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

Hello

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 !

TIA

You’ve made it this far, and you know what it takes to pass. Don’t be fooled by false promises and unrealistic claims. Schweser’s study packages give you the proven study tools and expert instruction you need to finish the job.

Not sure what your question is! How a min. E(r) 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

back against the wall. no retreat no surrender.

romero wrote:

Hello

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 !

TIA

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%

——————————————
Find useful resources on the CFA exams at http://www.youtube.com/c/FabianMoa

Thank you Fabian Moa,

It is completely clear now !!! :)

fino_abama wrote:

romero wrote:

Hello

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 !

TIA

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%

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

Las almas de todos los hombres son inmortales, pero las almas de los justos son inmortales y divinas.
Sócrates

“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”

romero wrote:

The investment is expected to earn a minimum return of 4.7% over 25 years investment horizon with 95% probability.

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.

romero wrote:

For more details you may check: “Section 4. Developing Goals-Based Asset Allocations” of “Principles of Asset Allocations”

Thanks!

Las almas de todos los hombres son inmortales, pero las almas de los justos son inmortales y divinas.
Sócrates