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The conditional expected return varies through time as a function of current market information. The return on an investment as estimated by an asset pricing model. It is calculated by taking the average of the probability distribution of all possible returns. The expected return is calculated as: It is important to note that there is no guarantee that the expected rate of return and the actual return will be the same.

The expected return is used to figure the taxable portion of pension that is taxed under the general rule. For a lifetime pension, it is computed by multiplying the annual pension by the applicable expected life multiple from government actuarial tables.

References in periodicals archive? Substituting 4 into 3 , we have the portfolio's expected return , [r'. Solutions to the portfolio choice problem with VaR objective functions. How does this expected return compare with the CRSP indexes for the same period? Returns to investors in stocks in new industries. Investment timing for dynamic business expansion.

In order to derive the expected return on the tax shield for this firm, let us start from the formula for [VTS. A general formula for the WACC: This variation in expected returns across stocks would not cause any trouble for traditional finance theory, if the characteristics associated with high average returns were also associated with large market betas.

The current treatment of return on assets under SFAS 87 is essentially an averaging process; periodic pension expense is a function of the long-term expected return on pension plan assets. Because this higher return is theoretically possible merely by taking a leveraged position in the broad market to double the beta so it is exactly 2.

If one of the managers' portfolios has an average beta of 3. Whether investors can expect the second manager to duplicate that performance in future periods is of course a different question. The x -axis represents the risk beta , and the y -axis represents the expected return. The market risk premium is determined from the slope of the SML.

The security market line can be regarded as representing a single-factor model of the asset price, where beta is exposure to changes in value of the market. The equation of the SML, giving the expected value of the return on asset i , is thus:. It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued because the investor can expect a greater return for the inherent risk.

A security plotted below the SML is overvalued because the investor would be accepting a lower return for the amount of risk assumed. The benchmark is often chosen to be similar to the assets chosen by the investor. In practice a standard index is used. The choice of the index need not reflect the portfolio under question; e. The restriction to stocks as a benchmark is somewhat arbitrary. A model portfolio may be stocks plus bonds. Sometimes the market is defined as "all investable assets" see Roll's critique ; unfortunately, this includes lots of things for which returns may be hard to measure.

A stock whose returns vary more than the market's returns over time can have a beta whose absolute value is greater than 1. A stock whose returns vary less than the market's returns has a beta with an absolute value less than 1. However, because beta also depends on the correlation of returns, there can be considerable variance about that average; the higher the correlation, the less variance; the lower the correlation, the higher the variance.

Beta can also be negative, meaning the stock's returns tend to move in the opposite direction of the market's returns. Higher-beta stocks tend to be more volatile and therefore riskier, but provide the potential for higher returns. Lower-beta stocks pose less risk but generally offer lower returns. Some have challenged this idea, claiming that the data show little relation between beta and potential reward, or even that lower-beta stocks are both less risky and more profitable contradicting CAPM.

Suppose an investor has all his money in an asset class X and wishes to move a small amount to an asset class Y. For example, X could be U. Then the new portfolio, Z, can be expressed symbolically. This assumes that variance is an accurate measure of risk, which is usually good. However, the beta does need to be computed with respect to what the investor currently owns.

Academic theory claims that higher-risk investments should have higher returns over the long-term. Wall Street has a saying that "higher return requires higher risk", not that a risky investment will automatically do better.

Some things may just be poor investments e. Further, highly rational investors should consider correlated volatility beta instead of simple volatility sigma. Theoretically, a negative beta equity is possible; for example, an inverse ETF should have negative beta to the relevant index.

Also, a short position should have opposite beta. This expected return on equity, or equivalently, a firm's cost of equity , can be estimated using the capital asset pricing model CAPM. An indication of the systematic riskiness attaching to the returns on ordinary shares. It equates to the asset Beta for an ungeared firm, or is adjusted upwards to reflect the extra riskiness of shares in a geared firm.

The arbitrage pricing theory APT has multiple betas in its model. Each risk factor has a corresponding beta indicating the responsiveness of the asset being priced to that risk factor. Multiple-factor models contradict CAPM by claiming that some other factors can influence return, therefore one may find two stocks or funds with equal beta, but one may be a better investment. To estimate beta, one needs a list of returns for the asset and returns for the index; these returns can be daily, weekly or any period.

Then one uses standard formulas from linear regression. The slope of the fitted line from the linear least-squares calculation is the estimated Beta. The y -intercept is the alpha. Myron Scholes and Joseph Williams provided a model for estimating betas from nonsynchronous data. Beta specifically gives the volatility ratio multiplied by the correlation of the plotted data.

To take an extreme example, something may have a beta of zero even though it is highly volatile, provided it is uncorrelated with the market. The relative volatility ratio described above is actually known as Total Beta at least by appraisers who practice business valuation. Total beta is equal to the identity: Total beta captures the security's risk as a stand-alone asset because the correlation coefficient, R, has been removed from beta , rather than part of a well-diversified portfolio.

Because appraisers frequently value closely held companies as stand-alone assets, total beta is gaining acceptance in the business valuation industry.

Appraisers can now use total beta in the following equation: Some interpretations of beta are explained in the following table: It measures the part of the asset's statistical variance that cannot be removed by the diversification provided by the portfolio of many risky assets, because of the correlation of its returns with the returns of the other assets that are in the portfolio.

Beta can be estimated for individual companies using regression analysis against a stock market index. An alternative to standard beta is downside beta. Beta is always measured in respect to some benchmark. Therefore, an asset may have different betas depending on which benchmark is used.

Just a number is useless if the benchmark is not known. Seth Klarman of the Baupost group wrote in Margin of Safety: Beta views risk solely from the perspective of market prices, failing to take into consideration specific business fundamentals or economic developments. The price level is also ignored, as if IBM selling at 50 dollars per share would not be a lower-risk investment than the same IBM at dollars per share.

Beta fails to allow for the influence that investors themselves can exert on the riskiness of their holdings through such efforts as proxy contests , shareholder resolutions, communications with management, or the ultimate purchase of sufficient stock to gain corporate control and with it direct access to underlying value.

Beta also assumes that the upside potential and downside risk of any investment are essentially equal, being simply a function of that investment's volatility compared with that of the market as a whole. This too is inconsistent with the world as we know it. The reality is that past security price volatility does not reliably predict future investment performance or even future volatility and therefore is a poor measure of risk.

At the industry level, beta tends to underestimate downside beta two-thirds of the time resulting in value overestimation and overestimate upside beta one-third of the time resulting in value underestimation. Another weakness of beta can be illustrated through an easy example by considering two hypothetical stocks, A and B.

The returns on A, B and the market follow the probability distribution below:. The table shows that stock A goes down half as much as the market when the market goes down and up twice as much as the market when the market goes up. Stock B, on the other hand, goes down twice as much as the market when the market goes down and up half as much as the market when the market goes up.

Most investors would label stock B as more risky. In fact, stock A has better return in every possible case.


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