Portfolio Hedging, Value at Risk and Volatility Bias

An increasing number of treasurers are now applying the portfolio approach to hedging. This means they do not consider individual positions, for example euro/dollar or dollar/yen exposure, but combine different exposures together to reduce risk of the total position.  The primary goal is to reduce risk and not to achieve profit. The risk of the diversified portfolio is lower then the sum of individual risk positions. Before any hedging measures are implemented, the treasurer asks, for example, how much the total portfolio will suffer when the euro/dollar rate moves unfavorably and not how much the dollar position is affected when the euro/dollar rate moves unfavorably. Looking from the perspective of the total risk position we can apply the value at risk approach to trigger our hedging decisions. Diversification can reduce risk as long as assets are not 100 per cent correlated, but even with 100 per cent correlation risk is not increased – it is simply not reduced. Less hedging is required if there is less risk.

Diversification does not relate only to different foreign exchange positions, but can also include commodities, investments and borrowings, etc. The treasurer calculates the value at risk (VaR) or earnings at risk (EaR) of the total position and when VaR exceeds the previously agreed amount, hedging measures can be implemented.

With the VaR approach we try to answer the following question: how big is probability X that the portfolio does not lose any more than V money units within the next N days. In essence the question is: ‘How bad can things get?’¹VaR is a function of the time horizon (N) and the confidence level (X). However, the most rigorous assumption is the hypothesis that prices of assets in our portfolio are log-normal distributed. When we cannot use the assumption of log-normal distribution the volatility is not the adequate measure of risk. All value at risk analysis has the implicit assumption that the future will in some sense be like the past according to the normal distribution. Under the assumption of normal distribution a five-standard deviation move in markets happens about once every 7,000 years but actually these jumps can be seen once or twice every 10 years. The VaR is not a sufficient measure of risk when we cannot exclude the extreme events. Therefore it can be used only in conjunction with stress testing. We have to test our portfolio under the assumption of extreme changes of exchange rates or interest rates, etc. to develop an appropriate hedging strategy. The objective is to increase the effectiveness of the hedge, which would eliminate the proportion of variance.

The hedging strategy will also depend on whether there is a volatility bias or not. All asset markets are influenced strongly by speculation. In the FX markets, with daily volume exceeding $1.9 trillion, only $50bn per day can be related to world exports and imports. The commodity markets also show a large amount of speculation, which is now mostly associated with hedge fund activity. The commodity hedge funds grew from $6bn in 1999 to $120bn in 2005. The speculative activity resulted in a 35 per cent spread between commodities that have listed futures contracts (and therefore can be invested in by hedge funds) and commodities that don’t have readily investable products.

In other words, much of the rise in the commodities that we see around the world is the result of speculation. If we can assume that volatility is strongly affected by speculation, we can adjust the method we use to calculate volatility using the approach that recognizes that volatilities and correlations are not constant. There are many models that attempt to keep track of variations in the volatility or correlation through time, such as the exponentially weighted moving average, or the auto-regressive conditional heteroscedasticity model. We can also use this information when implementing hedging. With the VaR approach, hedging is implemented when VaR exceeds a certain predefined amount. At that point, basket hedging can be implemented, which hedges the same percentage amount of each exposure or we can apply selective hedging. Selective hedging would mean that we hedge more in one asset than the other or we choose to hedge exclusively in one asset. If one asset shows abnormal volatility and we believe that this volatility will go back to the ‘normal’ values, we should choose this asset for hedging purposes. Otherwise there could be unwanted swings in VaR when volatility changes. This can easily be shown using a model of two assets.

Assume we have a long €10m position in US dollar and a long €5m position in Swiss franc. The correlation coefficient amounts to 0.3. The value at risk of the US dollar position is €200,000 and the Swiss franc position is €50,000. The VaR of the total position (as shown in the table above) runs at €220,000. The volatility of the euro/Swiss franc rate increases dramatically and the VaR of the Swiss franc position rises to €100,000. The VaR of the total position then rises to €248,000. To prevent the acceptable risk exceeding the VaR of €225,000, some hedging measures must be implemented. The treasurer could now apply basket hedging and reduce US dollar and Swiss franc exposure by 10 per cent. These activities would reduce VaR of the net position to €224,000. The same reduction could be achieved by hedging just €1,350,000 of the US dollar position or €2,100,000 of the Swiss franc position. At first, these three hedging measures generate the same VaR for the total net position. However, if the volatility of euro/Swiss franc goes back to the ‘normal’ level, hedging only the US dollar position or applying basket hedging will lead to higher swings in VaR. Therefore, if one asset in our portfolio shows volatility bias we should predominantly use this asset when implementing hedging. We reduce exposure predominantly in the asset (position) with the highest volatility bias. With this strategy we can achieve the highest hedge effectiveness and this means the lowest swings in VaR.

Nevertheless, if the assumption of log-normal distribution cannot be sustained (for example because of excessive influence of speculation such as in the current commodity markets or against a particular currency), VaR is an insufficient instrument and we have to apply stress testing using extreme values. If these extreme values for exchange rates, commodity prices and interest rates, etc, lead to a calculated EaR that is not acceptable, hedging for the worst case scenario using out-of-the money options, could be implemented. The out-of-the money options are most appropriate to cover worst-case scenarios. Out-of-the money options in context of portfolio hedging are relatively inexpensive instruments because they do not hedge individual positions but hedge the net position, benefiting fully from diversification advantage. By being prepared for the worst case scenario with out-of-the-money options, we can handle speculative swings in the volatility, thereby increasing hedging in the positions with highest volatility bias.

Applying findings from the two asset modesl to the current situation on commodity markets when VaR exceeds a certain predefined amount we should not hedge
the same percentage amount of each exposure but hedge predominantly in the commodity markets to reduce swings in VaR.

¹Walter Ochynski, Foreign Exchange Management Your key to success in volatile markets, Charleston 2006. John C. Hull, Options, Futures and Other Derivatives, fifth edition, Upper Saddle River 2003