasdaq-100, the Russell 2000 holds no more than 1% of its portfolio in any single stock.

From 2004 to the present, the Russell 2000 has landed within its expected 30-day range 82% of the time. Keep in mind that it’s only supposed to stay in the range 68% of the time. Thus fear—in either direction—is overstated.

Benefitting from history

Traders can begin taking advantage

“Positive drift” means the overall stock market increases over time.

of positive drift and overstated fear by investigating the short put strategy in index ETFs. The short put is a simple bullish strategy where a trader sells a single put option with a strike price typically below the current price of the stock or ETF.

The strategy’s goal is for the stock or ETF to increase in price, stay the same price or not fall too much. For example, if XYZ stock is trading for $100 per share, a trader may look to sell the 95 strike to express the assumption that the stock will increase or at least not drop below $95. This trade wants the stock to stay above $95 and the 95 put to expire worthless, meaning the trader keeps the credit received for selling the put option.

New traders who are learning about implied volatility and expected movement can use the delta values to help them pick their options strikes. The delta value tells a trader the expected probability that an option will not expire worthless.

Think of the example above. If the 95 put has a delta of 30, then there’s a 70% theoretical chance the option will expire worthless. If the delta was 40, there’s a 60% chance the option will expire worthless.

But because fear is overstated,