Hi all, I'm new to the forum and hope I'm posting at the right place !
I'm doing an assignment for college and got stuck on one of the questions regarding Portfolio Insurance. I got most of it done (I think ... ) but the last part proved to be a bit challenging due to bits and pieces I can't figure out so I'm asking for your help. Here's the actual question:
A portfolio manager in charge of a portfolio worth $10 million is concerned that the
market might decline rapidly during the next six months and would like to use options on
the S&P 100 to provide protection against the portfolio falling below$9.5 million. The
S&P 100 index is currently standing at 500 and each contract is on 100 times the index.
- If the portfolio has a beta of 1, how many put option contracts should be
purchased?
My answer: 1 x (10 000 000/100 x 500) = 200 contracts
- If the portfolio has a beta of 1, what should the strike price of the put
options be?
9 500 000/ 100 x 200 = $475
- If the portfolio has a beta of 0.5, how many put options should be
purchased?
0.5 x (10 0000/100 x 500) = 100 contracts
1 contract = 100 options => 100 x 100 = 10 000 options
And the one I can't figure out:
If the portfolio has a beta of 0.5, what should the strike prices of the put
options be? Assume that the risk-free rate is 10% and the dividend yield on
both the portfolio and the index is 2%.
I started the answer the following way but soon got stuck ...
Value of index in 6 months = 500 x 1.05 = 525
Return from change in index = 25/500 = 5%
Dividends from index = 6/12 x 2 = 1%
Total Return from Index = 5 + 1 = 6%
Risk Free Rate = 6/12 x 10 = 5%
Excess Return from Index = 6 – 5 = 1%
Excess return from portfolio = ............
Any help will be much appreciated ! Thanking you in advance !
I'm doing an assignment for college and got stuck on one of the questions regarding Portfolio Insurance. I got most of it done (I think ... ) but the last part proved to be a bit challenging due to bits and pieces I can't figure out so I'm asking for your help. Here's the actual question:
A portfolio manager in charge of a portfolio worth $10 million is concerned that the
market might decline rapidly during the next six months and would like to use options on
the S&P 100 to provide protection against the portfolio falling below$9.5 million. The
S&P 100 index is currently standing at 500 and each contract is on 100 times the index.
- If the portfolio has a beta of 1, how many put option contracts should be
purchased?
My answer: 1 x (10 000 000/100 x 500) = 200 contracts
- If the portfolio has a beta of 1, what should the strike price of the put
options be?
9 500 000/ 100 x 200 = $475
- If the portfolio has a beta of 0.5, how many put options should be
purchased?
0.5 x (10 0000/100 x 500) = 100 contracts
1 contract = 100 options => 100 x 100 = 10 000 options
And the one I can't figure out:
If the portfolio has a beta of 0.5, what should the strike prices of the put
options be? Assume that the risk-free rate is 10% and the dividend yield on
both the portfolio and the index is 2%.
I started the answer the following way but soon got stuck ...
Value of index in 6 months = 500 x 1.05 = 525
Return from change in index = 25/500 = 5%
Dividends from index = 6/12 x 2 = 1%
Total Return from Index = 5 + 1 = 6%
Risk Free Rate = 6/12 x 10 = 5%
Excess Return from Index = 6 – 5 = 1%
Excess return from portfolio = ............
Any help will be much appreciated ! Thanking you in advance !
