# Thread: Dich Giup Minh : Stock Return Là Gì ? Định Nghĩa Market Return Là Gì

Michael Boyle is an experienced financial professional with more than 9 years working with financial planning, derivatives, equities, fixed income, project management, & analytics.

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## What Are Excess Returns?

Excess returns are returns achieved above sầu & beyond the return of a proxy. Excess returns will depkết thúc on a designated investment return comparison for analysis. Some of the most basic return comparisons include a riskless rate and benchmarks with similar levels of risk to the investment being analyzed.

## Understanding Excess Returns

Excess returns are an important metric that helps an investor to lớn gauge performance in comparison lớn other investment alternatives. In general, all investors hope for positive excess return because it provides an investor with more money than they could have achieved by investing elsewhere.

Excess return is identified by subtracting the return of one investment from the total return percentage achieved in another investment. When calculating excess return, multiple return measures can be used. Some investors may wish to lớn see excess return as the difference in their investment over a risk-free rate. Other times, excess return may be calculated in comparison lớn a closely comparable benchmark with similar risk and return characteristics. Using closely comparable benchmarks is a return calculation that results in an excess return measure known as alpha.

In general, return comparisons may be either positive sầu or negative. Positive sầu excess return shows that an investment outperformed its comparison, while a negative sầu difference in returns occurs when an investment underperforms. Investors should keep in mind that purely comparing investment returns to a benchmark provides an excess return that does not necessarily take inlớn consideration all of the potential trading costs of a comparable proxy. For example, using the S&Phường 500 as a benchmark provides an excess return calculation that does not typically take into consideration the actual costs required to lớn invest in all 500 stocks in the Index or management fees for investing in an S&Phường. 500 managed fund.

Excess returns are returns achieved above & beyond the return of a proxy. Excess returns will depkết thúc on a designated investment return comparison for analysis.The riskless rate & benchmarks with similar levels of risk to lớn the investment being analyzed are commonly used in calculating excess return.Altrộn is a type of excess return metric that focuses on performance return in excess of a closely comparable benchmark.Excess return is an important consideration when using modern portfolio theory which seeks to invest with an optimized portfolio.

## Riskless Rates

Riskless và low risk investments are often used by investors seeking khổng lồ preserve sầu capital for various goals. U.S. Treasuries are typically considered the most basic khung of riskless securities. Investors can buy U.S. Treasuries with maturities of one month, two months, three months, six months, one year, two years, three years, five years, seven years, 10-years, 20-years, & 30-years. Each maturity will have sầu a different expected return found along the U.S. Treasury yield curve sầu. Other types of low risk investments include certificates of deposits, money market accounts, và municipal bonds.

Investors can determine excess return levels based on comparisons to risk không tính phí securities. For example, if the one year Treasury has returned 2.0% and the giải pháp công nghệ stochồng Facebook has returned 15% then the excess return achieved for investing in Facebook is 13%.

## Altrộn

Oftentimes, an investor will want lớn look at a more closely comparable investment when determining excess return. That’s where alpha comes in. Altrộn is the result of a more narrowly focused calculation that includes only a benchmark with comparable risk và return characteristics to lớn an investment. Alpha is commonly calculated in investment fund management as the excess return a fund manager achieves over a fund’s stated benchmark. Broad stochồng return analysis may look at alpha calculations in comparison lớn the S&P 500 or other broad market Indexes lượt thích the Russell 3000. When analyzing specific sectors, investors will use benchmark indexes that include stocks in that sector. The Nasdaq 100 for example can be a good altrộn comparison for large cap công nghệ.

In general, active sầu fund managers seek lớn generate some altrộn for their clients in excess of a fund’s stated benchmark. Passive fund managers will seek to lớn match the holdings và return of an index.

Consider a large-cap U.S.mutual fundthat has the same cấp độ of risk as the S&Phường 500 index. If the fund generates a return of 12% in a year when the S&P.. 500 has only advanced 7%, the difference of 5% would be considered as thealphagenerated by thefund manager.

## Excess Return và Risk Concepts

As discussed, an investor has the opportunity to achieve sầu excess returns beyond a comparable proxy. However the amount of excess return is usually associated with risk. Investment theory has determined that the more risk an investor is willing to lớn take the greater their opportunity for higher returns. As such, there are several market metrics that help an investor khổng lồ underst& if the returns and excess returns they achieve are worthwhile.

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Beta is a risk metric quantified as a coefficient in regression analysis that provides the correlation of an individual investment to the market (usually the S&Phường. 500). A beta of one means that an investment will experience the same màn chơi of return volatility from systematic market moves as a market index. A beta above sầu one indicates that an investment will have sầu higher return volatility và therefore higher potential for gains or losses. A beta below one means an investment will have sầu less return volatility & therefore less movement from systematic market effects with less potential for gain but also less potential for loss.

Beta is an important metric used when generating an Efficient Frontier graph for the purposes of developing a Capital Allocation Line which defines an optimal portfolio. Asmix returns on an Efficient Frontier are calculated using the following Capital Asset Pricing Model:

Ra=Rrf+β×(Rm−Rrf)where:Ra=ExpectedreturnonasecurityRrf=Risk-freerateRm=Expectedreturnofthemarketβ=BetaofthesecurityRm−Rrf=Equitymarketpremiumeginaligned &R_a = R_rf + eta imes (R_m – R_rf) &extbfwhere: &R_a = extExpected return on a security &R_rf = extRisk-không lấy phí rate &R_m = extExpected return of the market &eta = extBeta of the security &R_m – R_rf = extEquity market premium endalignedRa=Rrf+β×(Rm−Rrf)where:Ra=ExpectedreturnonasecurityRrf=Risk-freerateRm=Expectedreturnofthemarketβ=BetaofthesecurityRm−Rrf=Equitymarketpremium

Beta can be a helpful indicator for investors when understanding their excess return levels. Treasury securities have a beta of approximately zero. This means that market changes will have sầu no effect on the return of a Treasury and the 2.0% earned from the one year Treasury in the example above is riskless. Facebook on the other h& has a beta of approximately 1.30 so systematic market moves that are positive sầu will lead to a higher return for Facebook than the S&P. 500 Index overall và vice versa.

In active sầu management, fund manager altrộn can be used as a metric for evaluating the performance of a manager overall. Some funds provide their managers a performance fee which offers extra incentive for fund managers khổng lồ exceed their benchmarks. In investments there is also a metric known as Jensen’s Alpha. Jensen’s Alpha seeks to lớn provide transparency around how much of a manager’s excess return was related to lớn risks beyond a fund’s benchmark.

Jensen’sAlpha=Ri−(Rf+β(Rm−Rf))where:Ri=RealizedreturnoftheportfolioorinvestmentRf=Risk-freerateofreturnforthetimeperiodβ=BetaoftheportfolioofinvestmentwithrespecttothechosenmarketindexRm=Realizedreturnoftheappropriatemarketindexeginaligned &extJensen”s Alpha = R_i – (R_f + eta (R_m – R_f)) &extbfwhere: &R_i = extRealized return of the portfolio or investment &R_f = extRisk-miễn phí rate of return for the time period &eta = extBeta of the portfolio of investment &extwith respect khổng lồ the chosen market index &R_m = extRealized return of the appropriate market index endalignedJensen’sAlpha=Ri−(Rf+β(Rm−Rf))where:Ri=RealizedreturnoftheportfolioorinvestmentRf=Risk-freerateofreturnforthetimeperiodβ=BetaoftheportfolioofinvestmentwithrespecttothechosenmarketindexRm=Realizedreturnoftheappropriatemarketindex

A Jensen’s Alpha of zero means that the alpha achieved exactly compensated the investor for the additional risk taken on in the portfolio. A positive sầu Jensen’s Alpha means the fund manager overcompensated its investors for the risk and a negative Jensen’s Alpha would be the opposite.

In fund management, the Sharpe Ratio is another metric that helps an investor understvà their excess return in terms of risk.

SharpeRatio=Rp−RfPortfolioStandardDeviationwhere:Rp=PortfolioreturnRf=Risklessrateeginaligned &extSharpe Ratio = frac R_p – R_f extPortfolio Standard Deviation &extbfwhere: &R_p = extPortfolio return &R_f = extRiskless rate endalignedSharpeRatio=PortfolioStandardDeviationRp−Rfwhere:Rp=PortfolioreturnRf=Risklessrate

The higher the Sharpe Ratio of an investment the more an investor is being compensated per unit of risk. Investors can compare Sharpe Rattiện ích ios of investments with equal returns to underst& where excess return is more prudently being achieved. For example, two funds have sầu a one year return of 15% with a Sharpe Ratio of 2 vs. 1. The fund with a Sharpe Ratio of 2 is producing more return per one unit of risk.

## Excess Return of Optimized Portfolios

Critics of mutual funds & other actively managed portfolgame ios contend that it is next khổng lồ impossible to lớn generate altrộn on a consistent basis over the long term, as a result investors are then theoretically better off investing in stock indexes or optimized portfolios that provide them with a cấp độ of expected return & a level of excess return over the risk không lấy phí rate. This helps to lớn make the case for investing in a diversified portfolio that is risk optimized to achieve the most efficient màn chơi of excess return over the risk không tính tiền rate based on risk tolerance.

This is where the Efficient Frontier và Capital Market Line can come in. The Efficient Frontier plots a frontier of returns & risk levels for a combination of asphối points generated by the Capital Asphối Pricing Model. An Efficient Frontier considers data points for every available investment an investor may wish to consider investing in. Once an efficient frontier is graphed, the capital market line is drawn to touch the efficient frontier at its most optimal point.

With this portfolio optimization Mã Sản Phẩm developed by financial academics, an investor can choose a point along the capital allocation line for which to invest based on their risk preference. An investor with zero risk preference would invest 100% in risk không tính tiền securities. The highest cấp độ of risk would invest 100% in the combination of assets suggested at the intersect point. Investing 100% in the market portfolio would provide a designated màn chơi of expected return with excess return serving as the difference from the risk-không tính phí rate.

As illustrated from the Capital Asmix Pricing Model, Efficient Frontier, and Capital Allocation Line, an investor can choose the cấp độ of excess return they wish to achieve sầu above sầu the risk không tính tiền rate based on the amount of risk they wish lớn take on.

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