Question

[Requires appendix.] Could any combination of home price, mortgage, or further borrowing on a home result in a simple leverage ratio of \(1 / 2 ?\) If yes, provide an example. If no, briefly explain why.

Short answer

Yes, a combination of home price and mortgage can result in a simple leverage ratio of 1/2. For instance, if the home price is \$100,000 and the mortgage is \$50,000, the leverage ratio would be 1/2.

Step-by-step solution

Understanding Leverage Ratio

For a simple leverage ratio of 1/2, the debt should be half the value of equity. In our case, the debt is the mortgage or further borrowing, while the equity is the home price.

Determining the Possibility

Let's assume an arbitrary home price, say \$100,000. If we want to create a leverage ratio of 1/2, the mortgage should equate to half the equity. Hence, the mortgage should be \$50,000.

Confirming the Leverage Ratio

So, for a home price of \$100,000 and a mortgage of \$50,000, the resulting leverage ratio is: \(\frac{Mortgage}{Home Price} = \frac{50,000}{100,000} = \frac{1}{2}\), thus satisfying our requirement.