Language Anxiety and Vocabulary Learning

3. The errors are linearly independent of one another, 𝐶𝑜𝑣 𝑢 , 𝑢 = 0

4. There is no relationship between the error and corresponding x variety, 𝐶𝑜𝑣(𝑢 , 𝑥 ) = 0

5. The errors are normally distributed, 𝑢 ~𝑁(0, 𝜎 )

If these assumptions hold the estimators will be the best linear unbiased estimators of their true values. In this model, it is assumed that error term (𝑢 ) in equation 21 is normally distributed with a zero mean and constant variance or homoscedastic in order to conduct single or joint hypothesis tests about the model parameters. 𝑢 is also assumed to be uncorrelated, meaning that the covariance of the residuals of the spot returns and residuals of the futures returns is zero over time.

Assumption one is easy to test by including a constant term, 𝑢 in equation 21 (Brooks, 2008).

Due to the practical approach in this dissertation, with simulations, testing the other assumptions for all regression analysis is comprehensive and thought to be beyond the scope of this dissertation.

3.6 Is basic financial theory applicable in shipping?

The Ederington framework is a well-accepted method for estimating optimal hedge ratio and

framework has been applied by for instance Kavussanos and Visvikis (2000a) when investigating hedging performance of different freight routes. Their results indicate that it is optimal to use low hedge ratios, and that the corresponding hedging efficiency was low when hedging with FFA contracts. This has mainly been due to the low correlation between freight rates and the FFA contracts, as a result of no cost-of-carry relationship between them. Such low hedge ratios may question whether a financial theory, which is based on hedging instrument with high correlation, is applicable in practice to determine optimal hedge ratio and hedging efficiency in shipping.

Gray (1990) questioned whether an excessive degree of statistical accuracy in the calculation of correlations and the level of the hedge is necessary, and argues that this may be fundamentally misleading. The freight market is a difficult and hard-to-define market, in contrast to financial markets where each price is known on a penny basis on a second-to-second basis. He further argues that freight hedging is by definition a comparatively imprecise mechanism, and that a more sensible approach for estimating correlation is preferable. The correlation is not expected to be close to perfect, but there is still a reasonable correlation between actual earnings and freight derivatives that can be utilized. Even though the shipping industry and freight derivatives market has evolved since Gray presented his views, the fundamental of his arguments is still relevant.

There exist alternative methods for measuring hedging efficiency, which is not based on the correlation. An example of such a method is the dollar-offset method, which may be more sensible   than   Ederington’s   framework   and   linear   regression.   This   method   has   a   more   practical   approach and determines hedging efficiency based on absolute changes in the value of the underlying and the derivative. The method is commonly applied for measuring hedging efficiency in accounting. As an extension of the discussion above we will introduce the method, and later compare the results between the different methods.

3.6.1 The dollar-offset method

The dollar-offset method is a quantitative method that compares changes in fair value or cash flow of the hedged item and the derivative. It can both be applied period-by-period or cumulatively. If the change in the derivative exactly offsets the change in the value of the hedged

item, the negative of their ratio would be -1.00. The cumulative form of the dollar-offset method can be expressed mathematically as

𝐷𝑜𝑙𝑙𝑎𝑟  𝑜𝑓𝑓𝑠𝑒𝑡  𝑟𝑎𝑡𝑖𝑜 = −(∑ 𝑋  / ∑ 𝑌 ) ( 27 )

Where Xi is periodic changes in the value of the derivative and Yi is periodic changes in the value of   the   hedged   item.   Which   ratios   that   are   regarded   as   “highly   efficient”   is   a   matter   of   interpretation. Swad (1995) argued that ratios between 0.80 and 1.25 should be regarded as efficient. Hence, all ratios outside of this range have to be regarded as inefficient. This range has later become an industry standard in accounting (Finnerty & Grant, 2003).

An important drawback with the method is that the ratio test is very sensitive to small changes in the value of the hedged item or derivative. As an example, consider an inventory valued at

$1,000,000 and the hedge is a short position in a futures contract. If the fair value of the inventory and the basis only change by a small amount, for instance 1% and 0.33%, these changes imply an inefficient ratio of 33%, even though the correlation between the variables can be close to perfect.

Canaberro (1999) suggests that under reasonable assumptions, the 0.80-1.25 standard rejects 36%

of all hedges when the squared correlation, R², is 0.98 or better. However, due to the highly volatile freight rates observed in shipping, the problem with small changes is of less importance.

Charnes, Koch & Berkman (2003) argue that a meaningful measure of hedge efficiency should incorporate both the correlation between the hedged item and the hedging instrument and a hedge ratio included in a combined portfolio. These variables are not incorporated in the dollar-offset method. Therefore, they argue that the dollar-offset model is not preferred for measuring hedge efficiency.