Vertical sharing (quota-sharing) of a risk will not lower the total exposure=20=
ratio of the risk itself=2E =20=
However, vertical sharing will reduce the impact an added risk has on the=20=
exposure ratio of a portfolio=2E
In other words, vertical sharing of a risk will reduce the exposure ratio for=20=
the portfolio relative to taking the entire risk=2E=20=
See study manual question A19=2E (96 #11)=2E
The original portfolio has a SD of 100 and a mean of 1000, for an ER of 10%=2E
If a risk is added with a SD of 50 and a mean of 100, the new portfolio ER is=20=
(100^2 + 50^2)^1/2 / (1000+100) =3D =2E1016
If only 83% of this risk is taken, the portfolio ER is lower, (100^2 +=20=
41=2E666^2)^1/2 / (1000+83=2E33) =3D =2E1000
Taking even lower shares of this risk will further reduce the new portfolio=20=
exposure ratio=2E
Hope this helps=2E
Ben W