Your first investment
Let’s say you’ve decided to invest in the market for the first time. You buy two shares of Tesla for $100 total, at a price of $50 each, hoping to see it go up in value in the coming weeks.
When you check back in a week, the price of one share has dropped down to $40— your portfolio has lost value. For a moment, you consider not buying anymore shares, or even selling off your existing shares to cut your losses, but then you think about how you would respond if something you really wanted to buy was on sale. Why would a decrease in price make you want to buy less, when you are effectively getting a discount?
You buy two more shares at $40 each, while your friend tells you that you are wasting money and proceeds to sell off his Tesla shares at $40 each. In a week, Tesla shares jump back up in value to $50.
The average cost
Let’s do a quick analysis of the scenario above.
While your friend did cut off their losses at just $20, they missed out on two significant opportunities — being able to buy shares at a lower price of $40, and profiting from the rise in share prices from $40 to $50. We can see the consequences of this from the average cost of a share in both portfolios — while buying two more shares at $40 has lowered your average cost from $50 to $44.4, theirs still remains at $50. Subsequently, continuing to keep your shares exposes you to the increase in share prices from $40 to $50, which turns your original loss into a massive gain.
This is dollar cost averaging — the investment strategy of buying assets worth a fixed amount every period, regardless of how the market performs. As a result, when share prices are high, less shares are bought and vice versa, even with the same amount of cash being invested every period.
Similar to how people would buy more during a discount and less during a price hike, DCA ensures that when prices are low, you get more shares at a discount for the same amount invested and vice versa for when prices are high. Why is this so?
Unrealized profits
What determines our gain or loss on an investment is ultimately the difference between share prices and the average cost. As seen in the first table, the loss of $20 in Week 2 is exactly the same as the difference in share prices and average cost multiplied by the total shares. We can visualize this as a simple formula:
With PnL standing for profits and losses, ΔP being share prices minus average cost and Q being the quantity of shares. As mentioned prior, buying shares at a lower price will always lower the average cost of shares, as seen with how the average cost was lowered from $50 to $44.4 per share by buying more shares in Week 2. While this does not reduce the unrealized losses at the moment, this increases Q from 2 to 4.5 and reduces the magnitude of ΔP, which is currently negative.
In Week 3, when share prices appreciate back up to $50, ΔP has now flipped to being positive, and with a higher value of Q than prior, we have turned our unrealized losses into gains.
In contrast with the first example, if you had not bought more shares in Week 2 out of fear of share prices going lower, not only would Q still be at 2, ΔP would be lower in Week 2 and 3 than if you had continued to invest weekly. As a consequence, your unrealized gains Week 3 are zero.
Weighted vs. Inverse
It is clear by now that share prices and shares bought move inversely — as one goes up, the other goes down. We can go further with this using another investment strategy called weighted dollar cost averaging, or weighted DCA, where we actually invest more in cash when share prices go down and less when they go up, making the inverse relationship between share prices and shares bought even stronger. In comparison, investors who respond easily to fluctuations may do what is called inverse dollar cost averaging, or inverse DCA, where they buy more out of FOMO when share prices go up and buy less out of fear when they go down.
As a demonstration, we can visualize the three DCA methods as such:
The first column represents the percentage change in share prices between each period, and the rest being a multiplier for the periodic amount of cash invested. Using a market that fluctuates in value as an example, we see the following:
When the market goes down, an investor following weighted DCA makes use of the opportunity to invest even more in cash, while one following inverse DCA chooses to invest even lesser out of fear, and vice versa when the market goes up.
At the 10-year mark, we see that DCA results in an average share value of 1.47, while weighted DCA has outperformed with a value of 1.54, and inverse underperforming with a value of 1.40. More importantly, the average cost for weighted DCA is the lowest, followed by DCA and then inverse DCA.
As expected, buying more when share prices are low helps to decrease the average cost of shares invested, and as a result exposes the investor to even more potential gains when share prices go back up.
Leverage
Weighted DCA is ultimately an extension of the standard DCA strategy. By doing what can be considered “double” of an existing strategy, an investor opens themselves up to higher gains or losses — similar to that of leverage, another investment strategy that has much higher risks but also higher rewards.
