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## What Are Excess Returns?

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

## Understanding Excess Returns

Excess returns are an important metric that helps an investor to lớn gauge performance in comparison to lớn 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 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 tính phí rate. Other times, excess return may be calculated in comparison lớn 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 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 khổng lồ 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&P 500 as a benchmark provides an excess return calculation that does not typically take inlớn 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 sầu and beyond the return of a proxy. Excess returns will depkết thúc on a designated investment return comparison for analysis.The riskless rate and benchmarks with similar levels of risk to 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 and low risk investments are often used by investors seeking khổng lồ preserve capital for various goals. U.S. Treasuries are typically considered the most basic form 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, & 30-years. Each maturity will have 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, and municipal bonds.

Investors can determine excess return levels based on comparisons lớn risk không tính phí securities. For example, if the one year Treasury has returned 2.0% và 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 to lớn look at a more closely comparable investment when determining excess return. That’s where altrộn comes in. Altrộn 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 altrộn calculations in comparison lớn 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 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 sầu fund managers will seek khổng lồ match the holdings and return of an index.

Consider a large-cap U.S.mutual fundthat has the same màn chơi 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 and Risk Concepts

As discussed, an investor has the opportunity khổng lồ 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 lớn take the greater their opportunity for higher returns. As such, there are several market metrics that help an investor khổng lồ understand if the returns and excess returns they achieve sầu 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 level of return volatility from systematic market moves as a market index. A beta above one indicates that an investment will have higher return volatility & therefore higher potential for gains or losses. A beta below one means an investment will have 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-free 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 và the 2.0% earned from the one year Treasury in the example above is riskless. Facebook on the other hand 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&Phường 500 Index overall & vice versa.

In active management, fund manager alpha 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 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 to 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 Altrộn of zero means that the altrộn achieved exactly compensated the investor for the additional risk taken on in the portfolio. A positive sầu Jensen’s Altrộn means the fund manager overcompensated its investors for the risk & a negative Jensen’s Altrộn 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 khổng lồ understand 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 Portfoltiện ích ios

Critics of mutual funds & other actively managed portfolios contend that it is next lớn impossible lớn generate altrộn on a consistent basis over the long term, as a result investors are then theoretically better off investing in stoông xã indexes or optimized portfoltiện ích ios that provide them with a cấp độ of expected return and a level of excess return over the risk không tính tiền rate. This helps lớn make the case for investing in a diversified portfolio that is risk optimized to lớn achieve the most efficient level of excess return over the risk miễn phí 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 & 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 lớn consider investing in. Once an efficient frontier is graphed, the capital market line is drawn lớn touch the efficient frontier at its most optimal point.

With this portfolio optimization Model 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 tính tiền 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 phí rate.

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

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