# Investment performance

With many investments, the focus is on the financial goal, which is why the quality of the investment is measured by the return. The return is a key figure in which the result achieved in a period is divided by the capital employed (at the beginning of the period). For the following, consider a past period, such as the last year. Let us assume that the investor had partially borrowed funds for the financing the investment would be used by the Leverage effect the return has been changed, although the risks would have presented themselves differently.
In general, a higher return can be expected with more risk. The return therefore only allows an assessment of the success of the investment if something is also said about the risks. Performance indicators adjust the return by the risk taken.

The Sharpe ratio has become the most widely accepted in practice. The key figure is based on the idea of the construction of the tangential portfolio, with which the classical portfolio theory forms the frame of reference. As a result, the Sharpe ratio is suitable for measuring and assessing performance, provided that the prerequisites of classic portfolio theory are met, namely the normal distribution of simple returns. The tangential portfolio is found by placing the straight line with the highest slope on the efficiency curve.

In the light of this construction, SHARPE has proposed to measure the performance of a portfolio or an investment P in the reporting year by the slope of the straight line that leads from the interest rate i to the point which represents the return rP and the dispersion SD, of this portfolio in the reporting year. The greater this slope, the better the performance.

The Sharpe ratio SR expresses the excess return that could have been achieved with a risk of 100%, measured by the spread of the simple return in the reporting period.

In other words, the Sharpe ratio is used to determine the excess return or the reward per unit of total risk or variability (because a dispersion of 100% is a dispersion of 1). That explains the original designation reward-to-variability ratio.

To calculate the Sharpe ratio, you need the simple return on the portfolio in the reporting year and the one-year interest rate as it was at the beginning of the reporting year. So far, the data requirements are minimal. The excess return actually achieved is divided by the spread of the portfolio return or the return on the investment. Here it gets a little more difficult as far as the data is concerned:

If only the portfolio value is known at the beginning and at the end of the reporting year, initially nothing is known about the diversification of the returns. It is easy when the portfolio manager states the returns for some of the last few years and claims that they have pursued an investment policy that is balanced in terms of risk. Then we would estimate the variance as the sample variance.

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