True or False?
The answer is false. The return to the portfolio will always be less variable than the returns to the highest variability assets in it. But it need not be less variable than the variability of the return to the least variable asset in it. One could have less risk by holding only the asset with the least variable return---if one could determine which asset that is.
Identifying which asset has the least variable return is, of course, an impossible task unless one is prepared to assume that the asset that has had the least variable return in the past will continue to have the least variable return in the future. To make this assumption would be unwise. Even a casual knowledge of economic history will verify that nothing is certain---informative as it might be, the past is not an iron-clad guide to the future.
In addition, the issue of the average return that can be expected from the single least-variable-return asset must be considered. It might well be substantially less than the return to the multi-asset portfolio.
One also has to rule out the possibility of investing in a single asset earning a fixed real coupon yield, issued by a Government with no history of default. While the risk from holding such an asset will be virtually zero, the return from holding it will almost surely be less than the return from a large diversified portfolio of common stocks---otherwise, nobody would hold common stocks. No portfolio of common stocks of any feasible size would be expected to have a return with zero variability---there will be too much positive correlation between the individual stock returns.