R 6 example 3 (CFAI BB)

The portfolio will result in at least 2,067,451 euros with 85 percent probability rather than 2,100,000 euros with 80 percent probability

can someone tell how these probabilities of 85% and 80% derived?


Your job is to allocate assets among different layers that would fit with his needs and desires.

Layer 1, if you invest 1 dollar here, you will get 1% on your investment with a probability of 100%.

He invests 1,568,627 and expects a return of 1,584,313.

Layer 3,

The investment amount is 431,373. And there are three scenarios that could happen.

Scenario1: you lose 50% of 431,373. The probability of this happening is 15%. Your ending value in this layer is 215,687. Now, if you add this number to the return from Layer 1, you get 1,800,000. The chance of that stays 15%.

Scenario 2: you gain 12% on 431373, so the return is 483138. Add this number to return on layer 1 and you get 2,067,451, with a chance of 50%.

Scenario 3. The ending value is 2,339,216, with a chance of that happening being 35%.

How does 85% value come up?

“The portofolio will result in at least 2,067,451”. This means that you add the scenario 2 and scenario 3 together. 50%+35%=85%.

I got it now… Thank you!!