Assume that securitization combined with borrowing and irrational exuberance in
ID: 1180993 • Letter: A
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.
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 $4? (NOT THE PERCENTAGE)
Explanation / Answer
It is clearly seen that the common difference for the arithmetic series of the underlying assets worked as the common ratio of the geometric series of the financial securities. (Both are 2)
So, if the underlying assets price fall by 4, then the securities value will fall by a ratio of 4. So, the value of financial securities becomes 128/4 = 32.
Hence, the decline in the value of the financial securities = 128 - 32 = $96