## What Are Excess Returns?

Excess returns are returns achieved above sầu and beyond the return of a proxy. Excess returns will depend 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 lớn the investment being analyzed.

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## Understanding Excess Returns

Excess returns are an important metric that helps an investor to gauge performance in comparison khổng lồ 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 khổng lồ see excess return as the difference in their investment over a risk-miễn 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. Positive excess return shows that an investment outperformed its comparison, while a negative 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 inkhổng lồ 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 lớn consideration the actual costs required 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 sầu & beyond the return of a proxy. Excess returns will depover 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 khổng lồ invest with an optimized portfolio.## Riskless Rates

Riskless và low risk investments are often used by investors seeking to preserve sầu capital for various goals. U.S. Treasuries are typically considered the most basic size 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, và municipal bonds.

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

## Alpha

Oftentimes, an investor will want lớn 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 to 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 stock return analysis may look at altrộn calculations in comparison to the S&Phường 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 giải pháp công nghệ.

In general, active sầu fund managers seek khổng lồ generate some altrộn for their clients in excess of a fund’s stated benchmark. Passive fund managers will seek khổng lồ match the holdings & 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&Phường. 500 has only advanced 7%, the difference of 5% would be considered as thealphagenerated by thefund manager.

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## Excess Return and Risk Concepts

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 level 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 and 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 Asphối 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 sầu 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 sầu is riskless. Facebook on the other hand has a beta of approximately 1.30 so systematic market moves that are positive sầu will lead lớn a higher return for Facebook than the S&Phường 500 Index overall and 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 Alpha. Jensen’s Altrộn seeks to 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 lấy 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 Altrộn of zero means that the altrộn achieved exactly compensated the investor for the additional risk taken on in the portfolio. A positive Jensen’s Alpha 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 underst& 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 khổng lồ understvà where excess return is more prudently being achieved. For example, two funds have 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 và other actively managed portfolios contend that it is next khổng lồ impossible khổng lồ generate altrộn on a consistent basis over the long term, as a result investors are then theoretically better off investing in stoông chồng indexes or optimized portfolquả táo that provide them with a cấp độ of expected return & a cấp độ of excess return over the risk không tính phí rate. This helps khổng lồ make the case for investing in a diversified portfolio that is risk optimized khổng lồ achieve the most efficient level of excess return over the risk không tính tiền rate based on risk tolerance.

This is where the Efficient Frontier & Capital Market Line can come in. The Efficient Frontier plots a frontier of returns and risk levels for a combination of asphối points generated by the Capital Asset 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 khổng lồ touch the efficient frontier at its most optimal point.