CFA Level I - Reading 50

Markowitz assumptions:

• Returns distribution. Investors look at each investment opportunity as a probability distribution of expected returns over a given horizon.
• Utility maximization. Investors behave such that they maximize their expected utility over a given investment horizon, and their indifference curves exhibit diminishing marginal utility of wealth.
• Risk is variability. Investors measure risk as the variance of expected returns.
• Risk/return. Investors make all investment decisions by considering only the risk and return of an investment opportunity. This means that their utility (indifference) curves are a function of the expected return and variance of the returns distribution they envision for each investment.
• Risk aversion. Given two investments with equal expected returns, investors prefer the one with the lowest risk. Likewise, given two investments with equal risk, investors prefer the one with the greatest expected return

Covariance is a measure of the degree to which 2 variables move together relative to their individual mean values over time.

The magnitude of the covariance depends on the variances of the individual return series, as well as on the relationship between the series.

The zero correlation does not mean the 2 assets are independent.
If the correlation coefficient were -1, a zero variance portfolio could be constructed.

Covariance can be standardized by dividing by the product of the standard deviations of the two securities being compared. This standardized measure of co-movement is called correlation.



Adding a new security to a portfolio has 2 effects on the portfolio's std. deviation: 1. the asset's own variance of returns. 2. the covariance between the returns of this new asset and the returns of every other asset.

An important factor to consider when adding an investment to a portfolio is not the new security's own variance but its average covariance with all the other investments in the portfolio.

A portfolio is efficient if it (1) maximizes return for a given risk level, or (2) minimizes risk for a given return target. The efficient frontier represents the set of portfolios that will give you the highest return at each level of risk (or, alternatively, the lowest risk for each level of return).

The efficient frontier line bends backwards due to less than perfect correlation between assets.

The optimal portfolio for each investor is the highest indifference curve that is tangent to the efficient frontier. The optimal portfolio is the portfolio that gives the investor the greatest possible utility.