How Minimum expected returns for a given investment horizons and at specific probabilities are calculated ? It looks like the calc process is out the scope of the curriculum but I would like to get a general idea at least.
In the Reading 13, Exhibit 36 we’ve got “Annualized Minimum Expectation Returns” for each Time Horizons (5,10,15…) and at Required Success (Probabilities: 99,95…).
How the expected returns are different for different time horizons and probabilities ? I could guess that they may be different at different probabilities using corresponding number of Stdevs from the mean. But still in this case there would be a mismatch in the calculus !
Not sure what your question is! How a min. E® is calculated. Known to me are at least 2 methods. Binomial/BSM and Shortfall risk. Do you know of any more ?.
I will pick Module E (Exp return = 8%; Exp volatility = 10%); Time Horizon = 25 years; Required Success = 95% for illustration.
Expected return over 25 years = 8% x 25 = 200%
Expected volatility over 25 years = 10% x sqrt(25) = 50%
Based on Normal Distribution, for a 95% probability of the module return being more than a certain X% over 25 years, the standard normal variable Z is -1.645 (refer to Standard Normal Distribution statistical table).
“Minimum expectations are defined as the minimum return expected to be earned over the given time horizon with a given minimum required probability of success” CFAI
The investment is expected to earn a minimum return of 4.7% over 25 years investment horizon with 95% probability.
For more details you may check: “Section 4. Developing Goals-Based Asset Allocations” of “Principles of Asset Allocations”
I thought the same thing. I would use the word “minimum annual return of 4.7% on average over 25 years”. This calculation is removing volatility at a 95% confidence level.
