When I calculate "internal rate of return (IRR)", should I include cash balance?

Question

When investing in the stock market, some methods need a cash balance in the broker's account.

For example, a new investor has $20,000 to invest. She buys stock worth $10,000. The remaining $10,000 is in the cash account.

(a) When the market rises, some stocks are sold, according to a formula (known as "AIM", by Robert Lichello). Proceeds are now in the cash account.

(b) When the market falls, more stocks are bought according to the same formula. The cash to buy the stocks is taken from the cash account. In a long downward market the cash account may fall to zero. In that case, the investor simply waits for the stock to rise again, or adds more cash from his own resources.

In the simple case, and for the purpose of backtesting, the investor is not required to provide any more funds, other than the initial $10,000.

Rate of Return

Method 1: Some sites calculate the "rate of return" using IRR. I think the "inflows" and "outflows" are the sums of money paid to and from the cash account.

Method 2: I'm not an expert, but I have a suspicion that the rate of return should apply to the whole "black box". In other words to the complete portfolio of stock plus cash. I suggest that there are no inflows or outflows across the boundaries of the black box.

So, I suggest that the "rate of return" should be the "CAGR", as in:

Final Value = Initial Value ( 1 + r/100) ^ n

where n = number of years, and r is the CAGR that needs to be solved for.

For the AIM example, where the ratio of cash to stock might average around 50:50, IRR can be approximately double the CAGR.

So, which method is correct?

Added after the answer by @rhaskett

I'm investigating alternatives to "Dogs of the Dow", which has given me 7.6% CAGR since 2000, and 10.2% for last 10 years.

The Dogs is a "fully invested" method. In other words, there's no cash in my broker's account that is ring-fenced to be used by the Dogs. The Dogs stocks are "rebalanced" periodically. So if any stocks are sold, the proceeds are immediately invested in the latest Dogs candidates, so that the stock values are approximately equal (with an eye on keeping commissions to a minimum).

So, it now seems to me that I should use CAGR, based on @rhaskett's third paragraph (and allowing for the caveats):

If you want to understand how the whole investment strategy worked....

Answer 1

Both are correct depending on what you are really trying to evaluate.

If you only want to understand how that particular investment you were taking money in and out of did by itself than you would ignore the cash. You might use this if you were thinking of replacing that particular investment with another but keeping the in/out strategy.

If you want to understand how the whole investment strategy worked (both the in/out motion and the choice of investment) than you would definitely want to include the cash component as that is necessary for the strategy and would be your final return if you implemented that strategy.

As a side note, neither IRR or CAGR are not great ways to judge investment strategies as they have some odd timing issues and they don't take into account risk.