Dr. Jayanthi Sankaran
Well-Known Member
Hi David,
I seem to be stuck on Portfolio Insurance not able to move forward unless I understand it thoroughly. This is taking a lot of valuable time from Fixed Income which will be the next topic. Sorry about bombarding you with the same topic.
As referenced above and cited below:
Question #18.20
Suppose that $70 billion of equity assets are the subject of portfolio insurance schemes. Assume that the schemes are designed to provide insurance against the value of the assets declining by more than 5% within one year. Making whatever estimates you find necessary, calculate the value of the stock or futures contracts that the administrators of the portfolio insurance schemes will attempt to sell if the market falls by 23% in a single day.
Answer by Hull
We can regard the position of all portfolio insurers taken together as a single put option. The three known parameters of the option, before the 23% decline are S(0) = 70, K = 66.5, T = 1. Other parameters can be estimated as r = 0.06, sigma = 0.25 and q = 0.03. Then,
d1 = [ln(70/66.5) + (.06 - 0.03 + .25^2/2)]/0.25 = 0.4502
N(d1) = 0.6737
The delta of the option is (e^-qT)*[N(d1) - 1] = e^-0.03*[0.6737 - 1] = -0.3167
This shows that 31.67% or $22.17 billion of assets should have been sold before the decline.
After the decline, S(0) = 53.9, K = 66.5, T = 1, r = 0.06, sigma = 0.25 and q = 0.03
d1 = [ln(53.9/66.5) + (.06 - 0.03 + .25^2/2)]/0.25 = -0.5953
N(d1) = 0.2758
The delta of the option has dropped to e^-0.03*[0.2758 - 1] = -0.7028
This shows that cumulatively 70.28% of the assets originally held should be sold. An additional 38.61% of the original portfolio should be sold. So far so good!
I am a little unclear about this bit: 'The sales measured at pre-crash prices are about $27 billion. At post-crash prices they are about $20.8 billion".
Thanks!
Jayanthi
I seem to be stuck on Portfolio Insurance not able to move forward unless I understand it thoroughly. This is taking a lot of valuable time from Fixed Income which will be the next topic. Sorry about bombarding you with the same topic.
As referenced above and cited below:
Question #18.20
Suppose that $70 billion of equity assets are the subject of portfolio insurance schemes. Assume that the schemes are designed to provide insurance against the value of the assets declining by more than 5% within one year. Making whatever estimates you find necessary, calculate the value of the stock or futures contracts that the administrators of the portfolio insurance schemes will attempt to sell if the market falls by 23% in a single day.
Answer by Hull
We can regard the position of all portfolio insurers taken together as a single put option. The three known parameters of the option, before the 23% decline are S(0) = 70, K = 66.5, T = 1. Other parameters can be estimated as r = 0.06, sigma = 0.25 and q = 0.03. Then,
d1 = [ln(70/66.5) + (.06 - 0.03 + .25^2/2)]/0.25 = 0.4502
N(d1) = 0.6737
The delta of the option is (e^-qT)*[N(d1) - 1] = e^-0.03*[0.6737 - 1] = -0.3167
This shows that 31.67% or $22.17 billion of assets should have been sold before the decline.
After the decline, S(0) = 53.9, K = 66.5, T = 1, r = 0.06, sigma = 0.25 and q = 0.03
d1 = [ln(53.9/66.5) + (.06 - 0.03 + .25^2/2)]/0.25 = -0.5953
N(d1) = 0.2758
The delta of the option has dropped to e^-0.03*[0.2758 - 1] = -0.7028
This shows that cumulatively 70.28% of the assets originally held should be sold. An additional 38.61% of the original portfolio should be sold. So far so good!
I am a little unclear about this bit: 'The sales measured at pre-crash prices are about $27 billion. At post-crash prices they are about $20.8 billion".
Thanks!
Jayanthi
