An interesting discovery! An intern at a quantitative hedge fund examines the daily returns of around

$1000$ stocks over one year $($which has $250$ trading days$).$ She tells her supervisor that she has discovered

that the returns of one of the stocks, Google $($GOOG$),$ can be expressed as a linear combination of the

others, which include many stocks that are unrelated to Google $($say$,$ in a different type of business or

sector$).$

Her supervisor then says: $$It is overwhelmingly unlikely that a linear combination of the returns of

unrelated companies can reproduce the daily return of GOOG. So you$$ve made a mistake in your

calculations.$$

Is the supervisor right? Did the intern make a mistake? Give a very brief explanation