How this calculator works
Each scenario contributes its probability multiplied by its return. Asset A and B must describe the same mutually exclusive scenarios, and probabilities must exhaust the possibilities by summing to one. The allocation produces each portfolio scenario before its expected return and population standard deviation are calculated. Rates in the lists are percentages; probabilities are decimal fractions.
Formula
E(RA) = sum(p_i RA_i); RP_i = w RA_i + (1-w) RB_i; E(RP) = sum(p_i RP_i); sigma_P = sqrt(sum(p_i(RP_i-E(RP))²)).
Worked example
With equal probabilities, A returning 20% or -10% has a 5% expected return and B returning 10% or 0% also has 5%. A 50/50 allocation returns 15% or -5%, with 5% expected return and 10% standard deviation.
Advertisement
Frequently asked questions
Should probabilities be 50 or 0.5?
Enter 0.5 for a 50% probability. Return lists use 20 for a 20% return.
Is the expected return guaranteed?
No. It is a probability-weighted mean of the scenarios you supplied; an individual outcome can differ substantially.
Does diversification always reduce the displayed volatility?
It depends on how the assets move together within your scenarios and on the allocation.