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 !
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).