Vanguard's research says you'll probably yield more by investing the lump sum immediately.
https://personal.vanguard.com/pdf/ISGDCA.pdf
In Figure 1, we compare the historical performance of immediate and systematic investing across three markets: the United States, the United Kingdom, and Australia.
For the systematic plan, we invest the cash in a balanced 60% stock/40% bond portfolio in 12 equal monthly installments. We then evaluate the returns of both immediate and systematic investing across rolling 12-month historical periods. (See page 7 for additional details about the methodology.)
In each market, immediate investment led to greater portfolio values approximately two-thirds of the time. On average, immediate investment outperformed systematic
implementation by a high of 2.39 percentage points in the United States and a low of 1.45 percentage points in Australia. These findings are unsurprising. Stocks and bonds
have historically produced higher returns than cash, as compensation for their greater risks. By putting a lump sum to work right away, investors have been able to take advantage of these risk premia for a slightly longer period.
We also compared immediate and systematic plans over shorter and longer investment intervals using the same 60/40 portfolio. As the interval increased, immediate investment
outperformed more frequently. In the United States, for example, immediate investment of a lump sum outperformed a six-month series of investments in approximately 64%
of the historical periods. Over a 36-month interval, immediate investment outperformed approximately 92% of the time.