Posts in category: investing

What are Bollinger Bands?

Bollinger Bands are used in technical analysis to help calculate and measure volatility. There are three bands that are included in chart: a moving average, and a lower and upper band. Normally, the upper and lower band are set to be within two standard deviations of the moving average. The standard deviation helps measure volatility and determines the width of the bands. As volatility increases, the band widens, and the opposite happens when volatility decreases.

The Bollinger Bands are often used by traders to identify opportunities for when to buy or sell a stock. If a stock price gets closer to the upper band, then it is considered to be overbought, and hence, this can be a time to sell. If, on the other hand, it is approaching the lower band, then it is oversold, and it may be an opportune time to buy. A similar tool that traders may also use is the Relative Strength Index, as that too tracks momentum and helps traders identify when a stock is overbought and oversold.

Why should you use Bollinger Bands?

Traders may use Bollinger Bands for a variety of reasons:

• To identify buying and selling opportunities, such as when a stock is overbought or oversold. However, it’s important not to be overly reliant on a single indicator and it’s a good idea to also review other tools in conducting technical analysis to help confirm your trading decision.

• Bollinger Bands can help gauge volatility. When the volatility is high, there is an opportunity for traders to take advantage of a large spread. With a large spread, there are more opportunities to buy low and sell high than there are when volatility is low and price is trading within just a narrow range.

• Traders may also use Bollinger Bands to spot trends in the market as the bands will slope in a similar direction to price. This can help potentially identify buying and selling opportunities based on the stock’s trajectory.

How to create and chart Bollinger Bands

The process for creating a chart to show Bollinger Bands in Excel and Google Sheets is similar — the main difference is in how to pull in the stock price. The steps below go over the steps specific to Google Sheets:

• Start with downloading the stock prices. In my example, I have downloaded the stock price for Meta Platforms going back to 2020. This was done using the GOOGLEFINANCE function in Google Sheets, and the formula is as follows: =GOOGLEFINANCE(“meta”,”price”,”1/1/2020″,today())

• Calculate the 20-day moving average from the closing prices. This is done using the AVERAGE function. Assuming the closing prices start from cell B4, the formula would be as follows: =AVERAGE(B4:B23). Copy the formula down to all the cells.

• Calculate the standard deviation using the STDEV function. This is also based on the last 20 closing prices and is copied down to the bottom of the data set. This is the formula to calculate the standard deviation based on this example: =STDEV(B4:B23).

• Calculate the Upper Band. Do this by multiplying the standard deviation by 2, and adding that to the 20-day moving average. Assuming the 20-day moving average is in cell C23 and the standard deviation is in cell D23, this is what the formula would look like: =C23+D23*2

• Calculate the Lower Band. For this, multiply the standard deviation by -2, and add that to the 20-day moving average. Based on the above assumptions, the formula would be as follows: =C23+D23*-2

Once all those formulas are entered, your data set should look something like this:

Next, create a line chart to show the values on a graph. Then apply any formatting (e.g. dotted lines, colors, etc) and you should have a visual that looks like this:

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If you’re looking to buy stocks, a one of the more common ratios you’ll likely consider in your analysis is the price-to-earnings, or P/E multiple. You can look at either the trailing P/E or the forward P/E. Below, I’ll look at what the difference between those multiples is, how to calculate each one, and how you can use them to determine a company’s expected growth rate.

What is the difference between the trailing P/E and the forward P/E?

The P/E ratio looks at the stock price in relation to earnings per share. If it’s a trailing earnings multiple, then that means you’re looking at the company’s earnings over the trailing twelve months, or ttm. A forward earnings multiple is based on analyst expectations and what the company’s earnings will be over the next year.

If a company had a worse year than normal or analysts are expecting lots of growth in the year ahead, the forward P/E will be lower than the trailing P/E. If, on the other hand, the company performed exceptionally well and perhaps benefitted from one-time gains, then its trailing P/E may look better (i.e. lower) than its forward P/E if analysts don’t expect a significant change in the business over the next year.

The smaller the gap between the trailing P/E and the forward P/E, the more consistent the earnings numbers are and the less of a change analysts are expecting from the previous year. If, however, the gap is significant, that could be an opportunity for investors because if a stock has a high trailing P/E multiple (due to an abnormally bad year), it can be missed on stock screeners if people are searching for stocks with low P/E multiples.

You can think of a forward P/E as what the company’s earnings will be in a normal or typical year whereas the trailing P/E is one that may have been distorted for a number of reasons.

How to calculate the trailing and forward P/E ratios

Here are the steps you can take to calculate the trailing P/E multiple:

1. Add the company’s net income over the past four quarters. This is its income over the trailing twelve months.
2. Take that total and divide it by the averaged diluted shares outstanding over the course of the year. Unless there’s a significant variation over the course of the past year, you can often just use the shares outstanding as of the most recent quarter. The result of this calculation will give you diluted earnings per share, or EPS.
3. Get the current share price and divide it by EPS. This will be your trailing P/E multiple.

Here’s how I did the above calculations for Tesla’s stock in Excel, based on data as of Jan. 16, 2023 that was pulled from Yahoo Finance:

For the forward P/E multiple, the calculation is more straightforward since it is based on analyst expectations. Here are the steps to calculated the forward P/E multiple:

1. Obtain the average analyst earnings per share estimate for the next year.
2. Take the current share price and divide it by that estimate.

If you go to Yahoo Finance and go under the Analysis tab, you will see a series of analyst expectations for earnings for the new year:

Since I’m looking for the full year, I’ll take the average estimate for ‘Next Year (2023)’ which is an EPS of $4.79. By taking the share price of $122.40 and dividing by this figure, I arrive at a forward P/E of 25.55. This tells me that analysts are expecting Tesla to have a better year in 2023 as its forecasted EPS of $4.79 is higher than the $3.23 it has reported over the past four quarters.

You can use earnings multiples to estimate the earnings growth analysts are forecasting

This year, analysts are projecting that the company’s EPS will be $4.79, which is 48% higher than the $3.23 it reported over the past four quarters. However, you can estimate how much growth analysts are expecting from the business without having to dive into the EPS numbers.

Since the numerator, price, in the P/E multiples remains constant, the only change is the earnings, the denominator. You can do the same earnings growth calculation by taking the trailing P/E and dividing it by the forward P/E, and then subtracting 1 from that value:

If the forward P/E is lower than the trailing P/E, that tells you that analysts are expecting that the company’s earnings are expected to decline in the coming year.

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If you’ve ever looked up historical stock prices on Yahoo Finance, you know that there is both a closing price and an adjusted closing price. Sometimes the values are the same, but sometimes there’s a difference In this post, I’ll cover why that happens, and how you can calculate the difference yourself.

What is the difference between the two prices?

The adjusted closing price in Yahoo Finance factors in the impact of dividend payments. For stocks that pay dividends, the further back you go, the greater the difference there will be between the close and the adjusted closing price. With the closing price, you’ll just see the raw change in price, whereas the adjusted closing price will also factor in the dividend, and that can give you a better view of how the stock’s total returns have been over time, not just from the increase in share price. And thus, the longer of a duration you’re looking at and the more dividend income along the way, that creates more of a gap between the close and adjusted close.

For stocks that don’t pay dividends, there will be no difference between these two values.

How to calculate the difference

A difference between the two prices in Apple’s stock history doesn’t show up until the last time it issued a dividend, on Nov. 4. Technically the company didn’t pay the dividend on that day, but that was the date of record for the dividend, and so investors who owned the stock at that date were eligible for the dividend. The actual payment took place later, on Nov. 10.

To factor in for this difference, we need to take the amount of the dividend ($0.23) and divide it by the stock’s price immediately before this date. On Nov. 3, the stock price closed at $138.88. Taking $0.23 and dividing it by the stock price returns a value of 0.001656. If we take 1 minus that amount, that equals 0.99834389. That’s what the closing price needs to be multiplied by to arrive at the adjusted close. Here’s how it looks in the spreadsheet:

That ‘dividend impact’ factor will be applied to every value before the dividend. And when doing that, you arrive at the adjusted closing price. However, that’s not the end of this because if we go to the next dividend in August, the values are off again:

The issue here is that we need to factor in another dividend payment. It’s another payment of $0.23 and this time the stock price was $165.81. The discount factor is now 0.99861287. However, this needs to be multiplied by the first discount factor as well, in order to ensure we are adjusting for both dividend payments. And so the correct factor is 0.996959:

You would need to continue to make these adjustments the further back in time you go, and each time, taking into account all the dividend payments in-between today and the date of the stock price on that day. This is why over time, the difference gets larger.

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