# Performance Evaluation And Risk Management

Portfolio performance ratios and evaluation should appear as the main factor of the investment decision procedure. Such implements equip the investors with the required data helping them to analyse how efficiently their money has been or might be invested. Performance analysis demonstrates that portfolio surpluses are the only part of the whole procedure. It is also highly significant to analyse risk-adapted surpluses, which actually allow observing the whole investment procedure. The current paper will analyse the process of performance evaluation, the Sharpe ratio, the Treynor ratio, the Jensen’s Alpha ratio, M² measure, and investment risk management.

## The Performance Evaluation

Fiscal performance evaluation is believed to be the most unbiased method of analysing the monetary and fiscal performance of any firm (Buser 2015). The portfolio execution analysis and estimation incorporates the definition of how a managed portfolio has executed on a contrary to a particular comparison benchmark (Kang et al. 2011). In addition, the specific benchmark portfolio is supposed to demonstrate a realizable investment disjunctive to the managed portfolio, which has to be analyzed and estimated. Thus, when the main purpose regards the evaluation of the investment capacity of the manager or company, then the benchmark is supposed to demonstrate an investment disjunctive, which is reciprocal to the selected managed portfolio, taking into account all return-connected facets (Kang & Lee 2013). In addition, the benchmark portfolio should not repulse the investment capability of the selected manager or managed firm (Chen, Simai & Shuzhong 2011).Portfolio performance evaluation substantially consists of two functions, meaning the performance evaluation and performance measuring. Performance measuring regards the reckoning function, which estimates the surplus obtained on a portfolio within the holding period also known as investment period (Kang et al. 2011). On the other hand, performance evaluation regards such items as whether the effectiveness and execution was higher-ranking or lower-ranking, whether the efficiency resulted from capabilities or success, etc. The capability of the investor relies on the attenuation of the latest evolvements, occurring in the market. The performance relies on the investments timing and prevailing investment analysis selection capacities as well (Buser 2015). Generally speaking, all performance evaluation applications can be subdivided into two broad categories, meaning conventional and risk-adapted methods (Chen, Simai & Shuzhong 2011). The majority of commonly utilized conventional methods incorporate benchmark juxtaposition and style confronting. The risk-adapted methods accommodate returns and surpluses so that to consider discrepancies in hazard levels between the individual managed portfolio and the selected benchmark portfolio (Chen, Simai & Shuzhong 2011). The major objective of the present fiscal performance evaluation theory regards the return maximizing combined with return risk minimization. Therefore, the performance evaluation research studies attempt to elaborate a compound guide to evaluate risk-based return (Chen, Simai & Shuzhong 2011). The main methods of this category are the Sharpe ratio, Treynor measure, Jensen’s alpha ratio, M2 measure etc (Kang et al. 2011). Generally speaking, the risk-adapted methods are regarded to be preferential in regards with the conventional means.

### The Sharpe Ratio

The Sharpe Ratio is known to be an implement for analysing hazard-adjusted restitution, which appears to be an industrial norm for such estimations (Deborah 2011). The ratio has been evolved by Nobel prizewinner William F. Sharpe. William F. Sharpe initially developed this ratio as a sole-period predicting implement and denominating the ratio as the recompense-to-variability ratio (Deborah 2011). This ratio has been created as an ‘ex ante’ or progressive ratio used to define what recompense an investor might anticipate for depositing in a hazardous asset in comparison with the hazard-free asset (Chen, Simai & Shuzhong 2011). The Sharpe ratio is known to be the average return obtained in surplus of the hazard-free ratio per portion of unpredictability or general hazard (Kang et al. 2011). Deduction of the hazard-free ratio is taken from the average surplus, meaning that the performance connected with hazard-taking operations might be excluded (Chen, Simai & Shuzhong 2011). The major capacity of this analysis is related to the portfolio incorporated in “zero hazard” investment, for instance the acquirement of U.S. Treasury bills, in case of which the anticipated surplus would be the hazard-free ratio, meaning that a Sharpe ratio will be precisely zero (Steinnki & Mohammad 2015). Thus, the facts demonstrate that the higher the weight of the Sharpe ratio is, the more appealing the hazard-adjusted surplus would be (Deborah 2011).

Therefore, it becomes obvious that the Sharpe ratio can be regarded as the major risk versus surplus calculation measure (Kang & Lee 2013). For instance, the firm expects that their stock portfolio will reimburse 12 percent during the following year. Thus, when the surplus on risk-free ratio is, for instance, 5 percent, while the company’s portfolio demonstrates a 0.06 normal deviation, the formula of the Sharpe ratio for the company’s portfolio will look as follows: (0.12 - 0.05)/0.06 = 1.17. The formula demonstrates that for each point of surplus, the company is actually taking 1.17 “portions” of financial risks. The Share ratio can be analysed in a different manner. Thus, for instance, when some portfolio “X” creates a 10 percent surplus demonstrating a 1.25 Sharpe ratio and at the same time when another portfolio “Y” has 10 percent surplus equalling to a 1.00 Sharpe ratio, it means that portfolio “X” can be regarded as the better one due to the fact that it obtains analogous surplus depicting lower risk level.

The Sharpe ratio can be easily analysed through the vivid demonstration of its utilisation. Thus, when a company demonstrates a normal deviation of 18 percent, for example, over a 10-year period, the ratio can be easily calculated for the following managers:

**Table 1: Sharpe Ratio Calculation**

Manager |
Annual Surplus |
Portfolio Normal Deviation |
Ratio |

Manager X |
14% |
0.11 |
(0.14-.05)/.11 = .818 |

Manager Y |
17% |
0.20 |
(.17-.05)/.20 = .600 |

Manager Z |
19% |
0.27 |
(.19-.05)/.27 = .519 |

Thus, the above table vividly demonstrates that the best portfolio is not necessarily the portfolio demonstrating the greatest surplus. In fact, the table shows that the best portfolio is the one that demonstrates the most. It is the one with the most high-level hazard-adjusted surplus (meaning the results obtained in the case of manager X).This type of analysis is highly important as it vividly demonstrates that the greater the level of the Sharpe ratio is, the higher the level of surplus will be obtained by the investor per a portion of risk. On the other hand, the lower the Sharpe ratio is, the higher level of hazard the investor is supposed to undertake in order to obtain extra surpluses (see figure 1, Appendix A) (Kang et al. 2011). Therefore, the Sharpe ratio eventually “equalises the playground” among portfolios by demonstrating which of them are faced with superfluous hazards (Buser 2015). Nevertheless, despite the fact that the Sharpe ratio depends on the historical surplus, the major problem of the ration refers to the fact that illiquid investments lower a normal deviation of the portfolio due to the fact that such investments happen to be less unstable (Deborah 2011). Moreover, this ratio can also appear to be distorted when the investments do not demonstrate a standard distribution of surpluses.

### The Treynor Ratio

A ration evolved by Jack Treynor is known to measure surpluses acquired in surfeit of the costs, which could have been obtained in the case of a risk-free investment per each portion of market hazard (Steinnki & Mohammad 2015). This ratio can be calculated according to the following formula: “(Average Return of the Portfolio - Average Return of the Risk-Free Rate)/Beta of the Portfolio” (Chen, Simai & Shuzhong 2011). This formula practically means that the Treynor ratio can be regarded as a hazard-adjusted calculation of surplus grounded on systematic risk (Kang & Lee 2013). This ratio is known to be similar to the Sharpe ratio (Deborah 2011). Nevertheless, the major difference between these two ratios lies in the fact that the Treynor ratio utilises “beta” in the form of the unpredictability estimation (Steinnki & Mohammad 2015). Treynor ratio is also regarded as a ‘recompense-to-volatility ratio’. The ratio is utilised to standardise the hazard premium also known as the anticipated surplus over the hazard-free ratio, which is performed by separating the premium with the help of the portfolio beta (Deborah 2011). This indicates that when the firm has the premium, which is free from the portfolio hazard, the effectiveness and execution of two different portfolios can be easily compared regardless of the fact that they demonstrate discrepant betas (Chen, Simai & Shuzhong 2011). This fact makes Treynor’s ratio highly important as numerous portfolios might provide extra surplus and at the same time be more risky and demonstrate a greater beta.

In order to better understand the way the Treynor ratio works, it is important to observe the previous case and suggest that the 10-year annual surplus of a company accounts for 10 percent, while at the same time the medium yearly surplus on good proxies for the hazard-free ratio accounts for 5 percent. This ratio is also utilised to analyse three different portfolio managers.

**Table 2: Treynor Ratio Calculation**

Managers |
Average Yearly Surplus |
Beta |
Ratio |

Manager X |
10% |
0.90 |
(.10-.05)/0.90 = .056 |

Manager Y |
14% |
1.03 |
(.14-.05)/1.03 = .087 |

Manager Z |
15% |
1.20 |
(.15-.05)/1.20 = .083 |

Thus, the above table vividly demonstrates that the greater the Treynor ratio is, the better the overall manager’s portfolio would be. The ratio is highly beneficial, as when the portfolio or portfolio manager is analysed alone, the analysis might show that manager Z has obtained the best results. Nevertheless, when the risks of each manager, which have been taken in order to obtain the necessary surpluses, are analysed, it becomes obvious that manager Y has obtained a better result.

When the Sharpe and Treynor ratios are compared, it becomes obvious that the first ratio estimates the portfolio manager on the ground of both ratio of surplus and ratio of divergence due to the fact that the ratio refers to the general portfolio hazard as being estimated by normal deviation of its denominator (Chen, Simai & Shuzhong 2011; Grace et al. 2014). Thus, the Sharpe ratio is more relevant for all diversiform portfolios, as it takes into account the hazards of the portfolio more meticulously (Deborah 2011). On the other hand, the Treynor ratio is more relevant for well-defined portfolios (Chen, Simai & Shuzhong 2011). Moreover, the Sharpe ratio is utilised to estimate historical effectiveness, while Treynor ratio can be regarded as a more progressive and forward-looking effectiveness analysis (Chen, Simai & Shuzhong 2011). Therefore, it becomes obvious that these two effectiveness and performance analysis implements are used and operate in a highly discrepant manner (Deborah 2011).

### Jensen’s Alpha Ratio

Jensen’s Alpha Ratio is known to be a hazard-adjusted performance estimation, which demonstrates the medium surplus on a portfolio over and above of the predicted measures presented by the capital asset pricing model (also known as CAPM) (Bodnar et al. 2014). The ratio takes into account the beta of the portfolio and the medium market surplus. The latter are known to be the alpha of the portfolio (Grace et al. 2014). This ratio has been proposed by Jensen and is known to be the most widely used portfolio effectiveness and execution estimation in the financial sphere. Nevertheless, the facts demonstrate that this ratio cannot be regarded as a relevant performance analysis of the market timers (Buser 2015). The statistics depicts that the ratio frequently appoints negative figures according to the felicitous market timers, changing the second stipulation for an ideal performance analysis (Chen, Simai & Shuzhong 2011). The ratio estimates the extra surplus, which a portfolio creates over its anticipated surplus, meaning the alpha of a portfolio (Kang & Lee 2013). The ratio analyses how much of the portfolio’s rate of surplus is yielded to the manager’s capability to provide above-medium surpluses, which should be adapted to the overall market hazard (Steinnki & Mohammad 2015; Grace et al. 2014). Thus, the facts demonstrate that the greater the ratio is, the better the risk-adapted surpluses are (see fig. 2, Appendix B). Therefore, a portfolio characterised by constant and systematic positive extra surplus will have a positive alpha, while at the same time a portfolio featured by constantly negative extra surplus will demonstrates a negative alpha.

The formula for calculating Jensen’s Alpha ratio looks as follows: “Jensen’s Alpha = Portfolio Return – Benchmark Portfolio Return” (Chen, Simai & Shuzhong 2011). This formula demonstrates that it is highly important to know Benchmark Return (CAPM), which can be calculated as “Risk-Free Rate of Return + Beta (Return of Market – Risk-Free Rate of Return)” (Grace et al. 2014).

In order to understand how the Jensen’s Alpha ratio works, it is important to use the same firm with hazard-free ratio of 5 percent and a market surplus of 10 percent. This will help to understand the alpha of all previous funds.

**Table 3: Jensen’s Alpha Ratio Calculation**

Manager |
Average Annual Surplus |
Beta |
Expected Surplus |
Alpha |

Manager X |
11% |
0.90 |
.05 + 0.90 (.10-.05) = .0950 or 9.5% surplus |
11%- 9.5% = 1.5% |

Manager Y |
15% |
1.10 |
.05 + 1.10 (.10-.05) =.1050 or 10.50% surplus |
15%- 10.5% = 4.5% |

Manager Z |
15% |
1.20 |
.05 + 1.20 (.10-.05) = .1100 or 11% surplus |
15%- 11% = 4.0% |

The table vividly demonstrates that manager Y performed in the best manner, as even despite the fact that manager Z depicted the analogous yearly surplus, it had been anticipated that the manager Y would reveal a lower level of surplus, as this manager’s beta of portfolio had been essentially lower compared to the manager’s Z portfolio.

Nevertheless, it is quite obvious that both rates of surplus and hazard for portfolio will appear different with time (Kang & Lee 2013). This information presupposes that the Jensen ratio requires the utilisation of a discrepant hazard-free ratio of surplus for each time period analysed (Kang et al. 2011). Therefore, if to estimate the effectiveness of a fund manager for a five-year period, there will be needed yearly intervals. It is also significant to analyse the fund’s yearly surpluses minus the hazard-free surplus for each year and connect it to the yearly surplus on the market portfolio minus the analogous hazard-free ratio (Buser 2015). On the other hand, the Sharpe and Treynor ratios analyse medium surpluses for the whole period taking into account all factors of the formula, including the portfolio, market and hazard-free asset (Steinnki & Mohammad 2015). Similarly to the Treynor ratio, Jensen's ratio estimates hazard premiums according to beta (meaning systematic, undiversified hazard) and thus claims that the portfolio is already sufficiently diverged (Kang et al. 2011).

### M² Measure

M² analysis refers to estimations, which evaluate money supply, incorporating ‘near money’ (Rampini, Sufi, & Viswanathan 2014). The latter refers to retrenchment deposits, money market mutual funds and other time deposits, which are known to be less changeable and cannot be regarded as appropriate as exchange mediums, but they may be rapidly converted into cash or verification deposits (Deborah 2011). This ratio is known to be an improved variation of Sharpe ratio (Steinnki & Mohammad 2015, p. 8). The M2 ratio is known to be a type of percentage, which can be easily interpreted for the analysis of performance (Rampini, Sufi, & Viswanathan 2014). M2 ratio is calculated according to the following formula: “M2 = S(x) * S.D(y) + R(f)” (Chen, Simai & Shuzhong 2011). The formula presupposes that S.D(y) stands for the standard deviation of surplus of other investments of the analogical level (Buser 2015). M2, which stands for the differential surplus implies the extra surplus of the managed portfolio unlike the benchmark portfolio following the adaptation for discrepancies in the general hazard (Deborah 2011). Therefore, M2 can be regarded as more relevant compared to the Sharpe ratio (Deborah 2011). Despite the fact that the Sharpe ratio may be utilised in an attempt to rank portfolio performance, the ratio’s numeracy value is not easy to interpret, that is why M2 is so widely used (Buser 2015).

### Investment Risk Management

The risk is typically regarded as a predominantly negative term, meaning that is has to be avoided (Grace et al. 2014). On the other hand, the field of investment demonstrates that risk is undivided from performance and is absolutely necessary. Therefore, an investment risk can be regarded as a departure from an anticipated result (Kang et al. 2011). The departure might be positive or negative, as in order to obtain greater surplus in the long run, some more short-range volatilities should be accepted (Rampini, Sufi, & Viswanathan 2014). Risk management is quantifiable both in absolute and in relative terms (Grace et al. 2014). A sustainable insight of risk management in its various forms can assist investors to better understand the possibilities, trade-offs and funds incorporated in discrepant investment approaches (Grace et al. 2014).

### Conclusion

Fiscal performance evaluation can be regarded as one of most unbiased methods of estimating the fiscal and monetary performance of any firm. It actually defines how a managed portfolio has executed comparing it to a particular comparison benchmark. Therefore, fiscal performance evaluation utilizes the risk-adapted methods, which accommodate returns and surpluses in order to reveal discrepancies in risk levels between the individual managed portfolio and the selected benchmark portfolio. The major objective of the present fiscal performance evaluation theory regards the return maximizing combined with return risk minimization. Therefore, the performance evaluation research studies attempt to elaborate a compound guide to evaluate risk-based return. The main methods of this category are the Sharpe ratio, Treynor measure, Jensen’s alpha ratio, and M2 measure. The paper analysed these four different types of performance analysis. The Sharpe Ratio is typically implemented for analysing hazard-adjusted restitution, appearing as an industrial norm for such estimations. It is an average return obtained in surplus of the hazard-free ratio per portion of unpredictability or general hazard, while deduction of the hazard-free ratio is taken from the average surplus. Eventually, the Sharpe ratio “levels the playground” among portfolios depicting which of them faces superfluous hazards. On the other hand, Treynor ratio is used to measure surpluses acquired in surfeit of the costs, which might have been obtained during a risk-free investment per each portion of market hazard. Despite the fact that previous two ratios are quite similar, the major difference regards the fact that the last one use “beta” in the form of the unpredictability estimation. The analysis demonstrates that the Sharpe ratio is more relevant for all diversiform portfolios, while the Treynor ratio is more appropriate for well-defined portfolios. Jensen’s Alpha Ratio is a hazard-adjusted performance estimation, revealing the average surplus on a portfolio over and above of the predicted measures demonstrated by CAPM. In like manner to the Treynor ratio, Jensen’s ratio evaluates hazard premiums in accordance with beta that the portfolio has already sufficiently diverged. Finally, M² analysis regards estimations, which evaluate money supply and the ratio actually derives from the Sharpe ratio. On the other hand, M2 measure is believed to be more relevant on a contrary to the Sharpe ratio. Each measure is appropriate for each specific case. The selection of measure depends on investment assumptions and the required risk management. Thus, when the portfolio depicts the whole investment of a person, the Sharpe ratio can be used to compare the variables with the market ratio. On the other hand, when numerous alternatives are possible, it is better to utilise the Jensen’s Alpha or the Treynor ratio. Nevertheless, when it is important to mix the actively managed portfolios with passively managed ones, it is better to utilise M2 measure. Managing investment risk begins and ends with the portfolio management, analyzing both risk and surplus from each angle due to the fact that they navigate current compound investment landscape.