I would like to calculate an investor's average portfolio volatility as a measure of risk aversion. My problem is, that the portfolios are not continuous:
- the investor can have an open position for the first five days of the month, then have a week brake and then open further positions
- the investor can start by opening five positions, close two of them on day 3 and hold the other three until the last day of his investment horizon, which is not determined up front
So I cannot realistically calculate the end-day portfolio worth and use the series of this values to calculate day-to-day returns and from this calculate the volatility as a standard deviation of the returns. And as in the second case, the end-day worth from day 3 to 4 will drop by the amount of closed positions, however, this does not yield a loss for the investor by default, which would be the case when I compare end-day worth from day3 to day 4.
Are you familiar with approaches that would facilitate calculating portfolio volatility for such cases?