line of best fit.
Regression analysis uses the “least squares” method to fit a line through the set of X and Y observations. This technique determines the slope and intercept of the line that minimises the size of the squared differences between the actual Y observations and the predicted Y values. The linear equation estimated is commonly expressed as:
where
X is the change in the fair value (or cash flow) of the hedging instrument attributable to the risk being hedged;
Y is the change in the fair value (or cash flow) of the hedged item attributable to the risk being hedged;
α is the intercept (where the line crosses the Y axis);
β is the slope of the line;
ε is the random error term.
The third step of the regression process is to interpret the statistical results of the regression and determine whether the regression suggests that there is an economic relationship between the hedged item and the hedging instrument. The following three statistics must achieve acceptable levels to provide sufficient evidence for such a conclusion:
• R-squared, or the coefficient of determination, measures the degree of explanatory power or correlation between the dependent and the independent variables in a regression. R-squared indicates the proportion of variability in the dependent variable that can be explained by variation in the independent variable. By way of illustration, an R-squared of 95 % indicates that 95 % of the movement in the dependent variable is “explained” by variation in the independent variable. R-squared can never exceed 100 % as it is not possible to explain more than 100 % of the movement in the independent variable. IFRS 9 does not provide a minimum reference R-squared level, but an R-squared greater than or equal to 80 % may probably indicate a high correlation between the hedged item and the hedging instrument. In my view, and this is notably subjective opinion, an R-squared below 70 % is likely to imply an absence of economic relationship between the hedged item and the hedging instrument. In any case, it is important to remember that a pure high correlation is not sufficient; there also has to be an economic justification for such a high correlation. Moreover, from a statistical perspective, R-squared by itself is an insufficient indicator of hedge performance.
• The slope β of the regression line. There is no bright line for the slope. Under the previous financial instruments accounting standard (IAS 39) the slope was required to be between –0.80 and –1.25. Judgement is required to decide whether a given slope means that the economic relationship requirement has been met. The slope can provide an indication of the appropriate hedge ratio.
• The t-statistic or F-statistic. These two statistics measure whether the regression results are statistically significant. The t-statistic or F-statistic must be compared to the relevant tables to determine statistical significance. A 95 % or higher confidence level is generally accepted as appropriate for evaluating the statistical validity of the regression.
One way to draw meaningful conclusions about an economic relationship assessment is to test the behaviour of the changes in fair value of both the hedging item and the hedging instrument under a very large number of scenarios of the underlying risk being hedged. For some highly structured products, the use of the scenario analysis method may miss a potential scenario that has a substantial effect in the hedging instrument's payout. Monte Carlo simulation is a tool that provides multiple scenarios by repeatedly estimating hundreds of different paths of the risk being hedged, based on the probability distribution of the risk. In my view, a well-performed Monte Carlo simulation can be very effective in assessing hedge effectiveness when the payout of the hedging instrument is highly dependent on the behaviour of the underlying risk during the life of the instrument.
The entity shall use the method that captures the relevant characteristics of the hedging relationship, including the sources of hedge ineffectiveness. What follows is just my own personal recommendation (remember that an entity's external auditors always have the last word) regarding which method to use (see Figure 2.11):
• Use the critical terms method when the critical terms of the hedged item and the hedging instrument perfectly match. Remember, the critical term method is a qualitative assessment and therefore relatively simple to document.
• Use the critical terms method coupled with a single scenario analysis when there is a slight mismatch between the critical terms of the hedged item and the hedging instrument – for example, where there is a relatively short time lag between the interest periods of a swap and those of a hedged loan.
• Use the scenario analysis method when there is a mismatch in dates or notionals of the hedged item and the hedging instrument, and the latter is a vanilla hedging instrument (e.g., a swap, a forward, a standard option).
• Use the regression analysis method when there is a mismatch in underlyings of the hedged item and the hedging instrument (i.e., a proxy hedge has been used), and this instrument is a vanilla hedging instrument (e.g., a swap, a forward, a standard option).
• Use the Monte Carlo simulation method when the hedging instrument is complex and/or when its payout is highly dependent on the behaviour of the underlying risk during the life of the instrument (e.g., a range accrual with knock-out barriers).
Figure 2.11 Recommended decision tree of hedge effectiveness assessment methods.
2.7 THE HYPOTHETICAL DERIVATIVE SIMPLIFICATION
The hypothetical derivative approach is a useful simplification when assessing whether a cash flow (or a net investment) hedge meets the effectiveness requirements and when measuring hedge effectiveness/ineffectiveness. Whilst IFRS 9 does not preclude the use of the hypothetical derivative in fair value hedges, in my view, auditors will not allow its use in fair value hedges as a hypothetical derivative does not fully replicate the fair value changes of a hedged item. Therefore, I will use the hypothetical derivative simplification only in cash flow and net investment hedges throughout this book.
IFRS 9 allows determining the changes in the fair value of the hedged item using the changes in fair value of the hypothetical derivative. The hypothetical derivative replicates the hedged item and hence results in the same outcome as if that change in fair value was determined by a different approach. Hence, using a hypothetical derivative is not an assessment method in its own right but a mathematical expedient that can only be used to calculate the fair value of the hedged item.
The hypothetical derivative is a derivative whose changes in fair value perfectly offset the changes in fair value of the hedged item for variations in the risk being hedged. The changes in the fair value of both the hypothetical derivative and the real derivative (i.e., the hedging instrument) are then used to assess whether the hedge effectiveness requirements are met and to calculate a hedge's effective and ineffective parts. The terms of the hypothetical derivative are assumed to be the following:
• Its critical terms match those of the hedged item (notional, underlying, maturity, interest periods).
• For hedges of risks that are not one-sided, the hypothetical derivative is a non-option instrument (e.g., a forward, a
