instruments in interest-rate, currency and ... - Volksbank AG

JPY credit portfolio - period of observation 365 days (1 year)Daily change in EUR Days Days as percentage of total observation period+50.000 to +25.000 11 3.0%+25.000 to -0 169 46.30%0 to -25.000 175 47.95%-50.000 to -25.000 10 2.74%On 11 days, in the above example, the gain was between EUR 25,000 and EUR 50,000. For a large proportionof the period of observation, the gain or loss was between - EUR 25,000 and + EUR 25,000. Only on 10 daysin the year or 2.74% of the observation period was the loss greater than EUR 25,000.The assumption is now made that the past development is also representative for the future. Under thisassumption and from known data, the statement can therefore be deduced, that with a 97.26% probability theloss within 1 day will not be greater than EUR 25,000. After all, on 355 of 365 days, the loss from a single tradingday was less than EUR 25,000.The holding period of 1 day therefore emerges, as in the historical observation, the fluctuations in daily valueshave been observed for 365 days. If fluctuations in value had been observed on a weekly basis, then the valueat risk statement would apply for a week. This also reveals a problem with the historical simulation. In orderto obtain the same statement with the same degree of data integrity for a week, we would have required thehistorical data for the last 7 years. For a statement about how high the loss in a month would be, we wouldrequire data from the past 30 years.A degree of uncertainty always remains in value at risk statements (e.g. 100% - 97.26% = 2.74%). Thereforethe value at risk statements are frequently qualified with “under normal conditions”. If a value at risk is notgreater than EUR 25,000 for 97.26% of cases, what happens in the 2.74% of the cases that remain? Does theloss stand at EUR -25,500 or at EUR -1,000,000? Over the period of 1 year with 250 working days, thestatement also implies that on at least 7 working days the loss will be higher than the maximum expected lossof EUR 25,000.To answer this question, so-called “stress tests” are recommended, in which large historical fluctuations areentered into the equation.The “historical simulation“ works on the principle mentioned above regarding the measurement of value at risk.In the historical simulation, premises must be accepted that changes in risk factors (e.g. yields, interest rates andexchange rates) observed in the past are also relevant for the future. Put simply: What was the case in the past,will not change in the future. In very short holding periods e.g. of a single day, this assumption is unproblematicas a rule, and the volatility of the last 250 days can be viewed as being representative for another day. In thecase of longer holding periods or forecasts this statement becomes problematic.62