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I'm going to do some old school value investing, holding around ten stocks.

Other than investing say 2k every month, I also have around 100k in savings. I'm contemplating investing these alongside my 2k, say over the next 3 to 5 years.

I don't want to take too much risk in regard to market timings. Any thoughts on the period for investing the additional sum?

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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.

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