Minimum expected return in Constructing Sub-Portfolios using Goals-Based approach


I have a question regarding the subject.

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 ?.

May be magician can sprinkle some wisdom

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).

Z = (X - mean return)/volatility

-1.645 = (X - 200%)/50%

X = 200% - 1.645 x 50% = 117.75%

Return per year = 117.75% / 25 years = 4.7%


Thank you Fabian Moa,

It is completely clear now !!! :slight_smile:

what is the interpretation of the result? How is that 4.7% annual return interpreted?


“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.


So does this 4.7% act as the discount rate to estimate the initial capital to be set aside for the goal?

Yes :+1:

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