Two short-option desks

Two desks each sell a deep out-of-the-money option. Each desk's one-month loss is $-0.2$ (a gain of ₹20,000 from premium) with probability 0.97 and $+5$ (₹5 lakh) with probability 0.03, in ₹ lakh. The desks' outcomes are independent. (a) Compute each desk's 95% VaR. (b) Compute the 95% VaR of the firm (both desks). (c) Compute each desk's 95% ES and the firm's 95% ES from definition (14.10). Verify subadditivity. (d) Which measure would a risk manager allocating limits to desks prefer, and why?