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

## What Are Excess Returns?

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. 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 gauge performance in comparison to other investment alternatives. In general, all investors hope for positive sầu excess return because it provides an investor with more money than they could have sầu 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-không lấy phí rate. Other times, excess return may be calculated in comparison khổng lồ a closely comparable benchmark with similar risk & return characteristics. Using closely comparable benchmarks is a return calculation that results in an excess return measure known as altrộn.

In general, return comparisons may be either positive or negative sầu. Positive 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 khổng lồ a benchmark provides an excess return that does not necessarily take into consideration all of the potential trading costs of a comparable proxy. For example, using the S&P 500 as a benchmark provides an excess return calculation that does not typically take inlớn consideration the actual costs required to invest in all 500 stocks in the Index or management fees for investing in an S&P. 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 lớn the investment being analyzed are commonly used in calculating excess return.Alpha 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 lớn invest with an optimized portfolio.

## Riskless Rates

Riskless & low risk investments are often used by investors seeking to lớn 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 sầu years, seven years, 10-years, 20-years, and 30-years. Each maturity will have sầu a different expected return found along the U.S. Treasury yield curve. Other types of low risk investments include certificates of deposits, money market accounts, & municipal bonds.

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

## Alpha

Oftentimes, an investor will want khổng lồ look at a more closely comparable investment when determining excess return. That’s where alpha comes in. Alpha is the result of a more narrowly focused calculation that includes only a benchmark with comparable risk and return characteristics 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 to the S&Phường 500 or other broad market Indexes like 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 alpha comparison for large cap technology.

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

Consider a large-cap U.S.mutual fundthat has the same level of risk as the S&P 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.

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## Excess Return và Risk Concepts

As discussed, an investor has the opportunity lớn achieve 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 take the greater their opportunity for higher returns. As such, there are several market metrics that help an investor khổng lồ understvà if the returns và excess returns they achieve sầu are worthwhile.

Beta is a risk metric quantified as a coefficient in regression analysis that provides the correlation of an individual investment to lớn the market (usually the S&Phường 500). A beta of one means that an investment will experience the same cấp độ of return volatility from systematic market moves as a market index. A beta above sầu one indicates that an investment will have higher return volatility và therefore higher potential for gains or losses. A beta below one means an investment will have 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 Asmix 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 tính 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 & the 2.0% earned from the one year Treasury in the example above is riskless. Facebook on the other hvà has a beta of approximately 1.30 so systematic market moves that are positive sầu will lead to lớn a higher return for Facebook than the S&Phường 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 sầu for fund managers lớn exceed their benchmarks. In investments there is also a metric known as Jensen’s Altrộn. Jensen’s Altrộn seeks to lớn provide transparency around how much of a manager’s excess return was related khổng lồ 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-không tính tiền rate of return for the time period \ &eta = extBeta of the portfolio of investment \ & extwith respect lớn 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 Jensen’s Altrộn means the fund manager overcompensated its investors for the risk & a negative Jensen’s Alpha would be the opposite.

In fund management, the Sharpe Ratio is another metric that helps an investor understand 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 Ratquả táo of investments with equal returns khổng lồ understvà 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 Portfolquả táo

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

This is where the Efficient Frontier and Capital Market Line can come in. The Efficient Frontier plots a frontier of returns và risk levels for a combination of asmix points generated by the Capital Asset Pricing Model. An Efficient Frontier considers data points for every available investment an investor may wish khổng lồ 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 lớn invest based on their risk preference. An investor with zero risk preference would invest 100% in risk không lấy phí securities. The highest màn chơi 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 level of expected return with excess return serving as the difference from the risk-không tính tiền rate.

As illustrated from the Capital Asset Pricing Model, Efficient Frontier, và Capital Allocation Line, an investor can choose the cấp độ of excess return they wish lớn achieve sầu above sầu the risk không lấy phí rate based on the amount of risk they wish khổng lồ take on.

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