Sharpe ratio: definition, calculation rules and formula

2024 Author: Howard Calhoun | [email protected]. Last modified: 2024-01-02 13:48

Sharpe ratio shows how the return of an investment portfolio and risk are related. This ratio is interesting for investors who compare trading strategies or financial instruments.

The essence of the indicator

Sharpe ratio shows the efficiency of the used trading strategy or financial instrument. The higher it is, the more effective the target is.

The data of this ratio shows both an indicator of past estimates of profitability to risk, and predicts the level of stability of potential profit. In this regard, it is most often used by financial analysts in pivot tables that provide asset valuation.

Calculation

The calculation of the coefficient shows the investor what degree of risk is inherent in a particular asset. The Sharpe ratio is calculated using the formula specified in the article.

• Rx - average profit.
• Rf is the best available risk-free rate of return.
• StdDev - standard deviation of asset profitability.
• X - investment.

When calculatingthe Sharpe ratio in the numerator is the mathematical expectation.

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 of an asset.

Calculating the 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 completely reliable assets. This large return is called excess return. The latter characterizes the quality of management and the effectiveness of the decisions made by the investor.

The return of a zero-risk asset can be estimated in several ways:

• Return on bank deposits of the largest and most reliable domestic banks, primarily Sberbank and VTB24.
• The return on government securities with zero risk (these securities include OFZ and GKO in the Russian Federation, ten-year bonds in the USA), which have maximum reliability according to the rating agencies S&P, Moody's, Fitch.

Sharpe ratio estimate

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.

When the calculated value is in the range from 0 to 1, we can say that the degree of risk is higher than the amount of excess return. Here, in addition to the Sharpe ratio, it is necessary to evaluate other indicatorsinvestment 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 coefficients are compared, and one exceeds the other, then the first portfolio (asset) is said to be more attractive to the investor than the second one.

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 with the calculation. Consider an example of calculating the Sharpe ratio based on virtual companies.

Assume that our portfolio includes shares of three companies: A, B, C. The share in the portfolio of company A is 30%, company B - 25% and company C - 40%. Let's take quotes for one week as an example, although in reality it is necessary to evaluate for a longer period of time (month, quarter, year).

Enter into the spreadsheet data on quotes of all three companies for the estimated period. Next, we calculate the profitability of securities of each compared company, for which we enter the formula for finding the natural logarithm of the ratio of each subsequent day to the previous one in the cells, for example, in 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 return, its risk and evaluate the return on a risk-free asset. Asthe last value we will take the interest rate on deposits (8%). The portfolio return is calculated using the formula=СР. VALUE(E4:E9)B1+SR. VALUE(F4:F9)C1+SR. VALUE (G4:G9)D1 (the resulting value is one, nothing needs to be stretched or copied).

Portfolio risk is calculated using the formula=STAND. DEVIATION (E4:E9)B1+STD DEVIATION (F4:F9)C1+STD REJECT(G4:G9)D1

Calculate the Sharpe ratio as=(H4-J4)/I4.

Thus, the value of the Sharpe ratio is negative, which indicates that the portfolio is risky and needs to be reviewed. The return on the risk-free asset is higher than the return on the 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 Sharpe ratio calculation, instead of the standard deviation, a modified risk measure is used, which allows assessing the 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 – average portfolio (asset) return;}
• r_{f – average profitability of an asset with zero risk;}
• σ_{p – standard deviation of asset (portfolio) returns;}
• S – profitability distribution kurtosis;
• z_{c – kurtosis of asset (portfolio) profitability distribution;}
• K is the quantile of the distribution ofthe same indicator.

This model includes only statistical calculation, which increases the adequacy of the risk assessment.

Disadvantages of the Sharpe ratio

The main advantage of this ratio is that when using it, you can see which financial instrument will provide smoother profitability, and which one will be jumpy.

But the coefficient is not without flaws, the main of which are 3:

1. It calculates the average profit in percent for the period, which is incorrect in the case of a series of unprofitable periods.
2. When using this ratio, a sharp swing in any direction has a negative connotation, since it is considered as a risk.
3. When calculating this coefficient, a series of losing and profitable transactions are not taken into account, and this is necessary to evaluate the effectiveness of trading.

Sortino ratio

To level the second disadvantage of the Sharpe ratio, Sortino proposed its modification. Sharp's indicator takes into account both risk and positive and negative changes in profitability. 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 takes into account the volatility of the profitability of an asset or portfolio below the minimum acceptable degree of profitability.

In closing

Thus, the Sharpe ratio is a statistical indicator of the stability of an asset's return(portfolio). If the investor wants to take into account only the negative dynamics in the change in yield, it is necessary to use the Sortino coefficient.