Question

Assume that securitization combined with borrowing and irrational exuberance in Hyperville have driven up the value of existing financial securities at a geometric rate, specifically from $4 to $8 to $16 to $32 to $64 to $128 over a six-year time period. Over the same period, the value of the assets underlying the securities rose at an arithmetic rate from $4 to $6 to $8 to $10 to $12 to $14.

Rquired:
1. 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 $6?

Answer 1

The financial securities would decline by $106.7

Step-by-step explanation:

Given

Financial securities at a geometric rate= $128

Underlying Security Asset = $14

Decreased value of the underlying asset = $6

When there's a reduction of $6 in the underlying asset price, this means the securities value will also get a reduction by a ratio of 6.

Because of this, we'll only consider the financial securities because it increases at a geometric progression unlike underlying assets that increases by arithmetic progression.

First, the value of financial securities needs to be calculated using the following formula;.

Value of Financial Securities = Financial securities at a geometric rate ÷

Decreased value of the underlying asset

Value of Financial Securities = $128 ÷ 6

Value of Financial Securities = $21.3

Tthe decline value of the financial securities is calculated as follows:

Decline Value = Financial securities at a geometric rate - Value of Financial Securities

Decline Value = $128 - $21.3

Decline Value = $106.7

Hence, the financial securities would decline by $106.7