Estimating Expected Returns and Standard Deviation of a Portfolio | CFA Level I Portfolio Management

Welcome back to our journey of learning how to estimate the expected returns and standard deviation of returns of a portfolio. We’ll start with individual assets, discuss covariance and correlation, and end with constructing a diversified portfolio.

Calculating Expected Returns and Standard Deviation of Returns

In our previous lesson, we learned different ways to calculate the average return of an asset using its price history. This average return can be used as an estimate of the asset’s expected return. Another important aspect to study is the asset’s risk, commonly estimated through its standard deviation of returns.

Expected Returns and Standard Deviation of a Portfolio

Using expected returns and standard deviations for individual assets, we can form expectations for the risk and returns of a portfolio. However, there are some limitations to this approach:

1. Assumption of normal distribution: Returns distributions are actually negatively skewed and have greater kurtosis than a normal distribution.
2. Liquidity: This approach does not consider the liquidity of the portfolio assets, which can affect the selling price and expected return.

Despite these limitations, let’s learn how to estimate the expected returns and standard deviations of a portfolio. Consider a portfolio with 70% large cap US stocks and 30% treasury bonds.

The expected return is the weighted average return of the 2 assets: 8.43%.

The standard deviation of returns for the portfolio: 14.57%.

Covariance and Correlation

Covariance measures how returns of two assets move together over time. A positive covariance means returns move together, negative covariance means they move in opposite directions, and a covariance of zero means no linear relationship.

However, covariance has some shortcomings due to its magnitude and unbounded nature. Most practitioners prefer using the correlation coefficient, a standardized measure bounded between -1 and +1.

The correlation coefficient helps us understand how the returns of two assets move together over time. A coefficient of +1 indicates perfect positive correlation, -1 indicates perfect negative correlation, and 0 indicates no correlation.

By substituting the covariance term in the equation for the variance of a portfolio with the correlation terms, we get a more useful equation for practitioners who prefer dealing with correlation.