This is perhaps a rather silly question for the more experienced people in the community but it has been puzzling my mind for a while.
Let's say we have a portfolio of 10.000 dollar.
We will apply mean-variance model of Markowitz:
$$E[R_P] =w_1X_1 + w_2X_2$$
where $E[R_P]$ is the expected portfolio return and $w_i$ the weight for the return for a given asset $X_i$. I assume an investment horizon of one year.
So let's say the portfolio consists of stocks($X_1$) and bonds($X_2$) and it is an equal weighted portfolio (50/50).
The return will be 4% for bonds and 6% for stocks during the year. The return of the portfolio for one year is then
$$E[R] = (0.5 \cdot 0.06)+(0.5 \cdot 0.04) = 0.05$$
Now let's say the stock market had a really good run and in 6 months time, the target return of 6% was reached.
Now there are two possibilities according to me:
- You can continue the equity position and hope for an anything above 6% return.
- You close your equity positions and now you have 51.4% (6% return on 5.000 dollar) of your portfolio in cash that can either be put back in stocks or bonds.
My questions are as following:
- Are my assumptions about a certain time frame correct?
- Is there a method that can solve based on the standard deviation of bonds and equities to see where the cash should go?
I don't know if I have gone completely off the deep or not, any feedback would be more than welcome!