Hi all,
I am don’t understand the solution given in Example 3 of this Reading.
Here is the text of the example:
- “BPT investors developing portfolios. The portfolios will contain at most three layers: a layer of riskless investments, a layer of moderately risky investments, and a layer of highly risky speculative investments. The riskless investments (layer 1) are expected to return 1 percent; the moderately risky investments (layer 2) are expected to return –3 percent with 10 percent probability, 5 percent with 80 percent probability, and 9 percent with 10 percent probability; and the speculative investments (layer 3) are expected to return –50 percent with 15 percent probability, 12 percent with 50 percent probability, and 75 percent with 35 percent probability. The BPT investor has 2,000,000 euros and an aspirational level of 2,100,000 euros with a probability of 80 percent. Further, this investor can tolerate some potential loss in wealth but cannot tolerate the portfolio declining below 1,800,000 euros. Construct the BPT optimal portfolio for each investor.”
The proposed solution is:
- The second BPT investor has an aspirational level of return of 5 percent (100,000 euros). Given the safety level and a maximum potential loss of 50 percent on the speculative assets, the investor may put approximately 1,568,627 euros in layer 1 and 431,373 euros in layer 3. This portfolio will result in an expected return of 6.123 percent.This portfolio will result in 1,800,000 euros with 15 percent probability, 2,067,451 euros with 50 percent probability, and 2,339,216 euros with 35 percent probability. The safety objective is met, but the portfolio is short of the aspirational goal. 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. Based on risk tolerance, the investor may decide this is acceptable or may decide to lower her safety level objective.
My concern:
- if the investor chose 100% allocation to Layer 2, he would have reached his aspiration of 5% return at 80% probability and ensure he will not lose more than 3% of his assets (above his min level of 10% loss
am i missing something?
thanks