Led a team which wrote a CTA Trade Accounting/Order Management system some years back. The accountant generated the published numbers in Excel so there may be some rules of which I am unaware.
Q1) My understanding is that a CTA manages multiple managed accounts. Each account is segregated and has its own performance history. If this is the case, then how does a CTA show his track record?
A CTA has publish any of his accounts. CTAs typically have pools and then separate segregated accounts. Typically a CTA publishes a pool, but often tries to get you to invest in a "new" pool. The idea is to have cycle through a series. Having simultaneous pools allows the CTA to quote the most attractive (performance vs longevity) while leaving him the option to ditch a pool (transfer assets to other pools) when things go badly. There are probably other justifications as well.
Q2 How does client withdrawals and deposits affect the track record?
Whether a pool or a segregated account, withdrawals and deposits should not affect the track record to first order. The rules for Hedge Funds are more complex, but for a CTA, the idea is to convert assets into shares at the closing price (or as per forming documents). Starting with 1 shares of 100k. Next we have 1 share of 110k. Withdrawal change is to Then we have 0.909 shares of 100k and a check for 10k. At the end of February we have 0.909 shares of 110k. The accounting has a monthly return of 10% on both months.
I said "to first order"; because, both deposits and withdrawals create problems for the manager.
For withdrawals, he can't sell/buy-back fractional futures contracts. Depending upon the rate of redemption, there may be liquidity concerns such as money committed to physical Treasury Bills deposited as margin. A CTA has to look at his positions and judge the best thing to do for his remaining investors. He must decide which to scale back and by how much. He may, for example, close a trade early and leave another trade at its original size. Even that accounts are mark-to-market, a CTA will be reluctant to scale back a winning trade.
For deposits, the CTA will typically take larger new positions, but leave existing trades in play. As the investor it is not uncommon to negotiate this point, and some investors will insist on immediately committing their funds to the market. Even that accounts are mark-to-market, the CTA will be reluctant to add to a losing trade.
Either way, the other pool members suffer from these secondary affects.
For Hedge Funds, the asymmetries in ownership and in contract make the accounting. Although ultimately one wants the same effect as dividing things into fractional shares, the logic is often spelled-out in a convoluted (and potentially erroneous) way. I have a friend who has studies the subject, and is writing a book. The book includes a section on the pros/cons of different methods which is useful for negotiating these things.
For Hedge Funds, especially Fund of Funds, liquidity is a big concern, and I, personally, know a Hedge Fund manager whose fund was completely divested a couple of years ago even that he was beating the market and had no relevant exposure. The issue was that he offered quite liquid terms (being basically a CTA) so the Fund of Funds were able to initially meet their withdrawals by disproportionately divesting from their most liquid subfunds. Once investors see large withdrawals, they start to wonder if the last one to withdraw will find their money whole, and so large withdrawals beget more withdrawals. In this case, the investors all got their profits, fair and properly, but the employees all got sacked even that they were generating good returns without taking poor risks.
I am sure there are more details (whole books written,) but I hope my explanation helps.
