Efficient Portfolio: Market Beta and Beyond (2024)

FAQs

What is the beta of an efficient portfolio? ›

Beta is the risk-reward measurement that informs investors how sensitive their portfolio is to market changes. The market benchmark index sits at a 1.0, and for the lowest possible volatility in a portfolio, investors need to try to remain as close to a 1.0 as possible.

Beta Value Less Than One

A beta value that is less than 1.0 means that the security is theoretically less volatile than the market. Including this stock in a portfolio makes it less risky than the same portfolio without the stock.

According to the CAPM, this is the portfolio that delivers the maximum Sharpe ratio, in other words no other investment offers better reward for a given risk target. The immediate consequences of the market portfolio's efficiency are far-reaching.

The market is described as having a beta of 1. The beta for a stock describes how much the stock's price moves compared to the market. If a stock has a beta above 1, it's more volatile than the overall market. For example, if an asset has a beta of 1.3, it's theoretically 30% more volatile than the market.

The beta of a portfolio is determined by dividing the change in its returns by the change in returns of a market portfolio during a given period. Thus, the beta of a market portfolio will always be equal to 1 as the value of the numerator and denominator will be the same.

Portfolio Beta formula

Add up the value (number of shares x share price) of each stock you own and your entire portfolio. Based on these values, determine how much you have of each stock as a percentage of the overall portfolio. Take the percentage figures and multiply them with each stock's beta value.

A beta value greater than 1 indicates that the stock is more volatile than the broader market, while a value below 1 suggests the stock is less volatile.

A beta greater than 1 indicates a stock's price swings more wildly (i.e., more volatile) than the overall market. A beta of less than 1 indicates that a stock's price is less volatile than the overall market.

High-beta stocks tend to be riskier but provide the potential for higher returns. Low-beta stocks pose less risk but typically yield lower returns.

A portfolio is said to be efficient if there is no other portfolio that offers higher returns for a lower or equal amount of risk. Where portfolios are located on the efficient frontier depends on the investor's degree of risk tolerance.

How do you calculate efficient portfolio? ›

If we wish to find an efficient portfolio with a given expected return R₀, we just need to find the right value of R_f that will produce an expected return of R₀. This can be done by setting Z'R/Z'i = R₀, and solving for R_f, using the formula above for Z.

A portfolio is efficient if no other ensures a better profitability for the same risk or the same profitability at a lower risk. The portfolio analysis requires a large quantity of information and Sharpe was trying to diminish the number of these information using a set of simplifying hypothesis.

Values of beta should be kept small, but do not have to be as small as alpha values. Values between . 05 and . 20 are acceptable.

If a stock has a beta value less than 1.0, this is considered to be a good beta value for a stock, because it indicates that stock has a price volatility lower than the market index. In this way, a stock with a beta value less than 1.0 can be referred to as a low beta stock.

That depends on what kind of risk/return you're looking for. A beta value of 1.5 implies that the stock is 50% more volatile than the broader market. That means higher than average risk and the potential for greater upside.

Beta = covariance/variance

Covariance is a measure of a security's returns relative to the market's returns. Variance is a measure of the market's return relative to its mean or average.

The capital asset pricing model (CAPM) approximates return as a linear function of beta. Beta is a measurement of how much an investment fluctuates in sync with the markets. For a stable bond, beta might be zero. The markets as a whole have a beta of 1.0.

Beta measures the relative volatility of an investment. It is an indication of its relative risk. Alpha and beta are standard calculations that are used to evaluate an investment portfolio's returns, along with standard deviation, R-squared, and the Sharpe ratio.

The average asset beta represents the business risk of the proposed investment project.