We learned that the calculation of risk for a portfolio of two assets is not straight forward as we also have to account for the covariance between the assets in the portfolio. Depending on the correlation between the assets, the risk-return profile of the portfolio changes. Note that we can combine the two assets in […]

# Portfolio Management

## Standard Deviation and Variance of a Portfolio

We learned about how to calculate the standard deviation of a single asset. Let’s now look at how to calculate the standard deviation of a portfolio with two or more assets. The returns of the portfolio were simply the weighted average of returns of all assets in the portfolio. However, the calculation of the risk/standard […]

## Calculate Variance and Standard Deviation of an Asset

After discussing the calculation of returns on investments, let’s now learn about how to measure the risks associated with these returns. In general, the risk of an asset or a portfolio is measured in the form of the standard deviation of the returns, where standard deviation is the square root of variance. Let’s look at […]

## Nominal Returns and Real Returns in Investments

While calculating the returns on an investment, what we directly observe is the nominal returns. These are the returns which have not been adjusted for the inflation. The nominal returns can also be looked at as pre-tax nominal returns and post-tax nominal returns. Pre-tax nominal return, as the name suggests, is the return without adjusting […]

## How to Calculate Leveraged Returns

We have looked at a variety of return measures. However, till now we assumed that the investment is made by the investor’s own money. However, in reality, the investor will not use only his money for making investments. The position will be leveraged. For example, while trading in futures contracts, the investor may have to […]

## Gross and Net Returns Calculations

In an investment management company such as a mutual fund, you will come across two types of returns being calculated, namely, returns on a gross, or net of fee basis. While there are some industry practices for calculating these returns, all fund managers don’t strictly follow one method. In simple words, the gross returns refer […]

## How to Calculate Portfolio Returns

We have learned about how to calculate the returns on single assets. However, portfolio managers will have many assets in their portfolios in different proportions. The portfolio manager will have to therefore calculate the returns on the entire portfolio of assets. The returns on the portfolio are calculated as the weighted average of the returns […]

## How to Calculate Annualized Returns

When we make investments, we invest our money in different assets and earn returns for different periods of time. For example, an investment in a short-term Treasury bill will be for 3 months. We may invest in a stock and exit after a week for a few days. For the purpose of making the returns […]

## Arithmetic Returns Vs. Geometric Returns

While calculating the returns on financial assets, we will often look at the returns from multiple holding periods. For example, one may hold an asset for five years, and the asset may have earned total 150% returns over this period of 7 years. However, it is difficult to interpret these returns as we cannot compare […]

## Portfolio Risk and Return – Part 2B – Video

This video by Arif Irfanullah provides a very clear conceptual understanding of the portfolio risk and return concepts as a part of the CFA Level 1 syllabus. This video talks about: Beta – Calculation and Estimation Capital Asset Pricing Model (CAPM) Assumptions Security Market Line Applications of CAPM, including estimating expected returns, and evaluating portfolio […]