The standard deviation of a portfolio can only be reduced to the level of the risk-free asset in the portfolio. Essentially in any portfolio of investments, the standard deviation can only be reduced to the level of the instrument that has the smallest standard deviation. Even in the so call "risk free" assets, there can be a small standard deviation and the overall SD cannot be brought down further than that, as it is an average, no matter what weight distribution each instrument holds, it is not possible. It is possible to reduce the standard deviation to this level but only if you remove all other instruments from the portfolio, which would then just make it and investment in a "risk-free" asset. Therefore, technically it is not possible to hold a portfolio that can reach this level, as the more risky assets with higher standard deviations would increase the overall SD. You are able to get the SD fairly close to that of a risk free asset but it will never be at the same level. 

Theoretically if an investor were to make a portfolio of investments that have inverse returns, they could reach a 0 SD, as the two would essentially cancel each other out, leaving the investor with no risk of variability. Realistically this approach is nearly impossible to obtain because it is very challenging to find two securities that are exactly inverse of each other at the same time and there is no guarantee that the variances wont change in the process. There are also other market limitations that would make this impossible like transaction costs or lack of liquidity. Investors also have no control over the external environment that affect asset prices, which would affect the SD levels of the securities in the portfolio.

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