Why sharpe ratio

Alpha Defined. How to Use Alpha. The Sharpe Ratio Defined. How to Use the Sharpe Ratio. The Sharpe Ratio of a mutual can be easily calculated by using a simple formula or by following these two steps mentioned below: 1. Subtract the risk-free return of a mutual fund from its portfolio return or the average return 2. Standard Deviation: Standard deviation showcases the investment return that varies from the principal returns of an investment. A high standard deviation means there is a huge difference between the principal returns and the returns of an investment.

For example: The annual Sharpe Ratio of a fund is 2. The more returns generated by the fund during the same time will be 2. Funds having a higher standard deviation makes higher returns as their Sharpe Ratio is considered high. However, funds with a low standard deviation can earn High Sharpe Ratio and give consistent moderate returns.

Sharpe Ratio can be calculated annually or on a monthly basis. The above-given table shows the indicators of the good and bad Sharpe Ratio. Investments having less than 1. However, investments with Sharpe Ratio between 1. To avoid ambiguity, we define here both ex ante and ex post versions of the Sharpe Ratio, beginning with the former.

With the exception of this section, however, we focus on the use of the ratio for making decisions, and hence are concerned with the ex ante version. The important issues associated with the relationships if any between historic Sharpe Ratios and unbiased forecasts of the ratio are left for other expositions.

Throughout, we build on Markowitz' mean-variance paradigm, which assumes that the mean and standard deviation of the distribution of one-period return are sufficient statistics for evaluating the prospects of an investment portfolio.

Clearly, comparisons based on the first two moments of a distribution do not take into account possible differences among portfolios in other moments or in distributions of outcomes across states of nature that may be associated with different levels of investor utility. When such considerations are especially important, return mean and variance may not suffice, requiring the use of additional or substitute measures.

Such situations are, however, beyond the scope of this article. Our goal is simply to examine the situations in which two measures mean and variance can usefully be summarized with one the Sharpe Ratio.

Let R f represent the return on fund F in the forthcoming period and R B the return on a benchmark portfolio or security. In the equations, the tildes over the variables indicate that the exact values may not be known in advance.

Define d, the differential return , as:. Let d-bar be the expected value of d and sigma d be the predicted standard deviation of d. The ex ante Sharpe Ratio S is:. In this version, the ratio indicates the expected differential return per unit of risk associated with the differential return. Let R Ft be the return on the fund in period t, R Bt the return on the benchmark portfolio or security in period t, and D t the differential return in period t:.

In this version, the ratio indicates the historic average differential return per unit of historic variability of the differential return. It is a simple matter to compute an ex post Sharpe Ratio using a spreadsheet program. The returns on a fund are listed in one column and those of the desired benchmark in the next column.

The differences are computed in a third column. Standard functions are then utilized to compute the components of the ratio. For example, if the differential returns were in cells C1 through C60, a formula would provide the Sharpe Ratio using Microsoft's Excel spreadsheet program:. The historic Sharpe Ratio is closely related to the t-statistic for measuring the statistical significance of the mean differential return.

The t-statistic will equal the Sharpe Ratio times the square root of T the number of returns used for the calculation. If historic Sharpe Ratios for a set of funds are computed using the same number of observations, the Sharpe Ratios will thus be proportional to the t-statistics of the means. The Sharpe Ratio is not independent of the time period over which it is measured. This is true for both ex ante and ex post measures.

Consider the simplest possible case. The one-period mean and standard deviation of the differential return are, respectively, d-bar 1 and sigma d1. Assume that the differential return over T periods is measured by simply summing the one-period differential returns and that the latter have zero serial correlation.

Denote the mean and standard deviation of the resulting T-period return, respectively, d-bar T and sigma dT. Under the assumed conditions:. In practice, the situation is likely to be more complex. Multiperiod returns are usually computed taking compounding into account, which makes the relationship more complicated. Moreover, underlying differential returns may be serially correlated.

Even if the underlying process does not involve serial correlation, a specific ex post sample may. It is common practice to "annualize" data that apply to periods other than one year, using equations 7 and 8. Doing so before computing a Sharpe Ratio can provide at least reasonably meaningful comparisons among strategies, even if predictions are initially stated in terms of different measurement periods. To maximize information content, it is usually desirable to measure risks and returns using fairly short e.

For purposes of standardization it is then desirable to annualize the results. To provide perspective, consider investment in a broad stock market index, financed by borrowing. The resulting excess return Sharpe Ratio of "the stock market", stated in annual terms would then be 0. The ex ante Sharpe Ratio takes into account both the expected differential return and the associated risk, while the ex post version takes into account both the average differential return and the associated variability.

Neither incorporates information about the correlation of a fund or strategy with other assets, liabilities, or previous realizations of its own return. For this reason, the ratio may need to be supplemented in certain applications. Such considerations are discussed in later sections. The literature surrounding the Sharpe Ratio has, unfortunately, led to a certain amount of confusion. To provide clarification, two related measures are described here.

The first uses a different term to cover cases that include the construct that we call the Sharpe Ratio. The second uses the same term to describe a different but related construct. Whether measured ex ante or ex post, it is essential that the Sharpe Ratio be computed using the mean and standard deviation of a differential return or, more broadly, the return on what will be termed a zero investment strategy.

Otherwise it loses its raison d'etre. Clearly, the Sharpe Ratio can be considered a special case of the more general construct of the ratio of the mean of any distribution to its standard deviation.

In the investment arena, a number of authors associated with BARRA a major supplier of analytic tools and databases have used the term information ratio to describe such a general measure.

In some publications , the ratio is defined to apply only to differential returns and is thus equivalent to the measure that we call the Sharpe Ratio see, for example, Rudd and Clasing [, p. In others, it is also encompasses the ratio of the mean to the standard deviation of the distribution of the return on a single investment, such as a fund or a benchmark see, for example, BARRA [, p. While such a "return information ratio" may be useful as a descriptive statistic, it lacks a number of the key properties of what might be termed a "differential return information ratio" and may in some instances lead to wrong decisions.

For example, consider the choice of a strategy involving cash and one of two funds, X and Y. This can be achieved with fund X, which will provide an expected return of 5. The latter will provide an expected return of 5.

It is the most useful ratio to determine the performance of a fund and you, as an investor, need to know its importance. Sharpe ratio is a comprehensive mechanism to ascertain the performance of a fund against a given level of risk. The higher the Sharpe ratio of a portfolio, the better is its risk-adjusted-performance. However, if you obtain a negative Sharpe ratio, then it means that you would be better off investing in a risk-free asset than the one in which you are invested right now.

Sharpe ratio can be used as a tool to compare funds placed in the same category as analysing the performance of Fund A and Fund B, which are large-cap equity funds.

In this way, you will ensure that both the funds are facing a similar level of risk. Conversely, you might compare funds giving the same returns but which are at different levels of risk.

Sharpe ratio can tell you whether your preferred fund is suitable from an investment perspective as compared to peer funds in the said category. Ultimately, you get to know how well are you being compensated for the risk that you are taking in the investment. Sharpe ratio is one of the most powerful tools used in mutual fund selection. By looking at the Sharpe ratio, you can assess the degree of risk that two funds faced earning extra returns over the risk-free rate.

It is a standardised tool to compare funds which use different strategies like growth or value or blend. Ideally, you might consider a fund desirable which has a higher Sharpe ratio.

However, this kind of perception may not always be fruitful if the fund took a lot of additional volatility.