USA: I-Maps

I-Maps make portfolio positioning visual

  • I-Maps show the investment environment on a map.
  • I-Maps show where portfolios are positioned.
  • I-Maps provide a graphical, easy to understand interpretation of the risk characteristics of portfolios.
  • The software application the I-Maps System, has a powerful modeling tool for re-positioning portfolios.


Maps of the investment environment

I-Maps (an abbreviation for Investment Maps) are a graphical representation of the investment environment.  Investment securities, such as shares, bonds, commodities, currencies, stock market indices, etc.  are each represented by a point on a map-like graphic.  On the map, securities that are similar are positioned close to each other.  For example, there is a neighborhood of banks.  There is also a neighborhood of oil and energy stocks which is far from the bank's neighborhood.

Absolute map with USA shares  

I-Maps are easy to interpret

The maps are placed on a series of concentric circles. 

There are two simple interpretation rules:

  1. The distance from the origin is the volatility of the security.
  2. The angle made by two points at the origin is the correlation between them.

Correlation is a measure of the extent to which share returns experience good or bad returns at the same time.  If two points are in the same pie slice as each other, they are highly correlated.  For example, in the above map, the oil companies ExxonMobil, Chevron, ConocoPhilips and OccPetrol are all highly correlated with each other. If two points are at right angles to each other, such as ExxonMobil and  JPMorganChase, this indicates that the shares' returns are uncorrelated with each other. If two points are "across the origin from each other" this indicates that they are negatively correlated with each other.  In the map above there are no examples of this.

The map can be rotated around the origin without affecting its interpretation at all.  The absolute position of a point makes no difference, only the relative positions matter.

(Technically, the volatility is measured by the standard deviation of the returns.  The distances from the origin show annualized standard deviation.)


I-Maps make sense

Note how the map makes intuitive sense.  Cash sits almost exactly on the origin, because its returns are so stable.  (It is possible to put Cash right at the center.  This is discussed later.)  USBonds sit quite close to the origin.  In line with them in the center of the map ( indicating strong positive correlation with bond returns) are the interest sensitive stocks: closest to the origin (and so the least volatile) are the defensive consumer stocks like Procter&Gamble, Johnson&Johnson, as well as Pepsi and Coca-Cola; a little further out are the telecom stocks AT&T and Verizon and the computer stocks such as IBM, HP and Oracle which are more volatile.  The Oil and Energy companies sit off to the side because they are not as sensitive to interest rates.  They are typically subject to commodity price cycles.

The major appeal of I-Maps is that they make immediate intuitive sense.  Experienced portfolio managers look at them and know they are "right".  Newcomers to investments can get a quick understanding of the investment environment from I-Maps.


Adding portfolios to the maps

A portfolio is a collection of investment securities.  Each security has a weight in the portfolio, its percentage of the total market value.  Portfolios are positioned on the map according to the weights of their holdings.  The diagram shows some examples of portfolios holding just two securities.

Diagram of Portfolio Points 

As with securities the distance of the portfolio from the origin gives the portfolio's volatility.  A portfolio's volatility is also known as its absolute risk or total risk.

The adage "diversification reduces risk" can be seen graphically with I-Maps. 

  • Port1 in the diagram has far less risk than either of its two constituents, because securities A and B are not well correlated.  Note how Port1 is much closer to the origin than either securities A or B.
  • Port2 has only slightly less risk than either of its two holdings, because securities C and D are highly correlated.


See what's going on with your portfolio

Map showing various Mutual Funds 

This map shows some mutual funds. From it one can see immediately that the Dodge & Cox and the AF Growth mutual funds are the most aggressively positioned, while the Vanguard fund is the most defensively positioned. The AF Fundamental fund has a bias towards the left where the oil companies are and away from the banks. The Washington fund has an opposite bias to the AF Fundamental fund.

Portfolios can be constructed using a variety of methods,  from the  bottom-up, or from the top- down.  In the end though a number of securities  are put together.  The securities have complex correlations between them. The extent of the diversification that occurs is complicated to calculate, let alone to visualise. Without I-Maps it is impossible for a human brain to figure out the end result.  With I-Maps this is easily done and the result is shown visually in a way that makes immediate sense.

 This means that, for the first time, portfolio managers can actually see what they are doing.  They can see where their portfolio is positioned relative to its peers.      I-Maps can reveal that a portfolio is not positioned in accordance with the portfolio manager's investment view, or that the portfolio's risk characteristics are not in accordance with the investment mandate for the portfolio.


Point of view maps

Point of View maps can be produced with any security or portfolio at the origin.  The map below has a benchmark portfolio at the origin.

Point of view map with the benchmark at the center 

On Point of View maps, the positions of the securities are based on relative returns, the returns relative to that of the item at the center.  Often the item at the center is chosen to be an indicator of the (stock) market.  In that case, roughly speaking, the point of view is: It doesn't matter whether the market is going up or down, what matters is whether the share is doing better or worse than the market. 

On Point of View maps, the dual interpretations of distance and angle now apply to the relative returns.

  • The distance of a point from the origin now represents the volatility of the relative returns.  This is commonly known, for historical reasons,  by the unfortunate name of tracking error
  • The angle made between two points at the origin shows the correlation between the relative returns.

Absolute maps tend to have all the points in only a portion of the full circle, precisely because shares on the same stock-market (and to only a slightly lesser degree, shares world-wide) all tend to go up and down together.  Point of View maps tend to fill up the entire circle.  On Point of View maps there are shares that are "opposites", i.e. across the origin from each other.  Examples of these on the map above are the oil companies and the banks.  Their relative correlations are negative, i.e.  oil companies tend to do well (or badly) relative to the benchmark when banks are doing badly (or well respectively) relative to the benchmark.


Positioning using the I-Maps System

The I-Maps System is the software application that produces I-Maps and provides a number of other related tools.  Its most powerful feature is a modeling tool called the Positioner.  The Positioner allows users to model multiple portfolios each of which can have their own specific benchmark.   Users are able to create, name, save and later use 'Positioner Specs' that specify the funds and their corresponding benchmarks of interest.  Running a Positioner Spec produces a map with the relevant funds and benchmarks and their holdings.  The Positioner itself consists of a number of portfolio spreadsheets showing:

  • Portfolio weights, benchmark weights, and "tilts" (also known as active weights, the difference between the fund's weight and benchmark's weight).
  • Useful statistics such as risk statistics for the portfolios as a whole.
  • Complete risk decompositions for each portfolio down to individual securities.
  • Statistics that indicate the effectiveness of each share at altering the portfolio's risk characteristics such as total risk, tracking error and beta.

The user can then enter weights or trades.  The system shows the original values and the new values of the wweights and risk statistics, as well as showing the original and new positions of the portfolios on the map.

After moving the portfolio to the desired position, a trade report can be exported for execution.

The Positioner includes features to:

  • Automatically rebalance portfolios to 100% after unbalanced trades (such as purchases without corresponding sales), with control over which securities are used to rebalance.  The default security used is cash.
  • Set weights at sector or asset class level and the system assigns those weights proportionately to the securities within the sector or asset class.
  • Get portfolios to mirror their benchmarks.
  • Apply the tilts from a primary portfolio and benchmark to other portfolios which may have different benchmarks.  A number of different algorithms may be used to optionally prevent negative weights in the other portfolios.
  • Handle portfolio flows, such as cash inflows or cash withdrawals from a portfolio.

The Positioner includes tables that give a risk analysis for a portfolio and benchmark with full decomposition of the risk statistics (volatility, tracking error and beta) from total portfolio, through asset class, to sector, right down to individual securities, as shown in the table below.

One Fund Risk Graphic using USA securities 

Armed with all these statistics, which can be gleaned intuitively from the map as well, portfolio managers will know:

  • Which securities are causing their portfolios to have too much or too little absolute or relative risk.
  • Which securities are most effective in increasing or decreasing the various risk statistics.

Then in conjunction with their own investment criteria (such as their expected return for the share) they can decide which shares to buy or sell and the amount to trade.


The true value of the I-Maps System

The value of I-Maps themselves is that they show where a portfolio is positioned.  Portfolio managers (and their overseers) can now see at a glance how a portfolio is positioned, and everyone will know what to expect from that portfolio under future market conditions.

For example, if a number of mutual funds are shown on a map and a portfolio is in the middle of group of funds, then everyone will know in advance that no matter what happens to the market in general, the portfolio is not likely to have the highest or the lowest performance.

On the other hand if your portfolio sticks out from the rest, and is positioned where the oil shares are, then everyone will know that the real risk for that portfolio going forward is that oil shares under-perform.

With I-Maps, portfolio management is a lot clearer.  Everybody can see what is going on.  Using I-Maps is like turning the lights on.  There will be no surprises.

The I-Maps System produces maps that show where portfolios sit relative to their benchmarks and it gives the portfolio manager all the tools he/she needs to "fix" the portfolio's position: to get the portfolio positioned according to the manager's investment view and in accordance with mandate requirements.  Ultimately success in portfolio management is all about getting portfolio positioning right and  I-Maps is the best portfolio positioning tool there is.