Markowitz Portfolio Theory
Intro
Harry Markowitz developed the Modern Portfolio Theory (MPT), which shows how investors can optimize the trade-off between risk and return through diversification.
Key idea: By combining assets with different correlations, investors can reduce overall portfolio risk without necessarily lowering expected returns.
Let’s take the two key concepts from Markowitz’s Modern Portfolio Theory — Expected Return and Risk (Standard Deviation) — and show how to use them in practice, with clear, step-by-step examples.
Expected Return
The weighted average of the expected returns of each asset:
E(Rp)=i=1∑nwi⋅E(Ri)
Where:
- E(Rp): expected return of the portfolio
- wi: portfolio weight of asset i
- E(Ri): expected return of asset i
Example:
Let’s say you invest in two assets:
| Asset | Expected Annual Return | Portfolio Weight |
|---|---|---|
| U.S. Treasury Bonds | 3% | 60% |
| Microsoft Stock | 10% | 40% |
E(Rp)=(0.6×0.03)+(0.4×0.10)
E(Rp) = 0.018 + 0.04 = 0.058 = 5.8%
Interpretation
If your expectations hold true, your portfolio should earn an average annual return of 5.8%.
Risk
Measured by the variability of returns. Portfolio risk depends not only on individual asset risks but also on how the assets move relative to each other (their correlation).
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