The Sharpe ratio shows how investment portfolio returns and risk are related. This ratio is interesting for investors who compare trading strategies or financial instruments.
The essence of the indicator
The Sharpe ratio shows the operability of the used trading strategy or financial instrument. The higher it is, the more effective the object of assessment.
The data of this coefficient show both an indicator of past assessments of risk profitability and predict the level of stability of potential profit. In this regard, it is most often used by financial analysts in summary tables that provide an assessment of assets.
Calculation
The calculation of the coefficient shows the investor what degree of risk is inherent in a particular asset. The Sharpe ratio is calculated by the formula indicated in the article.
- Rx is the average profit.
- Rf is the best available rate of return for risk-free security.
- StdDev is the standard deviation of the asset's profitability.
- X is an investment.
When calculating the Sharpe ratio in the numerator, mathematical expectation is used.
Like any coefficient, this indicator is a dimensionless quantity. Most often, its data is compared with a benchmark, which is the risk-free interest rate of return on an asset.
Calculation of profitability of a risk-free asset
The investor wants to get a higher return compared to what he could get if he invested only in fully reliable assets. This high yield is called excess. The latter characterizes the quality of management and the effectiveness of decisions made by the investor.
The return on a zero-risk asset can be measured in several ways:
- The yield on bank deposits of the largest and most reliable domestic banks, primarily Sberbank and VTB24.
- The yield of government securities with zero risk (these securities include OFZs and T-bills in the Russian Federation, ten-year bonds in the United States), which have maximum reliability according to the rating agencies S&P, Moody's, Fitch.
Sharpe Ratio Estimation
If the calculated value is greater than 1, this indicates that the portfolio or asset is characterized by high returns, which makes it attractive for investment.
If the calculated value is in the range from 0 to 1, we can say that the degree of risk is higher than the excess return. Here, in addition to the Sharpe ratio, you need to evaluate other indicators of investment attractiveness.
If the calculated value is less than 1, this indicates that the excess return takes negative values, it is better to prefer an asset with a minimum level of risk.
If two considered coefficients are compared, and one exceeds the other, then they say that the first portfolio (asset) is more attractive to the investor compared to the second.
Evaluation example
When forming an investment portfolio, it is necessary to carry out a comparative analysis of different portfolios. To do this, you need to know the quotes of all securities of this portfolio. MS Excel can help facilitate the calculation. Consider an example of calculating the Sharpe ratio based on virtual companies.
Suppose that our portfolio includes shares of three companies: A, B, B. The share in the portfolio of company A is 30%, company B - 25% and company C - 40%. Take for example quotes for one week, although in reality you need to evaluate for a longer period of time (month, quarter, year).
We enter in the spreadsheet data on the quotes of all three companies for the estimated period. Next, we calculate the profitability of the securities of each company being compared, for which we enter the formula for finding the natural logarithm of the ratio of each subsequent day to the previous one, for example, in the cell E4 we enter = LN (B4 / B3) * 100, stretch (or copy the formula and paste it into subsequent cells) down and to the right.
Next, we calculate the portfolio profitability, its risk and evaluate the profitability of a risk-free asset. As the last value, we take the interest rate on deposits (8%). The portfolio yield is calculated using the formula = CP. VALUE (E4: E9) * B1 + CP. VALUE (F4: F9) * C1 + CP. VALUE (G4: G9) * D1 (the obtained value is one, you do not need to stretch or copy anything).
Portfolio risk is calculated using the formula = STD. DECLINE (E4: E9) * B1 + STD. DECLINE (F4: F9) * C1 + STD. DECLINE (G4: G9) * D1
The Sharpe ratio is calculated as = (H4-J4) / I4.
Thus, the Sharpe ratio is negative, which indicates that the portfolio is risky and needs to be reviewed. The return on a risk-free asset is higher than the return on a portfolio. This suggests that it is more profitable for an investor to put money in a bank at 8% per annum than to invest in this portfolio.
Modified Ratio
In this version of the calculation of the Sharpe ratio, a modified risk measure is used instead of the standard deviation, which allows an assessment of potential risks of the dynamics of the distribution of asset profitability.
In this case, the calculation is performed according to the formula specified in the article.
- r p is the average profitability of the portfolio (asset);
- r f is the average profitability of an asset with zero risk;
- Ο p is the standard deviation of the asset (portfolio) profitability;
- S - excess distribution of profitability;
- z c - kurtosis of the distribution of profitability of an asset (portfolio);
- K is the quantile of the distribution of the same indicator.
This model includes exclusively statistical calculation, which increases the adequacy of risk assessment.
Sharp ratio disadvantages
The main advantage of this ratio is that when you use it, you can see which financial instrument will provide smoother profitability, and which will be spasmodic.
But the coefficient is not without drawbacks, the main of which are 3:
- With its help, the average profit is calculated in percent for the period, which is incorrect in the case of a series of unprofitable periods.
- When using this coefficient, a sharp fluctuation in either direction has a negative connotation, since it is considered as a risk.
- When calculating this coefficient, a series of unprofitable and profitable transactions are not taken into account, and this is necessary to assess the effectiveness of trade.
Sortino coefficient
To level out the second drawback of the Sharpe coefficient, Sortino proposed its modification. At Sharpe, the indicator under consideration takes into account both positive and negative changes in profitability as a risk. The Sortino coefficient takes into account only negative trends. It is calculated in the same way as the main coefficient considered in this article, but the volatility in the profitability of an asset or portfolio is taken into account below the minimum acceptable degree of profitability.
Finally
Thus, the Sharpe ratio is a statistical indicator of the stability of the asset (portfolio) income. If the investor wants to take into account only the negative dynamics in the change in profitability, it is necessary to use the Sortino coefficient.