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The objective of hedging is to reduce the variance of the (position+hedge) portfolio. So which of these two solutions gives a smaller variance? You could calculate it numerically and compare the variances. However, in general ... the answer is going to be: whichever of commodity 1 or commodity 2 has higher correlation ($\rho$) with jet fuel. The percent of ...


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This sounds like quadratic hedging. If you have the return of the assets $r_X$ and $r_Y$ with negative correlation $\rho$ between the two (we could think of bonds and stocks) and more variance in one of them then the problem of weighting the two by $w$ is (assume zero expected returns for ease of presentation) $$ \text{risk} = E[(w r_X + (1-w) r_Y)^2] \...


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Bellow is how I learned to do this problem in graduate school (d) What is the optimal number of futures contracts with tailing of the hedge? Optimal Contracts = (Dollar Value of position being hedged/Dollar value of futures contracts)*h Optimal Contracts = ((55,000 * 28)/(5,000*27))*1.02125 = (1,540,000/135,000)*1.02125 =11.6498 Optimal Contracts = 12


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You are referring to the position to be hedged, as "spot position", which in gas markets means next day delivery. Hedging this with a longer-dated futured contract does not make sense, since the correlation will be rather low. If by spot you mean near-term deliveries, such as e.g. next month, next quarter etc. then a matching traded contract will usually be ...


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The keyword here is directional exposure. You first need to define what is the instrument that you do not want to have directional exposure to. Oftenwise in case of equities, this might be an equity index. Then you would need to estimate the betas of each security against the index and set the weights in any such way that the sumproduct of all the securities'...


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Without a risk free investment, the efficient frontier is described by a hyperbola, as you have already suggested. Efficient Frontier: Tour de force Given asset covariance matrix $\Sigma$ and the full-investment condition $w_1+\ldots w_N=1$, it can be traced out by optimising $$ \min_w w^T\Sigma w \quad s.t. \quad w^T\mathbf{1}=1 \quad \mathrm{and} \quad ...


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There's an old Salomon paper called "Principles of Principal Components: A Fresh Look at Risk, Hedging and Relative Value" which might answer your questions. You can find it online by Googling the title. HTH.


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If you regress spots and futures prices you are likely to end up with a case of spurious correlations. Perhaps a cointegration analysis would be a better tool. This is because the time series may not be stationary. Returns are typically (more) stationary which is why regressing them is usually more sensible. But no guarantee there either. That said, it is ...


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When fees are not symmetric, to take fees into account on orderbook needs to know if you want to provide or consume liquidity: you have in fact two different views (ie two ranking) on the same orderbook: Say you are a buyer, and do the calculation for the first limit only. $P^B(i)$ and $P^A(i)$ are respectively the prices at the bid and ask on venue $i$, ...


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Since SD in this case is usually the 1-day difference of log prices (i.e. 1-day returns) and corr is a dimensionless number, you shouldn't have to keep the units the same. After all that's how you're able to hedge a position using a different commodity that you have access to, for example jet fuel.


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What you call additional basis risk is unpredictable. It may win or lose in rolling strategy against buying 1 year futures once. But what is measurable is bid/offer spread. In 1 y contract it might be significantly wider that in quarter futures, even considering that you sell 4 times and buy 3 (lose 7 half spreads).


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In the case of N components: compute the NxN covariance matrix compute the N eiggenvectors and take the one that has the signs that you want the weights of this eiggen vector corresponds to the basket of N components that you wish to create


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