1. Risk-adjusted metrics
In this final lesson, you'll be introduced to risk-adjusted metrics. Risk-adjusted measures assess the reward obtained per unit of risk taken.
2. Sharpe ratio
The most popular risk-adjusted metric used in practice is the Sharpe ratio. It is defined as the excess reward of an investment over the risk-free rate, divided by the volatility of the returns. The ratio has no unit. The larger it is, the better your investment is.
3. Sharpe ratio
The risk-free rate used in the formula is the rate of return of a zero-risk investment, as for a money account. It is common to take the short-term interest rate of US Treasury bills issued by the US government. This is because the US government is supposed to be a very safe institution with no risk of default.
4. Sharpe ratio
Let's take an example with four returns. In this case the effective rate of return is 5% and the volatility is 30%. If we assume a risk-free rate of 1%, the Sharpe ratio is 0.13
Note it is also common among practitioners to use the average return in place of the effective rate of return in the numerator of the Sharpe ratio.
5. Sharpe ratio with Google Sheets
To find the Sharpe ratio of the ABC stock with spreadsheets, start by computing the effective rate of return. You can use GEOMEAN() and ARRAYFORMULA() as seen before.
Next, compute the volatility of stock returns using STDEV().
Finally, just apply the formula and you're done.
6. Volatility and Sharpe ratio
Note that high volatility penalizes the ratio. It makes sense, as volatility is bad from an investor perspective.
However, volatility can be the result of large positive returns only, which are actually good for investors. So, we could argue that only below-average returns should be used to measure the volatility.
7. Semideviation and Sortino ratio
A metric which only focuses on below-average returns for computing the volatility is the semideviation.
This new risk measure replaces the volatility in the Sharpe ratio, leading to the so-called "Sortino ratio".
8. Semideviation and Sortino ratio
With the same example as before, the semideviation is computed considering only returns lower than the average return; 8% in this case.
The semideviation is 17%.
9. Semideviation and Sortino ratio
The new metric replaces the volatility in the denominator of the Sharpe ratio leading to a Sortino ratio equal to 0.23.
The value of the Sortino ratio for this investment is larger than the Sharpe ratio, which is 0.13. That's because the major determinant of the high volatility, the 50% return, is now excluded from the computation of the semideviation as it is positive for the investor.
A smaller semideviation means a smaller denominator and, in turn, a larger Sortino ratio.
10. Semideviation with Google Sheets
Computing the semideviation with spreadsheets can be done by applying the formula.
A couple of operations must be done first: Computing the average return and the squared deviations of historical returns from the average return.
11. Semideviation with Google Sheets
Once this is done, you can apply the formula.
Use the function SUMIFS() to compute the sum of squared deviations from the average of only below-average returns.
12. Semideviation with Google Sheets
Next, the denominator is the count of below-average returns. COUNTIFS() does perfectly the job for you.
13. Semideviation with Google Sheets
Do not forget the "&" sign which is crucial to write the logical criterion correctly.
14. Semideviation with Google Sheets
Finally, use SQRT() and you come up with the semideviation.
15. It's time to practice!
Let's compute the performance of stock ABC with the risk-adjusted metrics. Time to practice!