Hi Conrad,
The intention of ROCAR is to give some credit for prudent portfolio management. It's not money we can take to the bank. It's more of a "feel good" calculation. However, like Return On Investment it has some information value relative to Total Return. Further, if we compare various methods of investing to see if we can maximize Total Return, we should also look to see if our gains are at the expense of prudence. If using a variation of our investment model Total Return increases and ROCAR remains constant, then we can assume we've done something productive while not adding significantly to the "riskiness" of what we're doing.
In my calculation I don't believe ROCAR could get to zero. The reason is that I look at the value that is at risk for each period of the time being analysed. So, even if it were just two periods, one being fully invested and one being sold out, there would still be the "average" value in the ROCAR statement that shows some residual portion being part of the calculation.
So, even if the number of periods being analysed were 100 and yet 99 of them were 100% CASH, there would still be some residual left on average preventing ROCAR from zero-ing out.
In my ROCAR calculation, any money that is invested in the market place and not in cash is considered "at risk." Obviously even cash or a money market fund is at some risk, but not to anywhere near the degree that money is when invested in the stock market.
Let's try an example:
Period Stock Value Cash Reserve Total Value at Risk
-1 8000 2000 10,000 0.800
-2 9000 2000 11,000 0.818
-3 9000 3000 12,000 0.750
-4 9000 4000 13,000 0.692
-5 8000 4000 12,000 0.667
-6 7000 4000 11,000 0.636
-7 7000 3000 10,000 0.700
-8 7000 2000 9,000 0.778
-9 8000 2000 10,000 0.800
-10 8000 3000 11,000 0.727
Average At Risk = 0.737
Our total return is End Value minus Starting Value divided by Starting Value times 100
((11,000-10,000)/10,000)x100 = 10%.
If we average the "at risk" amount we come up with .737.
Our ROCAR (Return On <average> Capital At Risk) is then
Total Return divided by the average amount at risk per period.
10%/0.737 = 13.6% ROCAR
Now let's change it:
Period Stock Value Cash Reserve Total Value At Risk
-1 8000 2000 10,000 0.800
-2 9000 2000 11,000 0.818
-3 0 11,000 11,000 0.0
-4 0 11,000 11,000 0.0
-5 0 11,000 11,000 0.0
-6 0 11,000 11,000 0.0
-7 0 11,000 11,000 0.0
-8 0 11,000 11,000 0.0
-9 0 11,000 11,000 0.0
-10 0 11,000 11,000 0.0
Average At Risk = 0.162
Here we still have a 10% total return. However, since the money was only partially invested for just two periods, the average amount per period at risk is much lower.
In this case we see ROCAR as:
10%/0.162 = 61.7% ROCAR
This shows us that we made a bunch of money relative to the amount that was at risk on average for any period.
The average at risk can approach zero, but never quite achieve it.
Best regards, Tom