Here's a conundrum I'm been mulling over recently: In the formula for calculation of efficient portfolio weights, one of the parameters going into the equation is "expected return". Mathematically speaking, this is quite straightforward as it's merely a matter of taking the average of daily returns over a certain time period. The question is, what's the optimal length of this time period? Basically, as I see it there are two approaches, namely 1) utilize all historical data available, or 2) apply a certain trailing time window. The advantage of 1) is of course long-term stability, as short-term fluctuations will have little impact, on the other hand, 2) has the advantage of capturing short term changes. The problem with 1) is that even amidst the global financial crisis in 2008, long-term average is like 7-8% of the S&P500, whereas when looking at it short-term, expected return would rather be -30% for the next year. On the other hand, with a short time window, there's also a risk of getting whipsawed. Any thoughts or ideas here?
OKI, no real correct answer to your question... In my experience, most people perform their calculations over a rolling window and use other, earlier historical extremes as stress tests. Obviously, there's an implicit assumption made here and you can do more sophisticated things, but simple is probably best in this case.
I tend to prefer simplicity, so we're on the same page there. Of course I could always do a simulation with different time window sizes, but would be interesting to hear whether there are any theoretical underpinnings here...