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Value at Risk (VaR) and Margin Lending – The Prime Brokerage case study

Using Value at Risk (Var) for Margin Lending Business – Prime Brokerage Case Study Practice Test Questions

Here is a short and brief case study that I would love to test you on if and when you apply to my margin lending desk or my risk management group. Over 15 years I have seen simpler variation of this question twice in an interview. Once at Goldman, once with a Citi treasurer who since then has moved to bigger and greener pastures. This year variations of this case study made it to my Risk Management final exam for my EMBA as well as GMBA students. Give it a shot, if you know this subject it shouldn’t take you more than 15 minutes on Excel to knock out answers to all 8 questions. If you don’t, wait for the solution that will hopefully be posted to this site in the next 24-48 hours.

The Value at Risk (VaR) Margin Lending Prime Brokerage Case Study

You are the head of Risk Management responsible for managing risk exposures at the Prime Brokerage desk at a large un-named bulge bracket investment bank on Wall Street. Three of your customers are Hedge Fund Manager A, Hedge Fund Manager B and Hedge Fund Manager C who all specialize in large, leveraged commodity trades.

The Prime Brokerage desk lends money on margin to hedge fund customers. As the Head of Risk Management it is your responsibility to decide and recommend a suitable margin haircut requirement in all margin lending transactions. As part of your agreement, the amount is lend against the security value of the account (the value of the commodity position) and will be liquidated if margin falls below a certain threshold. As the bank in question you are reputed on the street as “the” bank that hates writing off capital – (it is a capital offence) and since you report directly to the Board Risk Management Committee, your primary objective is to reduce the probability of capital loss.

Risk ParametersHedge Fund Manager AHedge Fund Manager BHedge Fund Manager C
Commodities Traded with portfolio weightsOil (50%), Gold (50%)Gold (100%)Oil (80%), Gold (20%)
Holding period of Trades20 days3 months6 months
Equity in Trades10%5%5%
Liquidation days (based on size of position as a percentage of market volume)30 days90 days270 days
Size of position500 Million US$1.5 Billion US$5 Billion US$
The attached MS Excel sheet includes the relevant data set (commodity prices for Gold and Oil). Please use the data set to calculate.

Value at Risk Margin Lending Prime Brokerage Case Study Practice Test Questions

a) Volatility for Oil and Gold for the complete period of the data set (10 points)

b) Portfolio volatility for Hedge Fund Manager A, Hedge Fund Manager B and Hedge Fund Manager C (15 points)

c) Suggest a suitable deposit (margin account / account equity) that each hedge fund manager should agree to make before your desk will release funds? (10 points).

Should this deposit (margin) be linked to the holding period of trades or the number of days it would take to liquidate the position? (5 points). The objective of the margin is to secure the interest of the desk and protect it against adverse price movement if the desk is forced to liquidate the position of the hedge fund.

d) Your technology and operations team suggests that in order to reduce the systems overhead, only one margin requirement should be charged across all customers and commodities. Your sales team agrees. Is this a good idea or bad idea? In 100 words or less describe your reasoning (10 points)

e) Using the Black Scholes Merton Structured approach, calculate the probability of default for each Hedge Fund under your suggested Margin regime? (30 points)

f) Using Value at Risk as a tool, create a simple model for calculating Loss Given Default (LGD) for each of the three Hedge Fund Managers.

Loss Given Default would be based on the worst case price that you would end up selling the Hedge Fund’s commodity portfolio if they fail to meet a margin call. Your holding period as the bank would be based on the liquidation period required to liquidate the portfolio and you would be subject to inventory losses on account of volatility as you try to sell the portfolio. Your loss should partially (or completely) be offset by your customers margin deposit. (15 points)

g) Your Margin requirement regime has now been reviewed by the Board of Directors and in their infinite wisdom that Board has suggested a change in your calculation process. Margin requirements should now be set in a such a fashion that the probability of default (PD) measure as per your PD model should not exceed 2% for any client. In addition loss given default after taking the margin under account should not exceed 5% of net exposure. Please recalculate your margin requirements and share your results. (30 points).

h) For a presentation to your board, in a simple table present a side by side comparison of the following metrics for each of the hedge fund manager

  1. Position Delta (%)
  2. Margin requirement
  3. Probability of Default
  4. Loss Given Default

With your new margin requirements do all hedge fund managers now represents equal risk? Plot the four elements above in the form of a graph against rising and declining volatility. Or is there a difference between them? Which one of these would you like to lend more? Exposure to which one of these should be reduced? (25 points)

Need the solved solution – Prime Brokerage Margin Lending Risk Management Case Study – Solved Solution.

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