Two Assets

Returns & Weights

Portfolio return is a weighted average of stated asset returns.

highlighted = computed this step

Stated inputs

Asset A has stated return 10% and asset B has stated return 6%. A fifty-fifty portfolio uses weight 1/2 in each asset.

wA=wB=1/2,rA=10%,rB=6%w_A=w_B=1/2,\quad r_A=10\%,\quad r_B=6\%

Weighted average return

Portfolio return is the weighted average of the stated returns. Here it is 8%, independent of correlation.

rp=wrA+(1−w)rB=8%r_p=w r_A+(1-w)r_B=8\%

Inputs, not estimates

In the real world, returns, sigma, and rho are estimated from data with uncertainty. Here they are stated exact model inputs. This is descriptive, not investment advice.

stated inputs, exact arithmetic\text{stated inputs, exact arithmetic}