CURRENCY ARBITRAGE
4.2 VALUE AT RISK
[( . . )
Probability or frequency
–a S
c
0
% confidence level
FIGURE 4.2 Value at risk.
. S+ 2 33s(S). Thus, VAR with a probability of 1% (a between S-2 33s(S) and .
confidence level of 99%) is equal to -K S-2 33s(S)] or 2 33 s(S Kif S =0, where Kis the size of the position. Table 4.2 shows the quarterly VARs, with probabil
ities of 1% and 2.5%, on a position of USD1,000,000 from the perspectives of investors with nine different base currencies. It can be seen that the lowest VAR is found when the base currency is the Canadian dollar, because the CAD/USD rate is the most stable rate, and the highest when the base currency is the Japanese yen.
One problem with the parametric approach is the assumption of normally distributed returns. It has for a long time been established that this is not the case and that the distributions of asset returns have fat tails and tend to be skewed to the left (for example, Mandelbrot (1963) and Fama (1965)). Because of this deviation from the normal distribution, the historical method may be preferred. In this case, VAR (with a probability of 1%) can be calculated by identifying the lowest 1% of the percentage change in the exchange rate, and then applying this value to the size of the position.
The third approach is the simulation approach. Instead of calculating VAR on the basis of the historical rates of change in the exchange rate or by assuming that they are normally distributed, this approach is based on their simulated values.
Pros and cons of the VAR methodology
Value at risk has become a widely used method for measuring financial risk, and justifiably so. The attractiveness of the concept lies in its simplicity, as it represents the market risk of the entire portfolio by one number that is easy to comprehend. It thus conveys a simple message on the risk borne by a firm or
TABLE 4.2 Value at risk on a USD1,000,000 position.
Base currency 2.5% VAR 1% VAR
AUD 82,868 68,216
CAD 36,105 29,260
CHF 127,106 105,572
DKK 104,835 86,520
GBP 101,144 83,828
JPY 142,866 120,592
NOK 98,076 80,612
NZD 86,297 71,164
SEK 137,581 113,272
an individual. The concept is also suitable for risk limit setting and for measuring performance based on the correlation between the return earned and the risk assumed. Moreover, it can take account of complex movements such as non-parallel yield curve shifts. In general, it has two important charac
teristics: (i) it provides a common consistent measure of risk across different positions and risk factors; and (ii) it takes into account the correlations between different risk factors (for example, different currencies).
There are, however, several shortcomings associated with the VAR method
ology. First, it can be misleading to the extent of giving rise to unwarranted complacency. And, as we have seen, the VAR is highly sensitive to the assump
tions used to calculate it. Jorion (1996) argues that VAR is a number that itself is measured with some error or estimation risk. Thus, the VAR results must be interpreted with reference to the underlying statistical methodology. More
over, this approach to risk management cannot cope with sudden and sharp changes in market conditions. It neglects the possibility of discrete, large jumps in financial prices (such as exchange rates), which occur quite often.
Losses resulting from catastrophic occurrences are overlooked due to depend
ence on symmetric statistical measures that treat upside and downside risk in a similar manner.
VAR is useful, but it should be handled with care and should be used in conjunction with other measures of risk. For example, it can be complemented by a series of stress tests that account for extremely unfavourable market conditions. It is imperative, however, that VAR should not be viewed as a strict upper bound on the portfolio losses that can occur.
Expected tail loss
The expected tail loss (ETL) is a measure of risk that is also known as expected shortfall, conditional VAR, tail conditional expectation, and worst conditional expectation. The concept is very simple: ETL is the expected value of a loss that is in excess of VAR. It is defined formally as
ETL = E(L | L > VAR) (4.13) While the VAR tells us the most that can be expected to be lost if a bad event does occur, the ETL tells us what we can expect to lose if a bad event does occur.
Kritzman and Rich (2002) argue that viewing risk in terms of the probability of a given loss or the amount that can be lost with a given probability at the end of the investment horizon is wrong. This view of risk, according to them, considers only the final result, arguing that investors should perceive risk differently because they are affected by risk and exposed to loss throughout the investment period. They suggest that investors consider risk and the possibility of loss throughout the investment horizon; otherwise, their wealth may not survive to the end of the investment horizon. As a result of this way of thinking, Kritzman and Rich suggest two new measures of risk: within- horizon probability of loss and continuous VAR. These new risk measures are then used to demonstrate that the possibility of making loss is substantially greater than what investors normally assume.
Is VAR used in practice?
VAR is widely used by major companies in real life. Microsoft, for example, uses VAR as a management tool to estimate its exposure to market risk, reporting the estimated VAR figures in its annual reports. For the purpose of calculating VAR, Microsoft uses a time horizon of 20 days, which is longer than what is typically used by banks. Another difference is that Microsoft uses a confidence level of 97.5% rather than 99%, which is what is used by banks.
In 1999, Moosa and Knight (2002) conducted a survey of the practices of Australian public shareholding companies with respect to the use of value at risk analysis. The results of the survey reveal significant unfamiliarity with VAR analysis, as half of the respondents indicated that they were unaware of the existence of this technique. Financial institutions, those involved in inter
national operations and those using derivatives tend to be more familiar with the technique. Moreover, not all of the companies with VAR awareness actu
ally use the technique for measuring risk. The results of the survey produced several findings, including the following: (i) companies that do not use VAR mostly employ scenario analysis; (ii) those not using VAR claim that it is not relevant to their operations; (iii) those using VAR predominantly employ the parametric approach; and (iv) the majority of users employ back testing and stress testing. The results also revealed that financial institutions, companies involved in international operations and those using derivatives are more aware of the existence of VAR analysis and more inclined to use it, and that companies not using VAR but intending to use it are predominantly those involved in international operations and those using derivatives.
According to the Reserve Bank of Australia (2000), the VAR of major Austra
lian banks was 0.02% of their capital base, much lower than the corresponding
TABLE 4.3 VAR of majorbanks.
Country Foreign exchange risk (% of Total market risk (% of
capital) capital)
Australia 0.02 0.08
Canada 0.02 0.12
Germany 0.15 0.71
Japan 0.07 0.31
Netherlands 0.02 0.20
UK 0.03 0.16
USA 0.03 0.15
Source: Reserve Bank of Australia (2000)
figures in other countries. In Germany, for example, the corresponding figure was 0.15%. The 1999 figures are shown in Table 4.3.