The most comprehensive educational resources for finance

Selecting Optimal Portfolio for an Investor

In the previous articles, we learned that an investor can invest in a combination of risk-free asset and risky assets anywhere on the capital allocation line. A rational investor is also risk-averse and has a utility indifference curve that characterizes his risk-return expectations. However, the problem is that on the capital allocation line, the investor can create

Capital Allocation Line with Two Assets

We know that an investor can combine many risky assets to create a portfolio with lower risks. By varying the weights of different assets in the portfolio many portfolios with different risk-return profiles can be created. If we plot the risk-return profiles of these different portfolios, what we get is an efficient frontier. The efficient

Utility Indifference Curves for Risk-averse Investors

In the previous article we learned that different investors exhibit different levels of risk aversion. For each investor the degree of risk aversion translates into certain utility (read satisfaction) that he gets from an investment. In our example of $100 for sure vs. a gamble where you get $200 or nothing, when a risk averse

Risk Aversion of Investors and Portfolio Selection

We have seen that different asset classes such as bonds, stocks, and commodities provide different levels of risk and return to investors. However, we also know that these investment options are not equally preferred by all investors. An equity stock providing high returns may be suitable for one investor but another investor may want to

Effect of Correlation on Diversification

In this article, we will look at how correlation affects the diversification benefits of a portfolio. Let’s take a portfolio with two assets. The correlation between the two assets can range from -1.0 to 1.0 and depending on the correlation figure the shape of the efficient frontier will change. The following graph shows how the

Efficient Frontier for a Portfolio of Two Assets

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

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