Stock probabilities

1. Stock probabilities

In the last exercises, you simulated potential stock prices. Instead, let's now focus on the probability of different prices to see what earnings or losses they might have.

2. Prices are lognormal

Over the next two videos, we will examine how stock prices are lognormal, which is the distribution shown in the graph. If you took the log of the values in a lognormal distribution, you would end up with a normal distribution. You previously learned that stock price change is normally distributed, and the distinction here is that the price is lognormally distributed.

3. Stock probability model

To estimate the most likely price of a stock and show how they are lognormal, we will set up a model to estimate stock probabilities across a wide range of values. The top portion of this model is very similar to our previous simulation model.

4. Expected return k

First, we will estimate expected return as k, in the same way as before with expected return mu minus volatility squared divided by two. A new portion to this model is the time return, which is the number of years to estimate holding the stock over. We can use 1-point-5 here to represent one and a half years.

5. A range of values

To create the range of possible stocks, we will calculate the expected stocks at four standard deviations above and below the mean. You will take the exp function of the natural log of the stock price plus k multiplied by time plus and minus four times volatility times the square root of time; the minus is used for the minimum stock price, and the plus is used for the maximum stock price.

6. Apple's range of prices

When we calculate the min and max values for Apple, we see that their stock could fall to 49 dollars or go all the way up to nearly 1000 dollars.

7. Stock price steps to calculate on

In this example, we will calculate 200 possible stock prices and their probabilities. You can pick any number of options, but having a large number of values allows you to visualize the distribution of stocks more accurately. To calculate the steps, type equals max price minus min price divided by 200.

8. Entering the steps

In our final step for this lesson, we will create a data table of stock prices and estimate their likelihood. In the first cell underneath stock price step A15, you will enter equals and click on the minimum stock price you calculated above. For every other step, you will use equals click on the previous value and then add the stock price step from B11. Be sure to use an absolute reference on the stock price step.

9. Finish the data table

You will now copy that formula until you reach 200 steps, which is 201 rows. You should see your maximum value as the last row of data, which was 986-point-87 for Apple's stock.

10. Let's practice!

Let's head over to the exercises to get started on estimating the most likely stock price.

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