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

A. Risk of ultra exchange-traded fund which are measured by standard deviation of daily return will never be twice of the risk of the underlying index because it is not about replicating the rate of return by having the similar amount of risk associated with the exchange traded fund because it can be said that portfolio which has been formulated are always having different standard deviation in respect to the overall underlying index because standard deviation is a representative of total risk, which will be including systematic risk as well as on systematic risk, whereas if we had represented the the risk with the beta than we had expected the rate of return which would have been doubled with the risk which is doubled but in this case it is not the case because the standard deviation is representative of total portfolio risk.

2. Monthly return of the exchange traded fund may not be equal to twice the monthly return of the index because exchange traded fund are not completely reflecting the rate of return of the index and there will be a deviation in respect to the overall market rate of the index but these definitions will be nominal because there are certain adjustments and payments along with there is continuous trading of the exchange traded fund which is not completely efficient and hence the rate of return is not completely replicated.