Instructions:

Estimating Market Value at Risk You are a market risk manager in Financial Institution XYZ. The trading book portfolio currently consists of • A position in 1-year U.S. Treasury Bill (zero coupon bond) with total face value ,000; • 2,000 shares of the S&P500 index; • A foreign cash position in British Pound of £50,000. The portfolio is denominated in U.S. Dollar. You estimate the market VaR via two approaches: the Risk Metrics Approach and the Historical Simulation Ap- proach. For both approaches, the risk factors are selected as: (1) the 1-year treasury yield; (2) the S&P500 index close value (3) the exchange rate close value (the value of U.S. Dollar per unit British Pound). The daily data of factor (2) and (3) can be downloaded from Yahoo Finance at https://finance.yahoo.com; the ticker for S&P500 index is “GSPC, and the ticker for the exchange rate is GBPUSD=X. The daily data of factor (1), i.e. 1-year Treasury Yield (quoted in percentage) can be found on the website of Federal Reserve Bank of St. Louis at https://fred.stlouisfed.org, with ticker DTB1YR. Under both approaches, on any given trading day, the VaR estimation is done by using the factor data on that day, as well as over the past 500 trading days. Questions: (a) What is the total portfolio value on March 2, 2020? (b) What is the 1-day 99% Market VaR on March 2, 2020, estimated by the Risk- Metrics and the Historical Simulation approach respectively? What is the per- centage of the VaR in the total portfolio value on March 2, 2020, under each approach? Assume no trading occurs in this portfolio, what are the daily portfolio losses over the next 10 trading days (that is, from March 3, 2020 to March 16, 2020), according to the data during this period? On how many days (out of these 10 days) does the loss exceed the 1-day 99% VaR value under each VaR estimation approach (calculated in (b))? Can you explain what you observed from this? (d) On March 16, 2020, you updated the estimation (using the data on this day, as well as over the past 500 days). What is the 1-day 99% Market VaR estimated on this day under each approach? What is the percentage of the VaR in the total portfolio value on March 16, 2020, under each approach? (e) Compare the VaRs and the percentages you obtained in (b) and (d). What differences do you observe comparing these numbers? Can you explain them? Remarks: • For the Risk Metrics Approach: – The changes in the risk factor i, that is, Ayi, are calculated as the difference between the values between adjacent trading days. As a result, there are 500 changes for each factor. For each risk factor i, the standard deviation Av is to be estimated as the sample standard deviation of the 500 changes; for each pair of risk factors i #j, the correlation coefficient pij is to be estimated as the sample correlation using the 500 changes of factor i and factor i. The estimation of sample standard deviation and correlation can be done using the STDEV and CORREL function in Excel, respectively. • For the Historical Simulation Approach: – 500 scenarios are to be generated. Data with Misaligned Dates: If the factor data have misaligned dates, use the S&P500 dates as the benchmark. For the remaining two factors: if data is available on a date without available S&P500 data, discard the data; if data is unavailable on a date with available S&P500 data, use the last available data. • When calculating the Treasury bill value, assume that it has a remaining life of 1 year
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