Question

An institution holds 10million shares of one company and 50million ounces of a commodity. The shares are bid $89.5, offer $90.5. The commodity is bid $15 offer $15.1. What is the liquidation cost in normal markets?

A protection buyer purchases 6-year protection on a company at a default swap spread of 400bp. The face value of the protection is K1, 000,000 million. What is the premium payment per year assuming that payments are done monthly?

Answer 1

1. The mid-market value of the position of the shares is equivalent to:

$10\times90=900$

Note that the mid-market price is halfway between the offer price and the bid price.

The mid-market of the position in the commodity is;

$50\times15.05=752.5$

The proportional bid-offer spread for the position of the shares is equivalent to

$s=\frac{offer price-bid price}{mid-market price}=\frac{90.5-89.5}{90}=0.0111$

Similarly, the proportional bid-offer for the position in the commodity is:

$s=\frac{offer price-bid price}{mid-market price}=\frac{15.1-15}{15.05}=0.0066$

And hence the cost of liquidation in a normal market is:

$900\times0.0111\times0.5+752.5\times0.0066\times0.5=4.995+2.48325=7.47825$

2.

The face value of the protection is K1, 000,000 million, rate 0.04

The protection buyer makes monthly payments 

$P=K\times r\times k$

$k=\frac{6}{6\times12}$

year count in months

$1 000 000\times 0.04\times\frac{6}{6\times 12}=3 333.33$