Risk on Portfolio ⚠️📊
Calculating the return of a portfolio is easy (weighted average). But calculating the Risk of a portfolio is much more complex. This is because the risk of a portfolio isn't just the average of the individual risks; it also depends on how the assets interact with each other.
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Important
The risk of a portfolio (Standard Deviation) depends on three factors:
- The Weights of the assets.
- The Risk (SD) of each individual asset.
- The Correlation (Inter-relationship) between the assets.
2. Formula for Two-Asset Portfolio Risk
For a portfolio with two assets (A and B), the Variance (sigma_p squared) is calculated as:
Var(Rp) = (Wa^2 * Sa^2) + (Wb^2 * Sb^2) + (2 * Wa * Wb * Sa * Sb * r_ab)
Where:
- Wa, Wb: Weights of assets A and B.
- Sa, Sb: Standard Deviation (Risk) of assets A and B.
- r_ab: Correlation coefficient between Asset A and Asset B.
[!TIP] To get the Standard Deviation (sigma_p), simply take the square root of the Variance.
3. The Role of Correlation (r)
The correlation coefficient (r) ranges from -1.0 to +1.0:
- r = +1.0 (Perfect Positive): Assets move together perfectly. Diversification provides NO risk reduction.
- r = 0 (Uncorrelated): No relationship. Risk is reduced significantly.
- r = -1.0 (Perfect Negative): Assets move in opposite directions perfectly. Risk can be reduced to Zero.
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Summary
- Portfolio return is simple weighted average; Portfolio risk is NOT.
- Correlation is the key variable that makes diversification work.
- Combining assets with low or negative correlation is the best way to reduce total portfolio risk.
Quiz Time! 🎯
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