1. Risk adjusted returns
In this video, you'll learn more about risk adjusted returns.
2. Choose a portfolio
Suppose I propose these two investment options to you. There is portfolio 1, which has a high expected annual return of 14%, but has a standard deviation of 8%, as its' indication of risk. Portfolio 2 has a relatively lower expected return of 6%, but at a lower risk level of only 3%. Which portfolio would you choose? Remember your pick as we'll come back to this later.
3. Risk adjusted return
Well, the choice between portfolio 1 and 2 will depend on risk appetite of course, but there is also smart way to compare returns of portfolios, and that is to look at risk adjusted returns.
Risk-adjusted return defines an investment's return by measuring how much risk is involved in producing that return. It's generally expressed as a number or rating. It basically weighs the return relative to the risk taken. You can calculate risk-adjusted returns for individual securities, investment funds and portfolios. Risk adjusted returns allow you to objectively compare across different investment options. It also tells you whether the return justifies the underlying risk that you are taking.
4. Sharpe ratio
The Sharpe ratio is most commonly mentioned when people talk about risk adjusted return. It is relatively easy to calculate. All you need is the portfolio's return, a return you get on a risk free asset, for example the interest rate on your savings account, and the portfolio's standard deviation. During a low interest period, like we experienced after the financial crisis in 2008, the risk free rate is often assumed to be zero.
In the previous chapter we discussed how to calculate the standard deviation of the portfolio? Do you remember this? You first calculated the portfolio variance using the portfolio weights and the covariance matrix. You then took the square root of the variance to arrive at the standard deviation.
5. Annualizing volatility
Suppose we use the annualized return in the Sharp ratio calculation, what volatility measure do we need to use? Well, you might want to use annual volatility in order to make sure both performance and volatility are measured over the same time period. This formula shows you how to convert daily volatility into an annual number. T is the number of data points per year. Since there are roughly 250 trading days per year, you often multiply with 250. Alternatively when you go from weekly returns to annual, you multiply with 52, etc.
You can apply this formula on either the standard deviation or the variance, the difference is simply the square root.
6. Calculating the Sharpe Ratio
Once you have the annual performance and volatility, calculating the Sharpe ratio is relatively easy. Let's take the Apple example again. Apple had an annualized return of 15%. Let's first calculate the annualized volatility. This turns out to be 22%. As you can see, this is relatively high when compared to the return. Let's define a risk free rate of 1%. And lastly, let's calculate the Sharpe ratio of return over risk. Which results in 0.64, which is indeed not as attractive as the annualized return would suggest. You can't directly compare the annualized return to the Sharpe ratio in terms of magnitude, as the Sharpe ratio is a dimensionless score, whereas the return is not.
7. Which portfolio did you choose?
So which portfolio did you choose in the beginning of this lesson? Let's see what the better option is. Let's assume a risk free rate of zero. Comparing the two, Portfolio 1 has a Sharpe ratio of 1.75, and Portfolio 2 has a Sharpe ratio of 2.
8. Let's practice!
Let's practice!