Question

Assume that securitization combined with borrowing and irrational exuberance in Hyperville have driven up the value of asset-backed financial securities at a geometric rate, specifically from \(2 to \)4 to \(8 to \)16 to \(32 to \)64 over a 6-year time period. Over the same period, the value of the assets underlying the securities rose at an arithmetic rate from \(2 to \)3 to \(4 to \)5 to \(6 to \)7. If these patterns hold for decreases as well as for increases, by how much would the value of the financial securities decline if the value of the underlying asset suddenly and unexpectedly fell by $5?

Short answer

The value of financial security will be $62 if the underlying asset suddenly and unexpectedly falls by $5.

Step-by-step solution

Step 1. The value of financial derivates when the underlying assets fall to $5

The value of the financial securities depends upon the underlying assets since these assets are included in the values of such financial securities. Therefore, if the value of the underlying asset decreases, the value of financial securities also falls by the same amount, other things being equal, and vice versa.

The current value of the underlying assets is $7, and the current value of the financial securities is $64. Now, if there is a decline in the underlying assets’ value by $5, the value of the underlying assets would change to $2. Hence, with the consequent value of $2, the value of financial security will also reduce by $2 and decrease from $64 to $62.