An efficient market is one, which is able to absorb new information into the security prices instantly. In the context of international markets, efficiency is not just about the individual markets but also about the pricing of these individual markets relative to the world index. The issue of international market efficiency revolves around international capital […]

# CFA Exam Level 2

## Markowitz, MPT, and Market Efficiency

Modern Portfolio Theory (MPT) is rooted in the mean-variance analysis research performed by Harry Markowitz conducted to allocate assets through a portfolio optimization process. The portfolio concepts presented in section I trace their roots to Markowitz groundbreaking work. The Efficient Market Hypothesis (EMH) contents that the market correctly prices all securities. MPT argues that all […]

## Risk Factors and Tracking Portfolios

Tracking portfolios Tracking Portfolio: A portfolio assembled with securities that will replicate a specific risk profile. Tracking portfolios commonly mirror an expected benchmark index, such as an index of global large capitalization stocks. The theoretical construction of a tracking portfolio done through multifactor modeling is done by setting each factor sensitivities equal to the factor […]

## Arbitrage Portfolio Theory (APT) – A Multifactor Macroeconomic Model

Arbitrage Portfolio Theory (APT) came along after CAPM as a multifactor model to explain returns. APT explains returns under the construct where: Multiple risks with an excess return above the risk free rate of return can be priced. Any security or portfolio has its own beta coefficient to each of the priced risk variables in […]

## Multifactor Models

While the Market Model uses only a single risk factor to price a security’s return, Multifactor Models apply a set of risk factors to describe an asset’s returns. Multifactor Model Types Macroeconomic Factor Models Apply economic variable as the risk factors that explain a security’s returns. Surprise Factor for betas of macroeconomic factor models: These […]

## Adjusted and Unadjusted Beta

Betas calculated purely based on historical data are unadjusted betas. However, this beta estimate based on historical estimates is not a good indicator of the future. This is also called the beta instability problem. Statistically, over time betas may exhibit mean reverting properties as extended periods significantly above 1 (one) may eventually decline and betas […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]