1. The portfolio return
Analyzing the portfolio weights reveals the investment bets.
2. Portfolio returns: relative value
The larger the weight of an asset in the portfolio, the more influential it will be in determining the future value of the portfolio. When studying this impact, investors typically do not analyze the change in the investment value in absolute terms, but in relative terms.
This leads them to compute simple returns, defined as the change in value over the period, relatively to the initial value.
The simple return is thus the final value minus the initial value, divided by the initial value.
3. Portfolio returns: relative value
As an example, suppose the
4. Portfolio returns: relative value
initial value is 100 dollars
5. Portfolio returns: relative value
the final value
6. Portfolio returns: relative value
is 120 dollars.
7. Portfolio returns: relative value
Then the return on that investment
8. Portfolio returns: relative value
equals 20%, obtained by
9. Portfolio returns: relative value
taking the difference between 120 and 100 and dividing it by 100.
10. Three steps
In the slide, I show you how we can apply this definition for computing portfolio returns. This involves three steps. First, for the initial date, we need to compute the total value invested as the sum of
11. Three steps
the values of the different investments. Second, for the final date,
12. Three steps
we have to sum the final values of the individual
13. Three steps
investments to obtain the final portfolio value.
14. Three steps
Then, we can
15. Three steps
compute the
16. Three steps
portfolio return as the percentage change of the final value compared to the initial value.
17. Example: two assets
As an example, let us consider a 2-asset portfolio
18. Example: two assets
that invests 200 dollars in asset 1 and 300 dollars
19. Example: two assets
in asset 2.
20. Example: two assets
The end value is 180 dollars and 330 dollars.
21. Example: two assets
If we sum the values, we find
22. Example: two assets
that the
23. Example: two assets
total initial value of the portfolio is 500 dollars, while the total final value is 510 dollars. It follows that the
24. Example: two assets
simple return on the portfolio is the 10 dollar change in value,
25. Example: two assets
divided by the initial 500USD invested, which gives us a return
26. Example: two assets
of 2%.
27. Example: two assets
28. Portfolio returns: weighted average return
A disadvantage of this calculation method is that it does not show how the portfolio weights determine the portfolio return. Let us, therefore, consider a different formula,
29. Portfolio returns: weighted average return
in which the portfolio return is computed as the
30. Portfolio returns: weighted average return
weighted average of the returns of the underlying assets.
31. Three steps
Its calculation proceeds also in three steps.
32. Three steps
First, the initial
33. Three steps
weights of the positions are computed.
34. Three steps
Secondly, the return on each of the
35. Three steps
individual positions is determined. Then, in the third step,
36. Three steps
the portfolio return is computed as the
37. Three steps
sum over the products between the initial weights and the corresponding returns.
38. Example: two assets
In the slide, you see how to apply this formula to compute the return for our example portfolio with two assets.
We first compute the initial portfolio weights.
39. Example: two assets
Since the initial value of the first asset is 200 dollars, and the total value invested is 500 dollars, the initial weight of asset 1 is 40 percent.
40. Example: two assets
The remainder of 60 percent
41. Example: two assets
is the weight of asset 2.
42. Example: two assets
Then, in a second step, we need to compute the returns for each of the assets. For asset 1, we obtain that the individual return
43. Example: two assets
minus 10 percent, while for asset 2, the return is
44. Example: two assets
plus 10 percent. Finally,
45. Example: two assets
we can combine those results and compute the portfolio
46. Example: two assets
return by summing over the weights multiplied by their respective returns. The first term is the weight of 40 percent times the returns of minus 10 percent, which gives us minus 4 percent. The second term is the weight of asset 2, 60 percent times its return of 10 percent, which gives us plus 6 percent.
Adding minus 4 percent and plus 6 percent gives us the portfolio return of 2 percent, which is exactly the same number as obtained before.
47. Let's practice!
The next interactive exercises put this theory in practice.