FIN435 • Chapter 8 — Study Guide
Risk & Return • Diversification • Efficient Frontier (Spring 2026)
Key Concepts & Formula Sheet
- Return (R): the reward you earn (often a percent).
- Risk (σ): volatility/variability of returns (standard deviation).
- Variance (σ²): standard deviation squared.
- Covariance (σij): how two assets move together (units: return²).
- Correlation (ρij): scaled covariance, from −1 to +1 (unitless).
- Diversification: reduce portfolio risk by combining assets with imperfect correlation.
- Efficient frontier: highest expected return for each level of risk (or lowest risk for each return).
Use decimals in calculations
Example: 18% → 0.18, weight 40% → 0.40.
Core formulas
| What to compute | Formula |
|---|
| Correlation and covariance |
ρij = σij / (σi σj)
and
σij = ρij σi σj
|
| Portfolio expected return (3 assets) |
E[Rp] = wA·E[RA] + wB·E[RB] + wC·E[RC] |
| Portfolio variance (3 assets) |
σp2 = wA2σA2 + wB2σB2 + wC2σC2
+ 2wAwBρABσAσB + 2wAwCρACσAσC + 2wBwCρBCσBσC
|
| Portfolio standard deviation |
σp = √(σp2) |
| Sanity check |
wA + wB + wC = 1.00 |
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Calculation Practice — 3-Stock Portfolio (Return & Risk) with solutions
Compute E[Rp] and σp. Report as percentages (2 decimals). Use decimals inside formulas.