Log Prices in Stock Market | Price vs Log Price | Why Log Price is Important | Quantra Course

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Part of the course Financial Time Series Analysis for Trading.
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Timecodes
0:00 - Title
0:10 - Tesla's Journey
0:20 - Hypothetical Scenario
1:30 - Log Prices
2:25 - Tesla's Price & Log Price
2:58 - End

Welcome to this video lesson on log prices. After completing this, you will be able to describe and calculate log prices.
Let us look at the price graph of Tesla over the years. Which years do you think would have been the best for investing in Tesla? We will come back to the answer later.
Consider a hypothetical stock whose prices for the past 5 days is shown on screen. A few observations from this table are as follows. On 23 and 26 June, the price doubles i.e. 100% returns. On June 24, the price increases by 50% when it goes from $200 to $300. On June 25, the price decreases by 33% when it goes from $300 to $200.
The plot of the prices looks like this. By looking at this graph, can you easily infer what you inferred from the data table before? Probably not.
The price doubled on June 23 and then increased by half on June 24. This is difficult to distinguish in the graph as the slope of the line is the same. Also, while the price doubled on both June 23 and June 26, the line is steeper for June 26 price increase. This shows that looking at a price graph does not give us the real picture. Can you think of a better way to visualize?
Yes, the plot of log prices. What is log? Or what is log to the base 10 of 100? 10 square is 100. In this example, it is log to base 10. In general we work with natural log.
Let us find the natural log of the prices and plot a line graph. This is perfect. You can see that the slope of the line from June 22 to 23 is the same as the line on June 25 to 26, as the price had doubled in both cases. The slope of the line on 22 to 23 is different to the slope of the line on 23 to 24. Using the plot of log prices it is easy to infer what we inferred from data table.
Let us go back to the Tesla example we asked initially. The price graph makes it seem that 2019 and 2020 were the only good period. But the log prices tell us a different story. Here, we can see that 2013 and 2014 were also good years to invest in Tesla. This is because the stock price increased from $34 in 2013 to $250 in 2014. This is almost equivalent to rise in 2019 and 2020.

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