értekezés - Budapesti Corvinus Egyetem

hedge their revenues fully since, while there might be liquidity needs out of the forwards,
they do not cause any costs. If, however, liquidity needs prior to the hedge horizon are
uncertain and credit spreads are positive, a firm should use less forwards than needed for a
full hedge, even if forward prices follow a martingale process (their expected value from
the market’s point of view is zero). Essentially, the firm is faced with the trade-off between
the costs (financing costs) and benefits (concave utility function) of hedging.
In a model with constant relative risk aversion (CRRA) utility function and a lognormally
distributed forward price, Korn [2003] shows that the hedge ratio decreases almost linearly
with the credit spread increasing. That is, for firms with investment grade rating, collateral
requirements do not seem to have a substantial effect on the optimal hedging strategy.
However, for firms with a non-investment grade rating, the size of hedge ratio can be
strongly affected (e.g. at 700 bp credit spread, a firm should hedge only two thirds of its
original price exposure – given his parameter specification).
Source: Korn, [2003, pp. 8.]
By varying the parameters that determine the benefits of hedging (i.e. risk-aversion,
operational leverage expressed in the form of relative production costs, price volatility), he
shows the optimal trade-off leading to the optimal hedging strategy. Increasing the riskaversion
of the firm’s stakeholders (e.g. firm is owned by non-diversified individuals) or,
alternatively, increasing the production costs 165 will amplify the benefit of hedging, so
even large credit spreads do not alter the hedge ratios substantially. Changing the volatility
has two effects. First, if volatility increases, the potential gain from risk reduction is higher
165 If average costs increase, the distribution of profits is shifted downwards in a region where a CRRA utility
function is more concave. Since higher concavity of the utility function essentially means that risk reduction
has higher benefits, hedging is more attractive and hedge ratios increase. Stated differently, if a firm has a
low expected profit margin, the risk of going bankrupt due to inverse price movements is relatively high and
hedging is more beneficial than for firms with higher expected profit margins.
164