Dollar Cost Averaging

When banks are promoting monthly investment plans (MIP) of stocks or funds, they typically emphasize the advantage of "dollar cost averaging" (DCA). But their illustrations often give people a misleading impression that DCA is "cheaper".

Just sampling an illustration from a local bank's website:

• You contribute $1,000 monthly to a MIP for 6 months.
• The monthly unit prices during this period are $1.0, $0.9, $1.1, $0.9, $0.8 and $1.0
• Number of units bought in each month is equal to $1,000 divided by the monthly price.
• Total number of units bought during this period is 6,381.
• Weighted average cost of MIP is $6,000 / 6,381 = $0.94
• Average market price = $(1.0 + 0.9 + 1.1 + 0.9 + 0.8 +1.0) / 6 = $0.95
• So, you have got an impression that MIP lowers your average cost.

Unfortunately, this is just a trick!

Mathematically, weighted average is always lower than simple average. But why should we compare MIP's weighted average cost with the simple average price? Such comparison is only meaningful for two investable strategies. MIP is of course investable: what you need to do is to pay $1,000 per month. But how about the strategy behind the simple average price?

Simple average price implies a strategy that every month you purchase the same number of units. For comparison with MIP, the total budget must also be $6,000. How do you know the number of units to be bought? This is only possible if you know the prices in the coming 6 months in advance! But are you the omniscient God?

Obviously the strategy behind simple average price is not investable, therefore comparing it with MIP's average cost is meaningless.