[Verse 1]
Picture assets scattered like puzzle pieces on your desk
Some stocks sprint wildly, bonds move slow but blessed
Expected returns whisper promises in your ear
While standard deviation measures how much you should fear
Correlations dance between minus one and plus
When assets move together or betray our trust
[Chorus]
Mean-Variance Optimization, calculation sensation
Expected return divided by the risk you take
Efficient Frontier, the curve that makes it clear
Maximum reward for every chance you make
Sharpe ratios climbing, portfolio timing
Find the sweet spot where the math won't break
[Verse 2]
Markowitz discovered gold in nineteen fifty-two
Don't put eggs in baskets, let statistics guide you through
Covariance matrices hold the secrets of the game
When oil zigs and tech stocks zag, diversification's name
Plot return on vertical, risk upon the horizontal
Watch the magic happen as efficiency goes orbital
[Chorus]
Mean-Variance Optimization, calculation sensation
Expected return divided by the risk you take
Efficient Frontier, the curve that makes it clear
Maximum reward for every chance you make
Sharpe ratios climbing, portfolio timing
Find the sweet spot where the math won't break
[Bridge]
Capital allocation line extends beyond the curve
Risk-free rate anchors what conservative minds preserve
Tangency portfolio kisses where the best slopes meet
Market portfolio theory makes the picture complete
[Verse 3]
Lagrange multipliers solve for weights that sum to one
Constraints and objectives battle till the war is won
Minimum variance hugs the bottom of the arc
While maximum Sharpe illuminates the dark
Rebalancing quarterly keeps you on the path
Modern Portfolio Theory backed by solid math
[Chorus]
Mean-Variance Optimization, calculation sensation
Expected return divided by the risk you take
Efficient Frontier, the curve that makes it clear
Maximum reward for every chance you make
Sharpe ratios climbing, portfolio timing
Find the sweet spot where the math won't break
[Outro]
From the minimum variance to the market's peak
Mean-variance shows you exactly what to seek