Question

Suppose that a trader has bought some illiquid shares. The trader has 100 shares of A, quoted at bid $50 and offer $60, and 200 shares of B, quoted at bid $25 and offer $35. What are the proportional bid-offer spreads? What is the impact of the high bidoffer spreads on the amount it would cost the trader to unwind the portfolio? If the bidoffer spreads are normally distributed with mean $10 and standard deviation $3, what is the 99% worst-case cost of unwinding in the future as a percentage of the value of the portfolio?

Answer 1

The proportional bid-offer spreads for share A and B are 10/55 =0.1818 and 10/30=0.3333. The
mid-market values of the positions are $5,500 and $6,000, respectively. The cost, associated with
bid-offer spreads, when the portfolio is unwound is
	0.5×0.1818×5,500+0.5×0.3333×6,000 =1,500
or $1,500. The standard deviation of the proportional bid offer spreads are 3/55=0.054545 and
3/30=0.1. The 99% worst case cost of unwinding is
	0.5×(0.1818+2.326×0.054545)×5,500+0.5×(0.3333+2.326×0.1)×6,000 =2547 or $2,547.