- Joined
- 9/22/14
- Messages
- 1
- Points
- 11
Optimal hedge ratio depends on the particular objective function to be optimized, and most widely-used hedging strategies is based on the minimization of the variance of the hedged portfolio.
r1t is the return of asset 1 at time t
r2t is the return of asset 2 at time t
the return of the portfolio at time t is r1t-h2*r2t or h1*r1t-r2t , and h1 or h2 is the hedge ratio.
the variance of return of the hedged portfolio is var(r1t-h2*r2t) or var(h1*r1t-r2t), which is to be minimized to obtain optimal h1* or h2*.
I think h1* is supposed to be 1/h2*, which actually is not the case.
The analytic solution are:
h1*=cov(r1t,r2t)/var(r1t)
h2* =cov(r1t,r2t)/var(r2t)
Can someone exlpain why h1* is not equal to 1/h2*? and In practice which ratio should I use, h1* or h2*?
r1t is the return of asset 1 at time t
r2t is the return of asset 2 at time t
the return of the portfolio at time t is r1t-h2*r2t or h1*r1t-r2t , and h1 or h2 is the hedge ratio.
the variance of return of the hedged portfolio is var(r1t-h2*r2t) or var(h1*r1t-r2t), which is to be minimized to obtain optimal h1* or h2*.
I think h1* is supposed to be 1/h2*, which actually is not the case.
The analytic solution are:
h1*=cov(r1t,r2t)/var(r1t)
h2* =cov(r1t,r2t)/var(r2t)
Can someone exlpain why h1* is not equal to 1/h2*? and In practice which ratio should I use, h1* or h2*?
