SPY Statistical Price Probability Range

Includes: IVV, IWB, SPY
by: Richard Shaw

Historical and options implied volatility are useful tools in estimating the likelihood of the price of securities reaching various levels. This article explores the 80% and 90% probability range for the price of SPY over the next 21 and 63 market days (1 month and 3 months).

Volatility-based projections do not provide directional indications. You must use other methods to decide whether you expect the direction of price movement to be up, down or flat.

In past articles, we have presented price probability cones based on historical volatility as one imperfect but helpful tool in the price projection game. It is useful in selecting strike prices when selling and purchasing options or futures contracts, setting stop loss parameters, and perhaps other forms of looking down the road. As with any fundamental, chart or statistical tool, it is not always right. However, like some tools, it is right more often than it is wrong.

Log-Normal Assumption:

The method assumes a log-normal price distribution. While actual prices tend to be skewed, the log-normal assumption is a reasonable and accessible approximation of reality. The Black-Scholes model for options pricing, for example, uses the log-normal assumption.

As we have all learned multiple times in life, extreme price changes do occur. This method cannot predict those situations. Those fat tail events, however, are infrequent and don’t negate the value of incorporating statistical assumptions into various investment risk decisions. Statistical methods help more often than they hurt.

Historical vs. Implied Volatility:

This presentation includes price probability ranges based on both historical volatility (what has transpired) and options implied volatility (what is expected by options investors). Neither is right or wrong, but both are worth examining.

This chart from the International Securities Exchange plots the historical and implied volatility of SPY over the live of several “front month” option contracts (the volume is option volume).

Volatility is expressed as an annual figure and represents 1 standard deviation.

click image to enlarge


Note that each is a smoothed number. Actual volatility in the future will be “bumpy”, and could be greater or less than either the historical or implied volatility, particularly due to major surprises or events in the physical world and macro-economic environment.

Back Testing the Tool:

Back in mid-Oct 2009, we presented a multi-year chart showing price probability cones for 63-day (1 quarter) forward periods based on 63-day historical volatility. That showed the tool to be correct most of the time, when using an 80% probability range.

Here’s that chart:

click image to enlarge


Projection Cones vs. Standard Deviation Channels:

Standard deviation channels (commonly known as Bollinger Bands for the man who popularized their use) and projection cones both rely on the same method of calculating standard deviation. They differ in that standard deviation channels identify the range that prices might have had in the past and might have had in the current period, whereas projection cones identify the exponentially expanding range of likely prices from the current price out day-by-day into the future.

This snippet of an image from a prior article illustrates the current and backward look of Bollinger Bands versus the forward look of price projection cones — each has its use:


Current Probability Projections for SPY:

These four charts present the 21-day and 63-day forward view based on 21-day and 63-day historical volatility of SPY, and on the S&P 500 1-month implied volatility of the VIX, and the S&P 500 3-month implied volatility of the VXV.

The charts based on history, also include a prior cone showing how that projection worked out.

The 63-day cone worked well, but the 21-day cone was “faked out” by the jolt to the markets from the triple whammy of European sovereign default concerns, Chinese tightening of its banking industry, and US shifts in political power and in its policy toward banks, all of which arose during that approximate 21-day period.

Fortunately, that kind of surprise is not a regular monthly or quarterly event — and if it was a regular kind of event, the volatility would be higher and the cones would be wider. You can see how the current 21-day cone widened compared to the prior 21-day cone. That was the result of the extra volatility from the triple whammy.

click images to enlarge

21-Day Projection (based on history)


21-Day Projection (based on VIX)


63-Day Projection (based on history)


63-Day Projection (based on VXV)


Don’t rely exclusively on these projections, but do take them into consideration as you ponder the likely parameters of possible up or down movements for SPY (or IVV or S&P 500 index mutual funds).

Note the price level of the S&P 500 is approximately 10 times the price of SPY.

As a practical matter, the percentage limits associated with the price projections should reasonably apply to other large-cap US index funds such as IWB (proxy for the Russell 1000), and to a great extent to more inclusive but market weighted US stock index funds.

Holdings Disclosure:
As of February 13, 2010, we do not have positions in any securities discussed in this document in any managed account.

Opinions expressed in this material and our disclosed positions are as of February 13, 2010. Our opinions and positions may change as subsequent conditions vary. We are a fee-only investment advisor, and are compensated only by our clients. We do not sell securities, and do not receive any form of revenue or incentive from any source other than directly from clients. We are not affiliated with any securities dealer, any fund, any fund sponsor or any company issuer of any security. All of our published material is for informational purposes only, and is not personal investment advice to any specific person for any particular purpose. We utilize information sources that we believe to be reliable, but do not warrant the accuracy of those sources or our analysis. Past performance is no guarantee of future performance, and there is no guarantee that any forecast will come to pass. Do not rely solely on this material when making an investment decision. Other factors may be important too. Investment involves risks of loss of capital. Consider seeking professional advice before implementing your portfolio ideas.