South Africa: 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 gold shares.  Close to that there is a neighbourhood of platinum shares, and a neighbourhood of resource companies.  There is also a neighbourhood of bank stocks which is far from the resources.

Absolute map with SA 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 map above, the bond indexes of increasing duration Albi1-3, Albi3-7, Albi7-12, Albi12+ are all highly correlated with each other. If two points are at right angles to each other, such as PicknPay and  Anggold, 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 above map 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.)  The various bond indexes sit quite close to the origin and off to the right.  Slightly anti-clockwise from the bonds but still close in an angular sense (indicating strong positive correlation with bonds) are the interest sensitive stocks: firstly (in an angular sense) the retailers PicknPay, MrPrice and Foschini, then the banks like Absa and Firstrand, and then the industrial stocks such as Imperial and Advtech.   On the left side of the map, are the gold shares Harmony and Anggold, which are highly correlated with- but more volatile than-, the gold price Gold-NY.  They are more or less at right angles to the bonds, implying that they are uncorrelated with interest rates.  Continuing in a clockwise direction from the gold shares there are the platinum shares Mvelares, Northam, Implats and Angloplat; they are more volatile than the gold shares.  Closer to the origin, because they are less volatile, are other resource stocks such as Illovo and Tongaat (both sugar companies).  A little further out from them are more resource stocks like Sasol, Billiton and Anglo.

The major appeal of I-Maps is that they make immediate intuitive sense.  Experienced portfolio managers look at them and know that 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 

The map shows a few of the General Equity unit trusts.  Peers is an (equally weighted) average of the other 5 managers.  From the map one can see immediately that AGL (Allan Gray) has the lowest volatility and also the largest tracking error from Peers.    AGL has the biggest tilt away from resources (on the left of the map).  AGL will underperform if the market as a whole and especially resources does well.  AGL will outperform if the market as a whole does badly especially resouces.  OMIG has the highest absolute risk.  RMB has the lowest tracking error.

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.

Using the map as an example, it may be that the RMB manager actually has a stronger view than is consistent with his close-to-the-peer-average position.  In that case, the portfolio will need to be moved away from the center, in the direction that the portfolio manager has conviction will out-perform.


Point of view maps

Point of View maps can be produced with any security or portfolio at the origin.  The map below has the Peers  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 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 defensive financial and industrials like Afgri and Discovery in the lower right corner and the resource stocks like AngloPlat and Anglo in the top right corner.  Their relative correlations are negative, i.e.  resources stocks tend to do well (or badly) relative to the benchmark when the defensive financial and industrials 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 weights and risk statistics, as well as showing the positions of the original and new 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 SA 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.


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 a portfolio sticks out from the rest, and is positioned in the area of the map where the resource shares are, then everyone will know that the real risk for that portfolio going forward is that resource shares under-perform.

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

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.