Alternative Investments in Wealth Management by Ewelina Sokołowska

Author:Ewelina Sokołowska
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.4)

where: S – Sharpe Ratio,

R – average rate of return achieved by the fund in the analysed period,

R f – rate of return on risk-free investment, called the risk-free rate, reached in the analysed period,

S m – standard deviation of the benchmark returns during the period.

In the denominator is the estimate of the standard deviation of the difference between the return on the fund (security) and the risk-free rate of return. If the risk-free rate of return is constant over time, then the equality μ0,t = μ0 for t = 1,…,T occurs, and the denominator has the form as in Sharpe’s original model. If the standard deviation of the return on the investment fund is higher than the standard deviation of the return on the benchmark, it means the assets of the fund achieved a higher rate of return than the risk premium of the reference portfolio. The larger the positive difference between these values, the higher the performance of the portfolio. If the standard deviation of the return on the investment fund is lower than the standard deviation of the return on the benchmark, it means that the assets of the fund achieved a lower rate of return than the risk premium of the reference portfolio.

If two different investments have the same rate of return, but different levels of the Sharpe ratio, it can be inferred that an investment with a higher level of the ratio carries a lower level of risk.

If two different investments have the same level of risk, but a different level of the Sharpe ratio, it can be concluded that the investment with a higher level of the ratio has a higher rate of return.

Another ratio which allows measurement of the efficiency of investment is the Treynor Ratio (Treynor index). It was introduced by Jack Treynor in 1965. The Treynor index, in contrast to the Sharpe ratio, uses the beta coefficient as a measure of risk. Ex-post data are used to calculate the ratio. It can be interpreted as the historical risk premium for investing in the fund (security) in relation to the historical beta coefficient of the fund (security), calculated relative to the respective index. The Treynor ratio allows the return on investment to be compared with statistical changes in the prices of securities.

When comparing different investments, it can be stated that the more profitable investment will have a higher value of the Treynor ratio. The index, which provides a reference framework, is characterized by the market or the relevant sector of market.

The Treynor ratio can be determined by the following formula (Treynor 1965):

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