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# beta of a risk free asset

A beta of 2 would be twice as risky as the market. In practice, risk is synonymous with volatility. A stock with a beta larger than the market beta of 1 will generally see a greater increase than the market when the market is up and see a greater decrease than the market when the market is down. So, the variance and standard deviation of each stock is:. Calculating Portfolio Betas. You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.

The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market, it must have the same beta as the market. Since the beta of the market is one, we know the beta of our portfolio is one.

We also need to remember that the beta of the risk-free asset is zero. It has to be zero since the asset has no risk. Post as a guest Name. Email Required, but never shown. Featured on Meta. The new moderator agreement is now live for moderators to accept across the…. However, according to the capital asset pricing model , stock A and B would have the same beta, meaning that theoretically, investors would require the same rate of return for both stocks. Of course it is entirely expected that this example could break the CAPM as the CAPM relies on certain assumptions one of the most central being the nonexistence of arbitrage, However, in this example buying stock A and selling stock B is an example of an arbitrage as stock A is worth more in every scenario.

This is an illustration of how using standard beta might mislead investors. The dual-beta model, in contrast, takes into account this issue and differentiates downside beta from upside beta , or downside risk from upside risk , and thus allows investors to make better informed investing decisions.

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May Main article: Security market line. Portfolio Theory and Capital Markets. McGraw-Hill Trade. Portfolio Selection. Basic Books. European Journal of Operational Research. This difference is called the equity risk premium, since it represents the additional return required for investing in equity shares on the capital market as a whole rather than investing in risk-free assets.

In the short term, share prices can fall as well as increase, so the average capital market return can be negative rather than positive. To smooth out short-term changes in the equity risk premium, a time-smoothed moving average analysis can be carried out over longer periods of time, often several decades. If a share has a beta value of 0.

Beta values are found by using regression analysis to compare the returns on a share with the returns on the capital market. An increase in the risk-free rate also increases the cost of the capital used in the investment and could make the stock look overvalued.

The market portfolio that is used to find the market risk premium is only a theoretical value and is not an asset that can be purchased or invested in as an alternative to the stock. The most serious critique of the CAPM is the assumption that future cash flows can be estimated for the discounting process.

If an investor could estimate the future return of a stock with a high level of accuracy, the CAPM would not be necessary. Using the CAPM to build a portfolio is supposed to help an investor manage their risk. The graph shows how greater expected returns y-axis require greater expected risk x-axis.

Modern Portfolio Theory suggests that starting with the risk-free rate, the expected return of a portfolio increases as the risk increases. Any portfolio that fits on the Capital Market Line CML is better than any possible portfolio to the right of that line, but at some point, a theoretical portfolio can be constructed on the CML with the best return for the amount of risk being taken.

As of yet, however, none of these more sophisticated models has proved clearly superior to CAPM. This continues to be a fertile area of research, focused primarily on investment management applications. In corporate finance applications of CAPM, several potential sources of error exist.

First, the simple model may be an inadequate description of the behavior of financial markets. In attempts to improve its realism, researchers have developed a variety of extensions of the model.

A second problem is that betas are unstable through time. This fact creates difficulties when betas estimated from historical data are used to calculate costs of equity in evaluating future cash flows. Betas should change as both company fundamentals and capital structures change. In addition, betas estimated from past data are subject to statistical estimation error.

Several techniques are available to help deal with these sources of instability. The estimates of the future risk-free rate and the expected return on the market are also subject to error. Here too, research has focused on developing techniques to reduce the potential error associated with these inputs to the SML. A final set of problems is unique to corporate finance applications of CAPM. There are practical and theoretical problems associated with employing CAPM, or any financial market model, in capital budgeting decisions involving real assets.

These difficulties continue to be a fertile area of research. The deficiencies of CAPM may seem severe. They must be judged, however, relative to other approaches for estimating the cost of equity capital. The most commonly used of these is a simple discounted cash flow DCF technique, which is known as the dividend growth model or the Gordon-Shapiro model.

With the assumption that future dividends per share are expected to grow at a constant rate and that this growth rate will persist forever, the general present value formula collapses to a simple expression. If the market is pricing the stock in this manner, we can infer the cost of equity impounded in the stock price.

Solving for the cost of equity yields:. The cost of equity implied by the current stock price and the assumptions of the model is simply the dividend yield plus the constant growth rate. One is the assumption of a constant, perpetual growth rate in dividends per share. If this is not the case, the equation is not valid. Zero-beta portfolios have no market exposure so are unlikely to attract investor interest in bull markets, since such portfolios would underperform diversified market portfolios.

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Related Terms Beta Beta is a measure of the volatility, or systematic risk, of a security or portfolio in comparison to the market as a whole. It is used in the capital asset pricing model.

Inside the Treynor Ratio The Treynor ratio, also known as the reward-to-volatility ratio, is a performance metric for determining how much excess return was generated for each unit of risk taken on by a portfolio.