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Anna opened a 100-share short position in DEF stock at the bid-ask prices of 41.10-41.20. She later added another 100 shares of DEF to her short position at the bid-ask prices of 36.10-36.20. When she closed her total position of 200 shares, the bid-ask prices were 31.00-31.10. The commission rate is 2.0%. a) What is Anna’s profit or loss? b) If the market interest rate is 4% and the short rebate rate is 3%, what is the lender’s gain from lending 200 shares to Anna? Ignore profit from commissions and spread

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Answer:

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Explanation:

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a. The annual profit or loss is 1778.80

b. The lender gain should be 77.20

Calculation of annual profit and the gain is:

a. Anna shorts 100 shares at 41.10

And,

Anna shorts another 100 shares at  36.10

So,

The average price of 200 shares short is 38.60

Now

Anna covers 200 shares at 31.10

So,

Loss per share is 38.7-31=7.5

Now

Commissions on short and the cover is

=  (38.7 × 200+200 × 31) × 2%

=278.8

So,

Total loss is

= 7.5 × 200+278.8

= 1778.80

b. Lenders gain should be

=  Market interest - Short rebate

=4% - 3%

=1%

So,

= 38.60 × 200=7720 × 1%=77.20

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