# VaR, Capital Attribution and Profitability

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Citigroup reports its proprietary trading activities as a business segment it calls “Principal Transactions.”

The attached spreadsheet contains a table of the profits/(losses) for the Principal Transactions segment, by transaction type, over the last 16 years (2003-2018). (This data was taken from Citigroup’s 10-K reports, filed with the SEC, with some reformatting to match the presentation format of 2018, and ignoring an immaterial amount of “Other”.)

Note: For all questions, assume (1) a Normal Distribution; (2) mean future return of zero; and (3) ignore any autocorrelation.)

1. Line of Business VaR vs. Total VaR
1. Using a lookback period of 2003-2018 (i.e., using all 16 years of data), what is the one-year 99% confidence level VaR for each transaction type?
1. What is the one-year 99% confidence level VaR for the Principal Transactions business segment as a whole?
1. How does the VaR of the total business segment compare to the sum of the VaRs of the individual transaction types? Explain in words what causes this difference.
• Varying Lookback Periods
• Using a lookback period of just the most recent five years (i.e., 2014-2018), what is the one-year 99% confidence level VaR for each transaction type? What is the one-year 99% confidence level VaR for the Principal Transactions business segment as a whole?
• Compare the VaR of the 2014-2018 lookback period, to the VaR of the 2003-2018 lookback period, both by transaction type, as well as a whole. Briefly discuss the implications of your comparison.
• Regulatory Capital Requirement

Assume that regulators require Citigroup to keep a multiple of 3 times VaR for capital adequacy.

1. For the one-year 99% confidence level VaR, how much capital would be needed for the overall Principal Transactions business segment, if using a lookback period of 2003-2018?
1. How much capital would be needed for the overall Principal Transactions business segment,  if using a lookback period of 2010-2018?
1. Using the lookback period of 2003-2018, allocate the required capital of the overall Principal Transactions business segment to the individual transaction types, based on their relative contribution to VaR.

Citigroup management wants to review the risk-adjusted returns of the Principal Transactions business segment. Using the required capital calculated in Question 3, for the lookback period 2003-2018:

1. What was the Return on Required Capital (“ROC”) for 2018 for the overall Principal Transactions business segment as a whole? (ROC is equal to the reported revenue divided by required capital.)
1. What was the ROC in 2018 for each transaction type?
1. What was the ROC for the average revenues in the post-Credit Crisis years (2010-2018), for each transaction type? What recommendations might you make to management to improve risk-adjusted profitability?

Useful hints and reminders:

• When the mean of future returns is assumed to be zero, VaR is calculated as the standard deviation multiplied by number of standard deviations that corresponds to the chosen confidence level.
• The Excel function for calculating standard deviation is =STDEV.P(datapoint1, datapoint2, …).
• The Excel function for calculating number of standard deviations is =NORM.S.INV(confidence level as a percentage).

Submission Guidelines:

Please submit the text portion of the assignment as a Word document

Please submit the calculation portion of the assignment as an Excel file. Full credit for correct answers will only be awarded if it includes formulas showing your calculations.