Portfolio Selection I – Visual Representation

A start-up, multinational, investment house or VC faces similar decisions in portfolio allocation. How should I put a finite pool of capital to work in a way that provides the best return with the minimum risk? There are a number of black box optimisation techniques that spit the optimum portfolio out given a set of inputs. Decision makers cannot build intuition using these types of approaches and are usually distrustful of a snazzy spreadsheet that does a lot of number crunching under the hood, which then provides an unqualified answer (even if it may be the correct one!)

Visual Representation of a Portfolio – download the excel model here

The representation should include the most salient variables while allowing me to drill down into regions of interest, make informed comparisons and optimum decisions.

The biggest constraint is available capital. I’m trying to make this work to provide the best return, so we choose these two variables are the key elements in the representation. Often plots are return vs risk but this can be conceptually difficult for the uninitiated to work with. Later we’ll introduce risk through Monte Carlo analysis and how we can input this data this representation.

Number Possible Portfolio Combinations = 2^Number of Projects

For example if there are two projects A and B I can arrange them in the following combinations (A,B), (A), (B), (none). For each project there will be an associated cost and expected return (we’ll add uncertainty in return later). If there is no interdependency between the projects then the total cost and return will be the sum of the individual project costs and returns. If there are interdependencies these can be easily captured using IF THEN rules, for example, if I do project A then project B will be half the cost because it reuses some development efforts.

As an example let’s take six hypothetical investment opportunities with the associated estimated cost and returns. I have labelled these A, B, C etc in a real world example these could represent any investment decision from product development to an investment in a start-up.


There are 2^6 = 64 possible combinations, ranging from do them all to do none of them. We can plot each of these individual combinations on the chart below.

This is straightforward matrix multiplication that can be implemented using MMULT function in Excel for both costs and returns; for example a two project matrix would look like


I find this plot useful for the following reasons

Key information – it has high information content and answers the investment vs return question for all possible combinations of investment decisions.

Discrete Representation– it takes care of the natural constraint that often you can’t do fractional projects. An investment decisions is a binary event (of course the investment can be staged and we’ll look at this later) I cannot do half of a product development or portfolio investment. This is especially important when we introduce uncertainty where a black box optimisation algorithm can give unhelpful recommendations that we should invest 80% of the time even though it is a Go – NoGo decision.

Low cognitive overhead – The representation is fairly accessible (I think! if you are looking at it wondering what the hell it is maybe I’m wrong on this one); a dot represents a project combination, the cost and the return. An executive can look at this and get it because it doesn’t introduce technical or obfuscating language or representations.

Portfolio Optimisation – this falls straight out. For a particular investment level e.g. $6M we can draw a line straight up and see what combination of projects is giving us the best return; in the example above we can see with $6M there are four project combinations with the top one giving us a return of approx $15M. What’s more, this is apparent, we are not relying on the output of an optimisation algorithm, we can see it with our own eyes very easily.

Interactivity – On a dash board the executive can click between the different combinations and explore portfolio landscapes. This is especially important when we have some project interdependencies and correlations where the name of the game is to build intuition and deeper understanding of a portfolio from a global perspective.

Investment Levels – Available cash is the hard constraint. As a start-up you will talk to VCs who have their own preferred investment ranges. If the question pops up “what happens is you have an extra $2M”, you can look at the portfolio and relax the capital investment constraint and show how that would allow you to do an extra project(s) (new product development, marketing campaign) and the optimum combination and extra return immediately drops out.

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