No - doesn't work that way. You owe ordinary income taxes on the amount of the IRA withdrawal attributable to pre-tax contributions and earnings. I assume you are over 59-1/2 and so don't owe an early withdrawal penalty as well, correct? Your IRA plan administrator will send you a 1099-R form in January that will show the $200K as a distribution to you - you report this on line 15 of Form 1040 as "Pensions and Annuities."
As for the $100K loss - you should receive a from 1099-B in January from whomever you invested with that documents the proceeds from the sale of the stock investments - this gets reported as a loss on Schedule D. However - when you say this person was investing for you "privately" - what does that mean? Did you write him a check which he used to buy and sell in his own acount? I certainly hope not - but post back and let us know. In any event, the 100K loss will be used to first offset any other capital gains you may have, and then any additional loss
up to a max of $3K can be used to offset your ordinary income. Any loss in excess of $3K is carried into future years to act as an offset then. So if you have no other income, or gains or losses, you'll be reporting $200K in income less $3K in losses, for total txable income this year of $197K. See the following for more information on reporting capital gains:
Tax Topics - Topic 409 Capital Gains and Losses