This kind of follows on from the Cash Cascade, which was a recent post about paying off debt:

Part of the decision-making process around paying down debt revolves around what you would choose to invest that money in, instead …

… and, that depends – at least in part – on your appetite for risk.

A while ago, I discussed the difference between what I call ‘technical risk’ and ‘absolute risk’ and Jeff (our resident ‘risk manager’) asks:

Ultimately, I just want to figure out how to calculate (take into consideration) the additional risk–or variance in outcome–that leveraging adds to an investment, so can make educated investment decisions.

It’s easy, Jeff: just attribute a risk % to each investment category based upon your perception of the various factors and multiply the expected return by that factor.

Or, you can try using the Standard deviation, and model thus:

r(V) = {V^2} – {V}^2 where curly braces represent average values. For compound returns:

r(V) = {N1^2}*{N2^2}*…*{Nn^2} – {N1}^2*{N2}^2*…*{Nn}^2

Now we can again use the definition {Ni^2} = v(Ni) + {Ni}^2 to get

r(V) = (r(N1) + {N1}^2)(v(N2) + {Nn}^2)…(v(Ni) + {Ni}^2) – {N1}^2*{N2}^2*…*{Nn}^2

Or, you can simply do what I suggest which is work backwards:

1. Decide WHY you need the money

2. Decide WHEN you need the money

3. Decide HOW MUCH money you need

4. Calculate the required Compound Growth Rate to go from where you are today to where you want to be

5. Decide if you can ‘stomach’ the inherent risks involved in the investment methods required to achieve that required compound growth rate …

… if not, then go back to 1. and downgrade your expectations for happiness.

When I wrote this comment I was looking for a context-independent way of determining how leveraging amplifies the returns of any investment. Unfortunately, this post did not come close to answering my question, and probably confused even those readers who understand statistics. But that was your point…

@ Jeff – You are actually helping all of our readers, perhaps more so than yourself … we truly appreciate your contribution, and that of everybody else who questions/comments/contributes/criticizes.

How ’bout this for a way to figure that out, Jeff?

Outline all the various what-if scenarios of “what can happen IF” something occurs. You have to figure out what they all are (which can be quite extensive).

Then run the costs on each other and start making comparisons. Simply put, but quite time intensive. It’s however a bit easier to understand than running the R-squared computates, which again are just numbers that are based on …WHAT? history? hmmmmmm…

Just remember this from the MBA Toolkit. Truly great CEOs have historically gone against the numbers run by the financial experts – using some ‘gut instinct’ – and been right. However, no figures exist on how many wanna-bes tried that method and failed 🙂 It only goes to show you that “running the numbers” only provides you with some information, not an answer.

@ Diane – Or, you can just work out one scenario: what will it take to get to my Number/Date and reiterate on that, if the compound growth rate scare you too much … kind of goes hand-in-hand with ‘go by your gut’ philosophy, which overly-analytical people tend not to be comfortable with. A shame, because they have a real ‘edge’ when it comes to analyzing the various options on the way to their Number.