Risks and rates of return. Portfolio return

Risks and Rates of Return

The investor’s return is a measure of the increase in the expected future returns to the investment, in other words, the creation of wealth. It is the change in the value of the investment over the initial investment for a specific time interval, usually for one year. The use of a mean or average measure of return aids in determining the returns.

The dispersion around the expected return is one calculation used to measure risk. This concept is expressed by using a statistical measure called standard deviation (S), which is the square root of the variance. The variance, S squared, is the average deviation from the mean. The deviation is multiplied by itself (squared) to measure the magnitude of the deviation, whether it is positive or negative. The standard deviation is a unit measure of the dispersion about the average expected return, rather than the squared measure of the variance.

Usually, investors prefer high returns and low standard deviation or risk. In this way, you can summarize stock return data using the arithmetic mean and standard deviation measures as proxies for expected returns and risk.

Over long periods, investors can earn more on stock than bonds, but they must incur more risk in doing so. Investors must choose to maximize return while minimizing risk. Managers must choose financing that minimizes the cost of funds, while not creating so much risk that it threatens the firm.

Portfolio Returns

A portfolio is any collection of financial assets and investments. Let's say that out of $100,000 you invest $50,000 in Stock A and $50,000 in Stock B. This is a two-stock portfolio. You can change the proportion of funds invested in each stock to create various portfolios with different risk-return characteristics. Portfolio returns are calculated by multiplying the stock returns with the proportion of funds invested in each stock and adding them. They are a weighted average.

A measure of the risk of an individual investment is the standard deviation around the expected return. The risk of a portfolio of stocks is each stock’s standard deviation plus/minus the correlation between stocks in the portfolio. This does not necessarily make a portfolio more risky than an individual stock. If the correlation between stocks in a portfolio is less than 100% directly related (their prices move in the same direction), then the portfolio of stocks will have less risk (variation) than an individual stock. In other words, the value of some stocks in a portfolio will not change in the same proportion. Some stock prices may rise more than others, or other prices may fall.

Diversification is a tool to lower the risk in holding financial securities. This is the most important benefit of creating portfolios. The higher the number of stocks in the portfolio, the more the risk is reduced. But the benefit of adding a stock to the portfolio diminishes as the number of stocks in the portfolio increases.

Capital Asset Pricing Model

If the economy contains a risk-free asset, it is easier to create portfolios. By combining the risk-free asset and the market portfolio in various proportions, you can devise a risk-to-return pattern that provides the highest return for a given level of risk.

One model of the relationship between a risk-free asset and the market return is described by the capital asset pricing model (CAPM). In this model, beta (ß) is the measure of an asset's systematic risk with respect to the market. Beta is a measure of relative risk, because it measures the risk relative to the market portfolio, unlike the standard deviation, which is an absolute measure of risk. Because the value of the beta of the market portfolio is one (1), and the beta of a risk-free asset is zero (0), you can develop beta as a measure of risk relative to the market of assets.

If an asset has a beta of 0.5, its variability of returns is half that of the market portfolio. If the beta of an asset is 1.2, the asset's returns are 20% more volatile than the market. This concept is one of the underpinnings of the CAPM. The CAPM states that the expected return on an asset depends upon its level of systematic risk.

• Historical or average return: This is the mathematical average of historical returns.

• Expected return: The expected return is the weighted average of the expected returns and their respective probabilities.

• Standard deviation as a risk measure: A unit measure of deviation or dispersion from the average return or expected return.

• Coefficient of variation: This measures the risk per unit of return of a security.

• Risk return tradeoff: There is a relationship between the risk and return of an asset; higher returns come with more risk but not a guarantee of that return.

• Portfolio returns: These are a weighted average of the returns of the stocks and their proportion in the portfolio.

• Diversification: This is used to lower the risk of a portfolio by adding securities that are not identical in risk and return.

• CAPM: CAPM stands for capital asset pricing model, which is used to estimate the expected return of an asset based on its risk relative to the market (its systematic risk).