Wednesday, November 19, 2014

What's the return on diversification?

Can you work this problem?
You've got something big to do -- a project or task -- and it has risk and uncertainty. Some of the estimates are way pessimistic, and some are actually more optimistic than you think the average outcome should be. So, the variance -- a figure of merit for how far the various estimates differ from the mean -- is quite large

You decide to divide the big thing into several smaller units -- say, N units -- so that you've got better visibility into each unit than trying to deal with one big thing, and the risks don't affect all units the same way. In fact the risks of the smaller units are now pretty much isolated one from the other

How much better is the overall variance of your project? In other words are N smaller units less risky overall than the one big thing before it was divided?

Answer: the overall risk is lower; the total variance of the project, calculated as the sum of all the variances of the smaller units, is lower than the variance of the one risky "big something" before dividing it up.

However, the total average value is unchanged; you didn't change the size of the pie; you just sliced it up.

If think of variance as a figure of merit for risk, how less risky is the overall project after dividing the big thing by N? Actually, it's pretty close to 1/N. That is, the sum of the variances of the smaller units is about 1/N the variance of the larger unit.

I've been writing about a functional description of the diversification rule: If you divide a risky thing into N smaller things; with risks independent between the smaller things; the overall risk -- defined as the variance from the mean value -- is lower by about 1/N

So, what things in the project domain could benefit from the rule? How about: personal or business investments, tasks, and portfolios?  All are all candidates for diversification.

"I understand this from a conceptual point of view. It makes sense. But is there a way to calculate the point of diminishing returns [of dividing things up]?

Obviously, this can be overdone and then we have so many smaller tasks that we spend more time updating action item lists and other project artifacts than getting things done."

Quite right, there is a trade between managing the variance (range of risk impacts) and managing the overhead (See: anti-lean, non-value add) of smaller units. There's no calculation per se; it's a matter of judgment and circumstance.

Typically, a work unit would not be smaller than a couple of weeks duration, and the scope is typically not smaller than what a handful of people can do in those couple of weeks.

That said, overhead is one of those things that usually does not scale linearly -- control and monitor costs are often unrelated to the nature of the content and often poorly correlated with the scope of the content. Example: the time and cost of making earned value calculations matters not a wit what the scope is about, or how big it is, or what it costs.

Of course, you could look at the actual overhead costs and compare them with the cost (impact) of the risk and decide which is the lesser cost, but only if the risk impact is strictly monetized [apples to apples comparison]

When the risk impact is not monetized, then you are into a qualitative judgment that only you can decide how big N should be.

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