Hi Guys, I’m hoping you can enlighten me. I just started my studies and I cannot figure out how they came up with portfolio Layer allocations for the second BPT investor. I’m sure I must be missing sthg basic there. Your help is much appreciated, have a great weekend!
- Assume the second investor puts X amount into Layer 3 and the rest in Layer 1 (2000000 - X). You can find X using the following equation : (2M - X)(1 + 0.01) + X (1 - 0.5) = 1.8M Note that Layer 1 is expected to yield 1% and Layer 3 -50% with 15% prob. Since the first Layer is risk-free, the above allocation should result in 1.8M, which happens to be his safety level, with 15% probability. 2. Solve the equaton for X: X = 431,373 (21.57%) (2M - X) = 1,568,627 (78.43%) - The 2nd investor would get 2,067,451 with 50% prob: 1,568,627 (1 + 0.01) + 431,373 (1+0.12) = 2,067,451 (12% of return given in the vignette) - He’d get 2,339,216 with 35% prob: 1,568,627 (1 + 0.01) + 431,373 (1+0.75) = 2,339,216 (75% of return given in the vignette) You might wonder why the 2nd layer is not being used at all. I bet CFAI won’t draw up a question with more than one unknown
Hope this helps.
The only thing I could think of with layer 2 is that it has some risk ( moderate ) , so you cannot guaranee 1.8 M final value. It is only by using layer 1 ( the insurance layer , a la Friedman-Savage) , that we can guarantee a specific level .
So if we’re using layer 1 to generate at least 1,800,000 final value , you get two equations:
if X is final value in layer 1 and Y is final value in layer 3 , then
X + Y = 1800000
X/1.01 + 2Y = 2000000 ( for a guaranteed 50% loss in layer 3 )
so X=1584313 or X/1.01= 1568627 ( investment in layer 1 ) or 78.43
2Y= 431373 or investment in layer 2 is 21.57%
Only being curious, what if the second investor wants a $2.2M instead of $2.1M ?