Communicating portfolio risk intuitively and effectively

Visualising risk

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A vision for making sense of portfolio risks

If only it were easier to explain risk. Having a simpler and more intuitive way to talk about a fund’s risk would encourage transparent dialogue and enable more investors to better understand the dynamics of their own portfolios.

Current conversations are frequently cumbersome and ineffective, partially because risk measures are often difficult to explain and even harder to interpret properly. To complicate matters risk numbers are not well behaved: they do not add up the way people expect.

Unlike returns and virtually every other metric in use in financial services, portfolio risk is not the sum of the risks of its parts. What is needed is a clear and compact way of showing people how risk behaves without the baggage of equations and laborious math.

Although risk does not add linearly as regular numbers do, risk does add according to specific rules. Fortunately, there is a convenient two-dimensional representation of those rules. The patent-pending VisualVaR was developed to capitalise on that representation with the specific goal of fostering easier and more intuitive conversations about risk.

As a tool designed to assist investors and fund managers in visualising their portfolio’s risk it can effectively demonstrate how risks add up, how every part of a fund contributes to the total risk and how a contemplated investment would affect the risk profile of an existing fund/portfolio.

This approach takes advantage of a useful geometric interpretation of the standard value at risk (VaR) equation for two investments, each with individual risks.

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The VisualVaR diagram (Figure 1) shows how the risks of two parts of a portfolio interact, giving rise to the total portfolio risk. One part of the portfolio is always drawn as a horizontal line from left to right (grey in the diagrams), representing the base or ‘starting point’ portfolio. The other part of the portfolio, representing the part of the portfolio to be analysed or a new investment (blue in the diagrams), is drawn starting from the rightmost end of that first line.

The direction of that second (blue) line is determined solely by the correlation between the two investments. The total risk is then the length of the line that completes the triangle (shown in red). Comparing the length of the red arrow (total risk) and the length of the grey arrow (initial risk) indicates whether the investment in question increases or decreases total portfolio risk.

To understand the range of possible ways in which two investments can add up to the total portfolio risk, it is helpful to consider the possible ways in which the two investments can be correlated. Figure 2 shows the range of orientations, from extremely highly correlated (+1) in which the blue arrow points to the right, to extremely anti-correlated (-1), where the blue arrow points to the left.

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To further illustrate this point, consider three possible investments all with the same volatility but with three very different correlations to an existing investment: highly positive, small but positive and somewhat negative. Putting all three of these potential investments into the same graph would allow direct comparison of their effect on the total risk (Figure 3).

In this case, the three blue arrows are all the same length because those investments have the same allocation and volatility. But their different orientations result in significantly different total portfolio risk, as shown in different red arrows.

High correlation corresponds with highest risk (longest red arrow), positive correlation with medium risk and negative correlation with the smallest amount of risk (shortest red arrow).
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This representation demonstrates how much diversification can be achieved with different strategies: investments in securities or funds that are positively correlated with the rest of the portfolio always increase risk. The only way to reduce risk is with negative correlations.

It is often mistakenly believed that adding an uncorrelated investment to a portfolio reduces risk. Figure 4 shows two possible investments with the same volatilities (blue arrows are the same lengths) but with different correlations: the arrow pointing up and to the right has a positive correlation and the arrow pointing straight up has zero correlation to the base portfolio.

In both cases, the resulting red arrow is longer than the original grey arrow, indicating that both investments increase total portfolio risk. The benefit of the uncorrelated investment is that it does not increase the total portfolio risk as much as the more highly correlated investment but it does still increase that risk.

acad9-0913To illustrate the mathematical accuracy of this technique, we consider two investments: a base portfolio with a risk (r1) of 10 and a second investment with a risk (r2) of 2. These two investments can be thought of in several ways: an existing portfolio plus a new allocation, such as a pension fund (grey) investing in alternatives (blue); an existing portfolio and one of its parts, for example a multi-manager platform (grey) and one of its managers (blue); and a manager examining a particular group of trades (blue) and comparing it with the rest of the investments (grey).

Given that the investments have individual risk amounts of 10 and 2, depending on the correlation between the two investments, the total portfolio risk can be any value between 8 and 12, as shown in Table 1. The equation behind VisualVaR is the standard VaR equation.

We envision at least three distinct uses of VisualVaR: allocators can use it to better understand their existing portfolio; individual managers can use it to demonstrate their improvement to an existing allocator’s portfolio; and all industry participants can use it to foster more intuitive risk communication.

Allocators can use the diagrams to examine their existing portfolio by considering each part of their portfolio in turn as the blue (incremental) arrow. The grey arrow is then made up of everything else in the portfolio.

Suppose an allocator thinks of its portfolio as being made up of four parts: equities, fixed income, alternatives and real estate. There would then be four diagrams to represent the four parts. The first diagram would have equities as the blue arrow and the combination of fixed income, alternatives and real estate as the grey arrow.

acad1-0913The second diagram would have fixed income as the blue arrow with equities, alternatives and real estate as the grey arrow and so on.

Another use by allocators would be for prospective/contemplative investments. Using the same example, the grey arrow would be the entire portfolio (all four parts) and the blue arrow would be the contemplative new allocation.

Use of VisualVaR enables individual managers to understand more fully the composition of their portfolio in much the same way as allocators would. The diagrams can also showcase how an individual manager’s fund fits into an allocator’s portfolio. This can be accomplished by using the grey arrow as the allocator’s existing portfolio and by using the blue arrow to represent the manager’s fund. If the manager presents the visual this way, it may be able to help position the manager’s fund in a more comprehensive risk/return perspective.
Investors, whether individual or allocator, would benefit from communicating risk analytics to their investors using diagrams that are visually understandable. These diagrams can be used to support existing risk reports, demonstrating incremental risks or to convey the results of stress tests.

Three different types of stress test can be performed with the VisualVaR approach: stressing allocation, stressing volatilities and stressing correlations.

Because the length of the input arrows (grey and blue in the diagrams) is determined by the product of the allocation and the volatility, both of these stresses are visualised the same way: increases (decreases) in allocation or volatility result in lengthening (shortening) of the corresponding arrow.

In Figure 5, the light arrows represent the original risk and the elongated darker arrows represent an increase in allocation or volatility of both the base (grey) and investment (blue).

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On the other hand correlation stresses are represented by a rotation of the blue arrow. In Figure 6 below, the original (light) arrows are identical and the only change is the orientation: toward lower correlations on the left and toward higher correlations on the right.

acad11-0913Fostering more frequent and more easily understood risk conversations can only help the industry. This approach offers a compact way of communicating how risks add, how different parts of the portfolio interact, how much (or little) diversification is being achieved and how various stresses impact the risk of the portfolio.

When employed effectively, VisualVaR helps to remove disagreements and mis-interpretations of risk and allows investment and financial professionals to make more intuitive and effective risk decisions.

Damian Handzy, CEO of Investor Analytics, wrote this article.
VisualVaR is a trademark of Investor Analytics and is used with permission.

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