Differences Between Portfolio Daily Average Returns

Question

I have a doubt about the average daily return for a 2 stock porfolio. I have the data of both stock returns over a 1511 day period. I used 2 approachs to calculate the average return. In the first one, I calculated the average of the returns of each individual stock over the 1511 days period, then I used the formula

$Average Return = (Weight 1*Return 1)+(Weight2*Return2)$

I'm getting 0.058%

In the second approach, I assumed a starting capital ammount, choose the same weights, and calculated the daily increase on the starting capital over the 1511 period. I calculated the returns for every day and got the average of those. The solution was 0.056%.

Is the second approach incorrect? Why are those differences found?

Answer 1

In the first case, you are assuming the weights are fixed. I guess one half to each weight. In the second case, the weights start out equal, but, since you're using a starting capital, the weights are changing at each time, t, implicitly, depending on the returns of the two stocks up to time t. This is because, when you multiply the capital by the return of the respective stock, the capital goes up ( or down) in proportion to what the cumulative return was up to that point.

So, given that your numbers are pretty close, you're probably doing things correctly and the difference is due to what I explained above.

The method you want to use all depends on how exact you want to be. Is the manager gonna be re-weighting his portfolio every day so that his weights truly are constant through out the investment period. Or is he just letting them start out that way and letting capital appreciation do whatever it does over time ? It's all about the assumptions you want to make. I hope that helps some.