Part B: Annual Yield Function

In this section, we will create and test a function that takes a simulated run as its input, and calculates the annual yield

during for that particular run.

Create a markdown cell that displays a level $2$ header that reads: "Part B: Annual Yield Function". Also add some text

briefly describing the purpose of your code in this part.

Write a function named find$\_$yield. This function should accept a single parameter called run, which is expected to be

an array of simulated daily prices for a stock. The function should return the annual yield for the stock over the simulated

period, rounded to four decimal places.

The formula for calculating the annual yield is as follows: annual yield $=$ ln $($

Final Price

Initial Price$)$

$252$

Days in Run

$.$ You can use the

function math.log in the math package to calculate the natural logarithm.

Recall that the number of days in a run is equal to one less than the length of the run since the run contains the starting

price.

Create a markdown cell that explains you are about to test your function by running it on the previously simulated run.

Call the find$\_$yield function on the run you created in Part A$,$ printing the result. If everything is correct, you should get

$0\mathrm{.}1196$ as the result. Note that this is quite a bit different from the expected $8\%$ annual yield that we used to simulate this

run. This is a result of the randomness involved in our simulation.

Create a markdown cell to explain that the next cell will explore the potential variability in our simulated runs by creating

and plotting $25$ simulated runs.

In a new cell, use a loop to create $25$ simulated runs for a stock with a current price of $100,$ an expected annual yield of $6\%,$

and an annual volatility of $0\mathrm{.}4$ over a period of $200$ days. Plot all $25$ runs in the same line plot. For each run, use find$\_$yield

to calculate the annual yield for the run, and store the value in a list. You should see a wide range of simulated results.

Hint: Each iteration of your loop should do three things: Simulate a run, calculate the yield for that run and add the result to

a list, and add a line plot of the run to a figure using plt$.$plot.

Create a markdown cell to explain that the next cell will display the yields for the $25$ simulated runs.

Print the list of annual yields created in the previous code cell. Again, you will likely see a wide range of results.