Mathematically the research suggests that lump sum will beat DCA, or my favorite, VCA (Value Cost Averaging) because there is an inherent drag on returns by the money on the side lines that cannot compete with the long term growth in equities. The low returns on cash right now makes this especially true.
Psychologically the answer may be to do DCA or VCA anyway, because in the short term it is quite possible your lump sum investment will go down after you buy before it goes up.
Value Cost Averaging involves 1) picking a time frame to invest-.
2) picking your investment intervals-
3) making an estimate of what return you expect
4)investing whatever amount it takes to bring your portfolio up to the expected return
Example:
you pick a 24 month time frame
time interval every 6 months. This would give 5 investments at 0, 6, 12, 18, and 24 months.
6% return yearly or 3% return expected every 6 months
Invest 1/5 to start or in your case $50,000
6 months later it has grown-by 3% ($51,500) so you put in another $50,000. If it had grown more than 3% reduce your next investment by however much it overshot the expected return. If it has returned less than 3% or lost money, put in enough to bring the total up to $51,500 and then add your planned $50,000. You are putting in more when low and pitting in less when doing well. The theory being that the market will likely reverse the trend sooner rather than later so you are buying more on the dips and buying less at the peaks.
Once you have exhausted your $250,000--return to your regular programming.