The portfolio management section contains a lot of material and much of it might never appear on the actual Level 2 test. Consider that this is one of the most in-depth study sessions from the official curriculum, but a candidate may only see one item set (six questions). That said much of this session’s content […]

# Portfolio Management L2

## Mean-Variance Analysis Assumptions

Mean-variance analysis gives investors a framework to assess the tradeoff between risk and return as mean-variance analysis quantifies the relationship between expected return and portfolio variance (or standard deviation). Mean-variance analysis is the theoretical foundation of Modern Portfolio Theory established by Professor Harry Markowitz and much of the material covered in this module traces its […]

## 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 […]

## The Minimum Variance Frontier & Efficient Frontier

Two asset classes (stocks and bonds for example) can be combined with varying proportions to create an infinite number of portfolios. An investor can calculate the expected returns and variances of a two asset portfolio and plotting these on the Y (returns) and X (variances) axis of a graph. Global Minimum Variance Portfolio: The portfolio […]

## Diversification Benefits

A diversification benefit exists when a portfolio’s standard deviation can be reduced without reducing expected return. The diversification benefit is possible when return correlations between portfolio assets is less than perfect positive correlation (<+1.0). If assets have less than a +1.0 correlation, then some of the random fluctuation around the expected trend rates of return […]

## The Capital Allocation Line – Introducing the Risk-free Asset

The discussion of diversification benefits focused on a portfolio consisting of risky assets; when a risk-free asset is incorporated, diversification is still prevalent but a linear trade-off between risk and return is established. The introduction of a risk-free asset does not change the construct of the minimum variance frontier graphical structure (y-axis = expected return; […]

## The Capital Market Line

On a graph, the Capital Allocation line (CAL) starts at the risk-free return and runs tangent to the minimum variance frontier for any group of risk assets. On a graph, the Capital Market Line (CML) starts from the risk-free return on the y-int and runs tangent to the efficient frontier at the market portfolio. Market […]

## CAPM & the SML

The Capital Asset Pricing Model (CAPM) assumes only one efficient portfolio, the market portfolio. CAPM and the CML are more strict than simple Mean-Variance and the CAL. CAPM and CAL similarities: Risk averse investors. Shared investor assumptions for expected returns, variances and standard deviations, and covariances of returns. The above variables are the only inputs […]

## Adding an Asset to a Portfolio – Improving the Minimum Variance Frontier

We can use the Sharpe Ratio to determine if adding an asset creates a better (higher) minimum variance frontier. The Sharpe ratio is calculated using the following formula: Sharpe Ratio = (E(Rasset) – RF)/σasset Calculate the Sharpe ratio for the current portfolio and then calculate the Sharpe ratio after adding the new asset. If the […]

## The Market Model for a Security’s Returns

When a portfolio manager considers a security for addition to a portfolio within the construct of mean variance analysis, he/she must determine what return for the x-variable represents “market portfolio”. The Market Model assumes that some security market index, such as the S&P 500, represents the market portfolio. The Market Model & Quant: The Market […]