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.
Rp = w1R1 + w2R2
 Rp = expected return for the portfolio
 w1 = proportion of the portfolio invested in asset 1
 R1 = expected return of asset 1
Expected Variance for a Two Asset Portfolio
The variance of the portfolio is calculated as follows:
σp2 = w12σ12 + w22σ22 + 2w1w2Cov1,2
 Cov1,2 = covariance between assets 1 and 2
 Cov1,2 \= ρ1,2 * σ1 * σ2; where ρ = correlation between assets 1 and 2
The above equation can be rewritten as:
σp2 = w12σ12 + w22σ22 + 2w1w2 ρ1,2σ1σ2
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:
wA\= 20,000/50,000 = 40%
wB\= 30,000/50,000 = 60%
Expected Returns = 0.40*0.12 + 0.60*0.20 = 16.8%
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
Standard deviation = Sqrt(0.046) = 0.2145 or 21.45%
Expected Variance for a Three Asset Portfolio
σp2 = w12σ12 + w22σ22 + w32σ32 + 2w1w2Cov1,2 + 2w1w3Cov1,3 + 2w2w3Cov2,3
 CFA Level 2: Portfolio Management – Introduction
 MeanVariance 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 Riskfree 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 JCurve – 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 TreynorBlack Model
 Portfolio Management Process
 The Investor Policy Statement