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 $2 to $4 to $8 to $16 to $32 to $64 over a six-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. Instructions: Enter your answer as a whole number. 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 $3? I followed the instructions from 2 other answers and a results I got were 60 and 42.7 which I rounded to 43. Both answers were incorrect.

Answer 1

Consider the following example. 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 $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. Assuming existing ratios, by how much would the value of the financial securities decline if the value of the underlying asset suddenly and unexpectedly fell by $3?

Since we are assuming the same ratios (or structure of the growth rates remain the same), a decline in underlying asset value by $3 results in a new value of $4 (falls from $7, the current value, to the new value of $4).

This implies that value of existing financial securities, which grew at a geometric rate, falls back to $4. This was the existing asset value associated with the underlying asset value 5 years ago (the underlying asset value was $4 five years ago). Thus, the value of the financial securities would fall by $56.

Ans is 56.