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.

However, as a general rule, a good stock market beta for an investment portfolio is around 1.0, while a good alpha is around 0.5.

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.

Beta (β) is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole (usually the S&P 500). Stocks with betas higher than 1.0 can be interpreted as more volatile than the S&P 500.

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.

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.

The ideal beta for a stock depends on your investment objectives and risk tolerance. Generally, a beta of 1 indicates the stock moves in line with the overall market. A beta greater than 1 suggests higher volatility.

A lower standard deviation indicates lower volatility and, often, better diversification. Beta: Beta measures a portfolio's sensitivity to overall market movements. A beta of 1 suggests the portfolio moves in line with the market, while a beta below 1 indicates less volatility.

In an efficient portfolio, investable assets are combined in a way that produces the best possible expected level of return for their level of risk—or the lowest risk for a target return. The line that connects all these efficient portfolios is known as the efficient frontier.

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.

High-beta stocks are those with a beta greater than 1, implying that they show a great degree of price movement – upward or downward. They are therefore high-risk investments with high volatility.

A high beta index refers to a market index that is made up of stocks with higher-than-average volatility as compared to the overall stock market. Some investors aim to maximize returns on investment by investing in high beta stocks, especially during periods when the overall stock market is extremely bullish.

If its beta were less than 1, it would be expected to be less volatile than the index — smaller increases and decreases. So a stock with a beta of 0.7 would rise by 0.7% on a day that the S&P 500 rose 1%, and would fall by 0.7% on a day that the S&P 500 fell 1%.

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.

Answer and Explanation:

The market portfolio is assumed to have a beta of 1.0. A stock that moves less than the market will have a beta of < 1, and a stock that moves more than the market will have a beta of > 1. A stock that has a beta of 2.0 can be viewed as twice as risky, or volatile, than the market portfolio.