In a market with 3 stocks:
- Stock A with price 25.00 USD;
- Stock B with price 32.50 USD;
- Stock C with price 50.75 USD;
Any portfolio optimization technique results in a vector of asset weights $\textbf{w}$ such that $0 \leq w_i \leq 1$ and $\sum_{i=1}^N w_i =1$. If I consider an equally weighted portfolio then: $$ w_i = \frac{1}{N}=\frac{1}{3} \approx 0.33 $$ If I am willing to invest 100.00 USD then I should buy:
- $q_1 = \frac{33.00\\\$}{25.00\\\$}=1.32$ quantity of stock A;
- $q_2 = \frac{33.00\\\$}{32.50\\\$} \approx 1.02$ quantity of stock B;
- $q_3 = \frac{33.00\\\$}{50.75\\\$} \approx 0.65$ quantity of stock C;
If stock prices are not fractionable (are they?) then I should buy, for example:
- ${\lfloor}q_1{\rfloor} = 2$ quantity of stock A;
- ${\lceil}q_2{\rceil} = 1$ quantity of stock B;
- ${\lceil}q_3{\rceil} = 0$ quantity of stock C;
With 17.50 USD of non-investable liquidity. Obviously the more one is capable to invest the more accurate will be the asset weights in relation to the absolute value of the stock price. How can retail investors deal with such a problem? Are stock prices fractionable? I can't find literature about that.