Question

You are investing in the ProShare ETFs in your trading account. The ultra ETFs are designed to provide twice the daily return of the underlying benchmark indexes. (10 points)

(i) Is the risk of the ultra-ETFs, measured by standard deviation of the daily return, twice the risk of the underlying index? Show your result.

(ii) Explain why the monthly return of the ProShare ultra-ETF may not equal twice the monthly return of the index.

Answer 1

Investing in ultra ETF's involve taking on a high risk and as a reward you have a higher expected return.

Point 01:

Ultra ETF invest in financial derivatives and they take on levered position to double the return you make. As a part of the levaraging activity the standard devation of the returns also goes up and thus the risk on ultra ETF if measured in terms of standard deviation is twice that on normal index.

Point 02:

The reason why Ultra ETF may not provide twice the return of bechmark in a months period is because they involve daily rebalancing with leverage that causes the results to vary significantly when seen over a longer duration of time.