Let's say I have fund A with 20% annualized volatility and portfolio B with 15% annualized volatility. If A and B have 0 correlation, can the combination of these funds have volatility < 15% ? Are there any papers explaining this?
The total volatility of a portfolio is calculated as follows:
Recall that Cov(a,b) is just (Correlation a,b)/(StD A * StD B). So in this case, no the portfolio could not have a total volatility of less than 15%. For this to happen, we would need negative correlation between the two assets.
Think of volatility in this case as the amount of movement in portfolio value. Only by having some degree of negative correlation between assets could one return offset the other (from a theoretical standpoint) on the same day and cause the price swing of the total portfolio to be less wild than the least volatile holding.