Discuss about the Value At Risk Bound With the Variance Constraints.
The calculation of marked to market value reveals that the bank holds total value of $ 597436.03. The maturity period of US government bond is 2 years; on the other hand, German government bonds have maturity values of 5 years. The yield to maturity for annual for US government bond was 2.278%; however, for German government bonds, it was negative as indicated in the calculation. The calculation is based on certain assumptions 1) annual coupon rate of US government bond is 2.5% whereas, for German government bond is nil. However, the annual rate is considered rather than semi-annual rate. Since the coupon rate is equal to YTM, these bonds are par value bond. Simultaneously, Exchange Rate, i.e. EUR: USD is 1.2395, and it was necessary to calculate because the bank is based in the US. The current price of US government bond, German, German government bonds, and cash is $99,920.79, € 3, 01,383.82 and 100000.00 respectively. Thus, total marked to Market Value in USD, $ 597436.03.
The bank portfolio includes various risks including exchange rates, interest rates, as well as default rate (Chu, Mathieu and Mbagwu, 2018). In case of present US bank, fluctuations in U.S. interest rate, Germany interest rate as well as exchange rate changes in USD: EUR are main risk factors affecting the portfolio. However, certain default risks are applicable on the US bank portfolio. It has been revealed that Local Bank has a strong bias toward risk mitigation. On the basis of correlation analysis, it can be stated that 5 Yrs German government bonds interest rates and exchange rates of USD and ERU are weakly correlated. However, there is a significant negatively correlated relationship between exchange rates.
Based on the correlation analysis, it can be interpreted that the U.S. based bank’s capital can be allocated in relation to the movement in USD: EUR exchange-rate. It has been assessed that USD appreciates in against EUR in the near future; therefore, German interest rate and the U.S. interest rate will be declined in future that will lead to increase in the prices of German Bond. The company will enjoy benefits of selling a portion of the German bond to earn good interest rates.
According to the given scenario, a slight increase in US yield by 50 bases lead to decline in German bond by 25 basis points, with a 1% appreciation in Euro. The face value of US government bond, German government bond and currency value is USD 100,000, EUR 300,000 and EUR 100,000. YTM annual after the charge is 2.75% and 3.25% on the other hand, YTM has 2.731%. The weights of each asset are 17.32%, 61.01% and 2.68%. However, total marked to market value of USD $ 571762.74. The yield to maturity rates before changes in domestic bonds is 2.28% and on foreign brands are -0.09%.
The rates of return for each asset on domestic bond are 1.28%, 0.16% and -1.09% for all three heads are a domestic bond, foreign bond and EUR cash. The movements in yield .50%, -.25%, -1% and returns of each asset 17.32%, 61.01% and 21.68%, at the end, the total portfolio 0.08%, which is too less.
Value-at-risk (VAR) is a famous probabilistic measure of the value of a portfolio considering the risk of loss for an investment (Bernard, Rüschendorf and Vanduffel, 2017). The financial risk involved with investment and the commercial bank can be measured on specific portfolios. VAR for a portfolio can be calculated by considering a variety of tools. Thus, a single organisation which is using different methods of calculating Value at risk can have a variety of results. The main methods of VAR calculation include correlation, Monte Carlo simulation and historical simulation; however, in this report, the correlation has been used. The basic information which is required for VAR calculation is the distribution of outcomes for the risk portfolio for some future period. Therefore it can be said that the current value and future values are the basis for VAR. The information used for calculating includes individual returns that are normally distributed along with confidence level (95% and 99%) (Dahl, 2017). The historical data portfolio or including bounds can be used to calculate mean, correlation and variance, simultaneously; the information related to interest rates and exchanges rates are also required.
Bernard, C., Rüschendorf, L. & Vanduffel, S., (2017). Value?at?risk bounds with variance constraints. Journal of Risk and Insurance, 84(3), pp.923-959.
Chu, L., Mathieu, R. & Mbagwu, C., (2018). The association between firm fundamentals and bank interest rates under different measures of risk. Advances in Accounting.
Dahl, R.E., (2017). A study on price volatility in the aquaculture market using value-at-Risk (VaR). Aquaculture Economics & Management, 21(1), pp.125-143.
Kremer, J., (2018). Value at Risk. In Marktrisiken (pp. 87-124). Springer Gabler, Berlin, Heidelberg.