You decide to create a Mortgage Real Estate Investment Trust, i$.$e$.$ Mortgage REIT. Mortgage REITs are companies that invest in mortgage$-$backed securities $($MBS$)$ using mostly borrowed funds $($i$.$e$.,$ using a lot of leverage$).$

You decide to start your Mortgage REIT with $$10$ million in equity. You will borrow $$90$ million by issuing a $1$ year bond with an annual coupon of $3\%,$ and use the total $$100$ million to buy MBS$.$ To make things simple, let's represent the MBS portfolio as a $10-$year zero$-$coupon bond that is trading at a yield of $5\%$ Use the future value formula to calculate the face value of the MBS you can buy with $$100$ million. Is it higher or lower than the price you paid? Why does this make sense?

If interest rates don't change, what will be the value $($price$)$ of the MBS portfolio in $1$ year? Is it higher or lower than $$100$ million? Why?

How much do you have to repay at the end of the $1$ year on the $$90$ million bond that you issued?

Suppose you sell the MBS at the price you calculated in $(2)$ and repay the amount owed you calculated in $(3).$ How much equity do you have left?

What is your return on equity? To calculate the ROE, divide the answer to $(4)$ by the amount of equity you started with and subtract $1.$ How does the ROE compare to the yield on the MBS portfolio? Why does this make sense?. Changes in interest rates can substantially affect the value of your MBS portfolio and your return on equity. Let's see how this works.

Suppose MBS yields fall by $1\%$ over the next year. So in $1$ year, the yield on the MBS portfolio is $4\%.$ What is the value of the MBS portfolio in $1$ year? What is your return on equity?

We will try this again for a few more interest rate values. To avoid duplicating your code over and over again, write a function that takes the yield on the MBS portfolio after $1$ year as an argument and returns your ROE. Use this function to calculate the ROE for the following scenarios $($hint: use a for loop$).$ For each scenario, print an output message that says "Yield: XX$\%-->$ ROE: YY$\%."$ Format and round the numbers so that the output looks nice.

MBS yield in $1$ year: $3\%$

MBS yield in $1$ year: $4\%$

MBS yield in $1$ year: $5\%$

MBS yield in $1$ year: $6\%$

MBS yield in $1$ year: $7\%$

How does your ROE change as the MBS yield changes? Why does this make sense?

Do you ever get ROE that's less than $-100\%?$ If you do$,$ what does that mean econonomically? When companies have limited liability, is this possible?

Modify your function to print a message that says "Yields of XX$\%$ lead to bankruptcy!" $($where XX is automatically replaced with value of the yield passed into the function$)$ if the ROE is less than $-100\%.$