For an individual security calculating it's Sharpe and Sortino ratios is straightforward.
What I'm curious about is the following:
Let's say I have a portfolio of several securities, which is a distribution of my total capital: for example Asset A has 25%, Asset B has 50%, and Asset C has 25%. At every timestep
t, let's assume that I can adjust these percentages to maximize my profits, and that the total distribution always has to add up to 100%.
So at each timestep
t my portfolio has a return of
r_t, which is the dot product of the distribution vector (
a) for each asset at time
t with the vector of the change in price for each asset since time
If I want to calculate the Sharpe and Sortino for the portfolio, would I:
- Calculate the Sharpe and Sortino ratios for each individual security at time
tand again take a dot product between my distribution vector
aand the vector of each sharpe/sortino ratio for each security
- Directly calculate the Sharpe and Sortino ratios of the portfolio using the returns of the portfolio (
r_t) across all timesteps
Another good question would be: are both of these approaches fundamentally the same?
Thanks in advance for your help!