- CFA Level 2: Portfolio Management – Introduction
- Mean-Variance Analysis Assumptions
- Expected Return and Variance for a Two Asset Portfolio
- The Minimum Variance Frontier & Efficient Frontier
- Diversification Benefits
- The Capital Allocation Line – Introducing the Risk-free Asset
- The Capital Market Line
- CAPM & the SML
- Adding an Asset to a Portfolio – Improving the Minimum Variance Frontier
- The Market Model for a Security’s Returns
- Adjusted and Unadjusted Beta
- Multifactor Models
- Arbitrage Portfolio Theory (APT) – A Multifactor Macroeconomic Model
- Risk Factors and Tracking Portfolios
- Markowitz, MPT, and Market Efficiency
- International Capital Market Integration
- Domestic CAPM and Extended CAPM
- Changes in Real Exchange Rates
- International CAPM (ICAPM) - Beyond Extended CAPM
- Measuring Currency Exposure
- Company Stock Value Responses to Changes in Real Exchange Rates
- ICAPM vs. Domestic CAPM
- The J-Curve – Impact of Exchange Rate Changes on National Economies
- Moving Exchange Rates and Equity Markets
- Impacts of Market Segmentation on ICAPM
- Justifying Active Portfolio Management
- The Treynor-Black Model
- Portfolio Management Process
- The Investor Policy Statement

# Expected Return and Variance for a Two Asset Portfolio

### Expected Return for a Two Asset Portfolio

The expected return of a portfolio is equal to the weighted average of the returns on individual assets in the portfolio.

$R_p = w_1R_1 + w_2R_2$- $R_p$ = expected return for the portfolio
- $w_1$ = proportion of the portfolio invested in asset 1
- $R_1$ = expected return of asset 1

### Expected Variance for a Two Asset Portfolio

The variance of the portfolio is calculated as follows:

$\sigma_{p}^2 = w_{1}^2\sigma_{1}^2 + w_{2}^2\sigma_{2}^2 + 2w_{1}w_{2}Cov_{1,2}$- $Cov_{1,2}$ = covariance between assets 1 and 2
- $\text{Cov}_{1,2} = \rho_{1,2} \cdot \sigma_{1} \cdot \sigma_{2}$; where ρ = correlation between assets 1 and 2

The above equation can be rewritten as:

$\sigma_{p}^2 = w_{1}^2\sigma_{1}^2 + w_{2}^2\sigma_{2}^2 + 2w_{1}w_{2} \rho_{1,2} \sigma_{1} \sigma_{2}$Keep in mind that this is the calculation for portfolio variance. If a test question asks for the ** standard deviation** then you will need to take the square root of the variance calculation. Percentage values can be used in this formula for the variances, instead of decimals.

**Example**

The following information about a two stock portfolio is available:

Stock A | Stock B | |
---|---|---|

Amount | 20,000 | 30,000 |

Expected Returns | 12% | 20% |

Standard Deviation | 20% | 30% |

Correlation | 0.25 |

The weights for the two assets are:

$\begin{align*} w_A &= \frac{20,000}{50,000} = 40\% \\\ w_B &= \frac{30,000}{50,000} = 60\% \end{align*}$$\textbf{Expected Returns} = 0.40 \times 0.12 + 0.60 \times 0.20 = 16.8\%$$\textbf{Variance} = (0.40)^2(0.20)^2 + (0.60)^2(0.30)^2 + 2(0.40)(0.60)(0.25)(0.20)(0.30) \\\ = 0.046$$\textbf{Standard deviation} = \sqrt{0.046} = 0.2145 \text{ or } 21.45\%$### Expected Variance for a Three Asset Portfolio

$\sigma_p^2 = w_1^2 \sigma_{1}^2 + w_2^2 \sigma_{2}^2 + w_3^2 \sigma_{3}^2 + 2w_1w_2 \text{Cov}_{1,2} + 2w_1w_3 \text{Cov}_{1,3} + 2w_2w_3 \text{Cov}_{2,3}$### You may find these interesting

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