DCA versus Value

I forgot to show y'all the DOW Index.
We assume that we are buying
DOW units, priced at DOW Index divided by 100 as shown

It looks like it cost us practically nothing to match the final DCA portfolio (see Figure 3), but before y'all git too excited about matching the final DCA portfolio (after ten years, with, eventually, very little out-of-pocket money) remember that we had to invest more in those early years
(see Figure 3, again!)
and that's usually the case when the market is going UP
and these extra funds grow
... and grow
... and grow.
The magic of compound interest, working on those original dollars

Indeed, had we invested enough money at the beginning, and contributed nothing more, eventually our portfolio would have doubled. We could then withdraw that original amount and wind up, after umpteen years, with a portfolio that has cost us nothing. The average price we've paid for our stock is then ... $zero.

>So VALUE is better? Does a Value investor always invest more, at the beginning? Is ...?
It depends upon the market.

Let's suppose that the stock (mutual fund?) prices are P₁, P₂, etc. and we're buying units each month: U₁, U₁, etc.
and, to simplify (and get a feel for what happens), we ignore inflation and the cost of buying units and Money Market returns:

For a DCA scenario:

We invest $A each month.
At month k we invest $A, hence buy U_k = A/P_k units.
After N months we have
U₁ + U₂ + ... + U_N = A(1/P₁ + 1/P₁ + ... + 1/P_N) units.

For a VALUE scenario:

We insist that our portfolio increase by $B each month.
At month N-1, we have U₁ + U₂ + ... + U_N-1 units.
The value of these units, at month N, is then V = P_N(U₁ + U₂ + ... + U_N-1)
This should have the value N B (since our portfolio must increase $B each month), so we buy
U_N = (N B - V)/P_N = B N/P_N - (U₁ + U₂ + ... + U_N-1) units.
After N months, we then have U₁ + U₂ + ... + U_N = B N/P_N units.
Now compare the eventual number of units (after N months ... or days or years):
DCA A (1/P₁ + 1/P₂ + ... + 1/P_N)
VALUE B N/P_N

We conclude that, in order to end up with the same portfolio ...
>The same? Why?
To see if we can achieve the final DCA portfolio, but with less money.

Okay, to end up with the same portfolio, the VALUE scenario requires a monthly portfolio increase, compared to the monthly DCA investment, of:
B/A =
The guy on the top is the average reciprocal and one might expect, for a (usually) rising market, that
(1/P₁ + 1/P₂ + ... + 1/P_N)/N > 1/P_N
'cause P_N gets bigger 'n bigger ... usually

so, since the VALUE investor invests $B at the beginning of the N month period, we'd expect that she invests MORE, at the beginning. If the market goes UP, and you have the money, maybe that's good, eh? However, be prepared for pretty violent swings in your monthly investment ... with a VALUE philosophy:

If you want your portfolio to increase by $200 per month and it drops by $1000, you've gotta invest $1200 that month.
If it increased by $1200, then you'll be withdrawing $1000.

>You're kidding, right? I mean ... what's the chance of that happening?

For our DOW/100 investments, for the 1980s (as shown above), our VALUE portfolio would be around $18K to $20K in 1987
(when our DOW/100 units were worth about $20) and our investments would range from:

withdrawing $2232 ... in Jan/87 when the DOW increased almost 14%, to
investing $4753 ... when the DOW dropped 23% ... in Oct, 1987

You must pray that, when you have to come up with $thousands, you have enough in the auxiliary pot where you're storing the withdrawals. Money Market, for example.

>Wow! What if I don't have the money?
Or, if I have the money, why wouldn't I invest it all, every month?
And how do I know whether 1/P_N is going to be smaller ... in the future.?
And how do I know ...?

You can borrow this.

If we generate random returns (Normally distributed with Mean = 10% and Standard Deviation = 30%) and assume we invest each year and want a $5000 per year portfolio increase, then we can produce some "typical" results, like so ... where, for Value Averaging (if you have the money and stomach for the wild swings in VA purchases - which are often quite negative), it's possible to achieve a negative cost per unit: