I have been trying to construct an efficient portfolio based on 5 assets named A, B, C, D and E. Because of the most rewarding risk-return characteristics of C and D, the result suggested 35% and 65% combination respectively. The portfolio created will have 10% return and 5% standard deviation. However, when I used C and D solely to construct a portfolio under the same way, the return significantly dropped to 5.5% with the same standard deviation. I understand the former favorable result is due to the diversification effect of A, B and E. But if I am going to invest in C and D with 5% risk, should I expect its return be 10% or 5.5%?
It seems like you didn’t calculate the returns correctly in one of the scenarios. If the efficient frontier portfolio only contains C and D, then you should be able to easily calculate the weighted average returns (return of C x 0.35 + return of D x 0.65) to see whether 10% or 5.5% is correct.
Something is strage here, since it looks like the optimizer looked at A B C D E and said: 35% C and 65% D for a 10% return 5% SD target (which would be a darned nice sharpe ratio for only two assets, even at normal interest rate levels). 35% and 65% add up to 100%, so if you are fully invested (all asset weights adding up to 100%) that means you have 0% A B and E, which is the equivalent of optimising a portfolio with only C and D in it.
Or you have a long-short portfolio where you have long C and D and short A B and E, where the sums add up to 100% (or maybe 0% if you are self funding).
Or maybe you have misinterpreted your homework problem (I’m guessing, because 2 asset portfolios with sharpe ratios between 1 and 2 only pop up in homework problems, as far as I have seen), and the 35% 65% portfolio is the one you get when you only put C and D into the optimizer.
Diversification is generally a risk-reducing feature (though individual assets will sometimes be classified as return enhancers or risk reducers based on whether their sharpe ratios are higher or lower than the existing portfolio). So if you levered up the C+D portfolio to deliver a 10% return, you’d then be able to check if the accompanying risk is higher or lower than the 5% it says that the A+B+C+D+E portfolio will deliver.