Sharp ratio overview
The research of modern investment theory shows that the risk plays a fundamental role in the performance of portfolio. Risk-adjusted rate of return is a comprehensive index that can consider both income and risk to eliminate the adverse impact of risk factors on performance evaluation. Sharp ratio is one of the three classic indicators that comprehensively consider income and risk.
There is a conventional characteristic in investment, that is, the higher the expected return of the investment target, the higher the fluctuation risk that investors can tolerate; Conversely, the lower the expected return, the lower the risk of fluctuation. Therefore, the main purposes of rational investors in choosing investment objects and portfolios are: to maximize returns under the condition of fixed risks; Or pursue the lowest risk under the fixed expected return.
1990 William Sharpe, the winner of the nobel prize in economics, started from CAPM (capital asset pricing model), the most important theoretical basis of investment science, and developed the famous Sharpe Ratio, also known as the Sharp Index, to measure the performance of financial assets.
The core idea of william sharpe's theory is that rational investors will choose and hold an effective portfolio, that is, a portfolio that maximizes the expected return at a given risk level or a portfolio that minimizes the risk at a given expected return level. The explanation is simple. He believes that investors should at least require a return on investment that is risk-free or more.
Sharp ratio calculation formula
The calculation formula of Sharp ratio: = [E (RP)-RF]/σ p.
Where E(Rp): the expected rate of return of the portfolio.
Rf: risk-free interest rate
σp: standard deviation of portfolio
The purpose is to calculate how much excess return will be generated by the total risk per unit of a portfolio. This ratio is based on the concept of capital market line (CML) and is the most common measurement ratio in the market. When the assets in the portfolio are all risky assets, the Sharp ratio applies. Sharp index represents that investors can get several points of return for each additional risk; If it is positive, it means that the fund's rate of return is higher than the risk of fluctuation; If it is negative, it means that the risk of fund operation is greater than the rate of return. In this way, each portfolio can calculate the Sharp ratio, that is, the ratio of return on investment to more risks. The higher the ratio, the better the portfolio.
For example, the yield of national debt is 3%, the expected yield of your portfolio is 15%, and the standard deviation of your portfolio is 6%. Then use 15%-3% to get 12% (representing the income other than your risk-free investment), and then use 12%.
Sharp theory tells us that when investing, we should compare risks and try our best to exchange small risks for big returns. Therefore, investors should grow up and try to avoid some unworthy risks. At the same time, if you lack investment experience and research time when investing, you can let real professionals (not just salesmen who sell financial products to you) help you build a portfolio that suits you and minimize risks. These portfolios can measure the ratio of risk to return through Sharp ratio.
Problems needing attention in the application of Sharp ratio
Problems needing attention in the application of Sharp ratio Although the calculation of Sharp ratio is simple, we should pay attention to the applicability of Sharp ratio in specific applications:
The standard deviation of 1. is used to adjust the risk of return, and the implicit assumption is that the portfolio under investigation constitutes all the investments of investors. Therefore, the Sharp ratio can only be used as an important basis for considering buying a certain fund among many funds.
2. It is also considered inappropriate to use standard deviation as a risk indicator.
3. The effectiveness of Sharp ratio also depends on the assumption that you can borrow at the same risk-free interest rate;
4. Sharp ratio has no benchmark, so its size itself is meaningless, and it is only valuable when compared with other combinations;
5. Sharp ratio is linear, but on the effective frontier, the conversion between risk and return is not linear. Therefore, the Sharp Index is biased in measuring the performance of funds with large standard deviation;
6. Sharp ratio does not consider the correlation between combinations, so there is a big problem in constructing combinations simply according to Sharp value;
7. Sharp ratio, like many other indicators, measures the historical performance of the fund, so it is impossible to simply conduct future operations based on the historical performance of the fund.
8. In calculation, there is another stability problem of Sharp Index: the calculation result of Sharp Index is related to the choice of time span and time interval of income calculation.
Although there are many limitations and problems mentioned above, Sharp ratio has been widely used in practice because of its simple calculation and no need for too many assumptions.
The higher net growth rate of the fund may be obtained under the condition of taking higher risks, so it is not comprehensive to evaluate the performance of the fund only according to the net growth rate. The performance, income and risk of the fund should be considered, and Sharp ratio is an index that can consider both income and risk. Sharp ratio, also known as Sharp Index, was first put forward by Nobel Prize winner william sharpe in 1966, and now it has become the most commonly used standardized index to measure fund performance in the world.
Calculation of Sharp Ratio and Its Significance
The calculation of Sharp ratio is very simple. The Sharp ratio of the fund can be obtained by subtracting the risk-free interest rate from the average value of the fund's net growth rate and then dividing it by the standard deviation of the fund's net growth rate. It reflects the extent to which the net growth rate of unit venture fund exceeds the risk-free rate of return. If the Sharp ratio is positive, it means that the average net growth rate of the fund during the measurement period exceeds the risk-free interest rate. In the case that the interest rate of bank deposits in the same period is risk-free interest rate, it means that investment funds are superior to bank deposits. The greater the Sharp ratio, the higher the risk return of fund unit risk. When the Sharp ratio is negative, sorting by size is meaningless.
The theoretical basis of ranking fund performance with Sharp ratio is that investors can borrow at risk-free interest rate, so that under the same risk, funds with high Sharp ratio can always get higher investment income than funds with low Sharp ratio by determining appropriate financing ratio. For example, if there are two funds A and B, the average annual net growth rate of Fund A is 20%, the standard deviation is 10%, the average annual net growth rate of Fund B is 15%, the standard deviation is 5%, and the average annual risk-free interest rate is 5%, then the Sharp ratios of Fund A and Fund B are 1.5 and 2, respectively. We can invest the same amount of money in B at the level of risk-free interest rate (the financing ratio is 1: 1), then the standard deviation of B will be expanded by 1 times, reaching the same level as that of A, but at this time, the net growth rate of B is equal to 25% (that is, 2 # 15%), which is more commonly used as the monthly Sharp ratio and.