What must be the daily interest rate (expressed in continuously-compounded and annualized terms) for the tailed hedge ratio to be 90% of the untailed one for a one-year hedge? Assume a hedging horizon of 365 days.
A) 10%
B) 15%
C) 20%
D) 25%

Question

Quizplus · Accepted Answer

The tailed hedge ratio being 90% of the untailed one implies that the tail effect (due to daily compounding of returns) reduces the effectiveness of the hedge by 10%. In continuously compounded terms, this effect can be modeled using the formula for continuous compounding, $e^{rt}$, where $r$ is the daily interest rate and $t$ is the time in years. For a one-year hedge (t=1), and wanting the tailed hedge ratio to be 90% of the untailed, we set $e^{r*1} = 0.9$. Solving for $r$ gives a rate that approximates to 20% when annualized.

What Must Be the Daily Interest Rate (Expressed in Continuously-Compounded