Should you invest your available capital all at once, or spread it over several months? Compare the final value and gain of each strategy at a given annual return.
Same total for both strategies
Assumed market return for both
Lump-sum investing deploys your full capital immediately, giving every dollar maximum time to compound. DCA spreads the same total over weeks or months, reducing the risk of investing everything at a market peak.
Historical research (Vanguard, 2012; various academic studies) shows that lump sum outperforms DCA roughly two-thirds of the time in trending markets, simply because markets rise more often than they fall.
Every month you wait with DCA means some capital misses a month of growth. At 10%/yr, 12 months of missed compounding on half your capital costs ~5% of its starting value — that gap shows up in the final number.
The math is identical, but the risk profile differs. Lump-summing into a single stock concentrates timing risk. For broad index funds, time in the market matters more than timing the market.
XIRR (Internal Rate of Return with exact dates) measures the annualized return on capital deployed, accounting for timing. DCA XIRR ≈ the market return because each dollar grew at the same rate for its specific duration. The difference shows up in final value, not XIRR.