## Dollar Cost Averaging

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**Nov. 25th, 2005 | 04:55 pm**

**mood:** analytic

This is a technique used to reduce risk by investing over a period of time, instead of in one lump sum. Consider 4 situations, which taken together can intuitively cover all possible situations.

1. The unit price increases only during the period of the investment.

2. The unit price decreases only during the period of the investment.

3. The unit price increases at first, then decreseases.

4. The unit price decreases first, then increases.

If the investment period is 1 year, then you may choose to invest a lump sum at the start, or you could invest at regular intervals, say once a month. Each investment would be 1/12 of the total sum to be invested.

1. If the price increases throughout the period, then it is clearly preferable to invest the lump sum at the start.

2. If the price decreses throughout the period, then it is clearly preferable to buy in instalments (I am considering only these 2 options). Notice that as the price decreases, your money is able to buy more and more units. At the end, you will own more units than if you had invested a lump sum at the start.

3. If the price increases then decreases, then it is best to invest a lump sum at the start. During the increase period, you will be able to purchase fewer units due to the higher price.

4. If the price decreases then increases, then it is best to invest in instalments. During the decrease, you can buy more units than you would have bought with the lump sum at the start.

But the reality is that you have NO idea whether the price will increase or decrease. If you did, then could choose a far more optimal investment strategy. So given that you have no idea what will happen, how should you invest? I'll now take a look at the risk of the two approaches.

1. If the price goes up, then dollar cost averaging will still give some return. But not as much as the lump sum investment.

2. If the price goes down, dollar cost averaging will also lose money, but not as much as the lump sum investment.

3. If the price goes up then down, dollar cost averaging will lose some money, but not as much as you stand to lose in cases 1 or 2.

4. If the price goes down then up, dollar cost averaging will gain some money, but not as much as you stand to gain in cases 1 or 2.

The effect of dollar cost averaging is to smooth out gains and losses. Effictively it reduces risk. Instead of gambling all your money on the unit price at time point T, you are making 12 seperate gambles at T1, T2 ... T12. The odds of losing on all 12 gambles is much lower than the odds of losing on 1 gamble. Likewise, the odds of winning on all 12 is much lower.

I have only found one criticism of dollar cost averaging on Google. Part of it is bogus, but there is one good point he makes - Over time, the stock market goes up on average. That means there are more up periods than down periods. This means that case 3 above, where the price increases, occurs more often than case 4. That case favour lump sum investment.

But there are 2 problems here - a lump sum investment still exposes you to the *risk* of case 2, which can be quite bad (if you had invested just before September 11, you would be just barely scraping your money back 4 years later). Even though the theoretical returns of lump sum investement *are* higher, the theoretical *risk* is lower.

1. The unit price increases only during the period of the investment.

2. The unit price decreases only during the period of the investment.

3. The unit price increases at first, then decreseases.

4. The unit price decreases first, then increases.

If the investment period is 1 year, then you may choose to invest a lump sum at the start, or you could invest at regular intervals, say once a month. Each investment would be 1/12 of the total sum to be invested.

1. If the price increases throughout the period, then it is clearly preferable to invest the lump sum at the start.

2. If the price decreses throughout the period, then it is clearly preferable to buy in instalments (I am considering only these 2 options). Notice that as the price decreases, your money is able to buy more and more units. At the end, you will own more units than if you had invested a lump sum at the start.

3. If the price increases then decreases, then it is best to invest a lump sum at the start. During the increase period, you will be able to purchase fewer units due to the higher price.

4. If the price decreases then increases, then it is best to invest in instalments. During the decrease, you can buy more units than you would have bought with the lump sum at the start.

But the reality is that you have NO idea whether the price will increase or decrease. If you did, then could choose a far more optimal investment strategy. So given that you have no idea what will happen, how should you invest? I'll now take a look at the risk of the two approaches.

1. If the price goes up, then dollar cost averaging will still give some return. But not as much as the lump sum investment.

2. If the price goes down, dollar cost averaging will also lose money, but not as much as the lump sum investment.

3. If the price goes up then down, dollar cost averaging will lose some money, but not as much as you stand to lose in cases 1 or 2.

4. If the price goes down then up, dollar cost averaging will gain some money, but not as much as you stand to gain in cases 1 or 2.

The effect of dollar cost averaging is to smooth out gains and losses. Effictively it reduces risk. Instead of gambling all your money on the unit price at time point T, you are making 12 seperate gambles at T1, T2 ... T12. The odds of losing on all 12 gambles is much lower than the odds of losing on 1 gamble. Likewise, the odds of winning on all 12 is much lower.

I have only found one criticism of dollar cost averaging on Google. Part of it is bogus, but there is one good point he makes - Over time, the stock market goes up on average. That means there are more up periods than down periods. This means that case 3 above, where the price increases, occurs more often than case 4. That case favour lump sum investment.

But there are 2 problems here - a lump sum investment still exposes you to the *risk* of case 2, which can be quite bad (if you had invested just before September 11, you would be just barely scraping your money back 4 years later). Even though the theoretical returns of lump sum investement *are* higher, the theoretical *risk* is lower.