Question

Using the portfolio and hedge ratio from the previous question, and assuming the S&P 500 intitial value is 3109.55.

What is our portfolio value if the market drops 6%?

What is the change in value of our puts?

What is our total profit or loss?

Answer 1

Value of Portfolio = $ 1,297,282.50

If market drops by 6%, our portfolio will drop by = portfolio beta x % change in market portfolio

If market drops by 6%, our portfolio will drop by = 0.905 x -6% = -5.43%

Therefore change in portfolio value = $ 1,297,282.50 x -5.43%

Therefore change in portfolio value = -$70,442.44

Therefore our portfolio value = $ 1,297,282.50 - $70,442.44

Therefore our portfolio value = $ 1,226,840.06

% Change in put options = change in market portfolio x delta

% Change in put options = -6% x -0.4278

% Change in put options = +2.5668%

Position in put options = Original portfolio value x hegde ratio

Position in put options = 1,297,282.50 x 2.1157

Position in put options = $2,744,660

Therefore change in value of put options = 2,744,660 x 2.5668%

Therefore change in value of put options = $ 70,449

Therefore Total gain or loss = -70442 + 70,449

Therefore Total gain or loss = $7 or Nil

{Since portfolio is hedged, total gain must be nil. Difference of $7 is due to rounding off}