When we procure different fuels at prices linked to different price indicators, we should understand the spillover effect of the price level and the risk between these indicators. We should determine the diversification effect of procurement based on the total connectedness of an energy portfolio. We must monitor the connectedness of the portfolio, including potential price indicators and grasp the impact of excluding components already in our portfolio. Quantitative measures of risk of such a potential portfolio is extremely important. It is beneficial to consider what components we should have and how much we should hold to reconstruct the portfolio. Moreover, the measurement results may affect the financial strategy.

This chapter describes the connectedness index proposed by Diebold and Yilmaz [4], which can capture the spillover effect between markets. We then introduce Baruník and Křehlík’s [1] spectral decomposition method, which determines when spillover factors occur. Moreover, we explain the EGARCH model, which can generate each volatility series needed to examine the risk spillover effects.

We illustrate two cases: a crude oil portfolio and a natural gas portfolio. We examine each portfolio, which consists of representative markets for Europe, North America, and Asia; specifically, Brent, WTI, and Dubai-Oman to represent crude oil markets and the TTF, HH, and JKM to represent natural gas markets, respectively.
First, we describe the crude oil markets. While Dubai-Oman’s returns and volatility are smaller than those of Brent or WTI, the price series, return series, and volatility series of these three indicators appear to fluctuate synchronously. The total connectedness of the return and volatilities series are $42.95$ and $62.00 \%$, respectively. These crude oil markets appear to be integrated at a relatively high level. The spillover effects of returns and volatility between Brent and WTI are mutually strong. Dubai-Oman receives considerable risk from both Brent and WTI.

We next describe the natural gas markets. The prices, returns, and volatility for the TTF, HH, and JKM fluctuate in three different ways. Although the total connectedness of volatility is $16.90 \%$, that of returns is $1.72 \%$. This result indicates that intercontinental natural gas market liquidity may still be low. Any spillover effect of returns is less than $1 \%$, except between TTF and JKM. The volatility spillover effects larger than $10 \%$, are from $\mathrm{HH}$ to TTF, TTF to JKM, and HH to JKM.

## 金融代写|交易策略作业代写Trading strategy代考|Hedging Strategy with Futures Contracts

A futures contract is a promise to buy or sell a security at a currently agreed upon price at a predetermined time in the future. Futures are one of the most representative derivatives along with options and swaps. Commodity futures are those whose underlying assets are specific standardized commodities (e.g., precious metals, agricultural products, energy, etc.) and are often listed on commodity exchanges. Although they can be sold and bought within their maturity, they will automatically settle at maturity. The main purposes of trading commodity futures are risk hedging, speculation (e.g., diversified investment beyond traditional financial securities and trading based on market forecasts), arbitrage (e.g., pair trading between highly correlated securities and trading between securities with different maturities considering risks and interest rates), and procurement only in the case of physical settlement.

For many non-financial companies, commodity futures represent a means to hedge risk. Trading futures can eliminate uncertainties arising from price fluctuations because they determine future cash flows. We can not only determine profits in advance but also avoid unacceptable losses by trading futures. For example, firms often buy crude oil futures to avoid losses caused by future spot price increases when procuring crude oil. If the crude oil spot price actually rises, the profit obtained by liquidating the futures can cover the loss from the price increase in the spot market. As a completely opposite example, when selling electricity, firms often sell electricity futures to avoid losses due to future spot price declines. If the electricity spot price actually falls, the profit gained by counter-trading futures can cover the loss from the actual price drop. Many futures trades have the advantage of lowering hedging costs because of margin trading, which itself often reduces hedging costs in futures trades.

If we trade futures to hedge the risk of spot price fluctuations, we must be careful to curb the diversification of the portfolio return consisting of a spot and its futures. The ratio of future positions to the spot position that minimizes this variance is the optimal hedge ratio (OHR). The OHR is obtained by dividing the covariance of the spot and futures returns by the variance of the futures return. Various multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models have been proposed to capture the conditional covariance between multiple asset returns and the conditional variance of each return. Traders can monitor the OHRs calculated from the estimated multivariate GARCH model to design an optimal portfolio.

# 交易策略代考

## 金融代写|交易策略作业代写Trading strategy代考|Hedging Strategy with Futures Contracts

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