From Five Ways to Avoid Getting Madoffed :

Ask the advisor how often and by what means you can obtain an independent and verifiable statement of your investments. Here's why: If the investment advisor is also responsible for preparing and issuing customer statements and reports, then that should raise a warning flag.

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From Madoff Investors Missed Red Flag:

Investors may have missed one major red flag that could have tipped them off that something was amiss at Bernard Madoff's now-infamous hedge fund: He acted as his own prime broker.

Nearly all hedge funds use prime brokers, which provide critical back office functions, such as settling trades. Run by large banks, the prime brokers also frequently lend to the hedge funds and, if they start posting heavy losses, the prime broker may require them to post additional collateral. "There could not be a bigger red flag," says Gary Shugrue head of Ascendant Capital Partners, a fund of hedge funds based in Radnor, Penn. "The prime broker really acts as the custodian would at a traditional asset manager. It's where the money is."

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From Opinion: Madoff Implosion Is No 'Tragedy':

Madoff was making 1% per month, year after year with no losses and nobody else on Wall Street or anywhere could explain his returns. Even Madoff didn't explain it.

Plenty of people openly told the SEC and the media that he had to be either running a Ponzi scheme or doing something else illegally. Nevertheless, so many of these "sophisticated" investors piled their money into his fund. Many of them invested a huge percentage of their personal net worth, charitable trust, inheritance or future bequests to their heirs. What were they thinking?

Many were just following their friends. Many were lazy. Many were stupid. Many were greedy. None of them stopped to think that Madoff's returns were literally impossible unless he was doing something illegal.

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From Kass: Madoff Was Made Up:

About three years ago, an investor of mine, who already was an investor with Madoff, came to me and asked my advice as to whether he should add to that investment. I requested and received his monthly brokerage statements. Now, I am very good with math, but after hours of analysis over a weekend, I could not understand how he generated his returns and suggested that he should withdraw his capital. (The investor discarded my advice and decided to add materially to his investment.)

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