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It's also well known that the type of risk that the manager is averse to will ultimately affect his/her investment decisions. Monitoring how each investment decision affects the various risks is critical to setting and managing the risks appropriately. As it turns out, the only accurate decision a manager can make upfront is the amount of risk he'll take on.
Absolute, relative, benchmark and selection risks are some of the terms used frequently in the modern fund manager's vocabulary. One can clarify these concepts both graphically, by looking at the important risks from the eyes of those parties who ultimately bear them.
By "walking" around the diagram in figure 1, one gains a visual perspective on the risk the various players bear.
Our starting point in Figure 1 is the depiction of the scatter diagram of returns of a perfect tracker fund, plotted against the benchmark's returns. In other words, each point on the diagram represents a co-ordinate matching the fund's return at a point in time with the benchmark return.
The fund's returns are represented on the vertical axis, while the benchmark returns are found on the horizontal axis. In this hypothetical situation depicted in Figure 1, the perfect tracker fund is precisely the benchmark as well. Hence the 45 degree upward sloping line represents the line on which all perfect tracker fund returns will fall.
By associating the various participants with the risks they ultimately bear, Figure 1 gives a graphical summary of these concepts:
The absolute risk (or total risk) is typically taken to be the dispersion or, more specifically, the standard deviation of the fund returns. Looking at Figure 1 from the left-hand side, one sees the dispersion (total risk) of the fund returns. Since the investor typically bears this dispersion, or volatility of the fund returns, it could also tentatively be termed the investor's risk.
To give some insight into the typical magnitudes of these risks: over the past three years the average total risk of the general equity class of unit trusts was 15,6%/year. The equivalent figure for the largest 10 pension funds in SA averaged 12,3%/year.
Clearly, pension funds are designed to have lower absolute risk than equity unit trusts. That's of course intuitive, as absolute risk captures the risk of losing money - a significant concern for the pension fund industry.
The risk of the benchmark, by contrast, is portrayed by the dispersion of the benchmark returns (depicted on the horizontal axis), hence the dispersion of these returns can be seen by viewing Figure 1 from the bottom looking upwards.
The benchmark is typically comprised of the universe of assets from which the manager is instructed to make investment choices. Clearly, the person who specifies the mandate and the investment universe for the fund, in so doing, accepts the risk of that benchmark.
Who might that person be? Typically, the owner or the trustees of the fund. In Figure 1 we've tentatively termed this benchmark risk the trustee's risk.
The third significant player is the manager. A perfect tracker fund is only exposed to the risk of the benchmark it tracks. Since that risk is ultimately beyond the control of the manager, the manager of the perfect tracker fund, in essence, bears no risk. That's the case depicted in Figure 1.
Managers only bear risk when they actively attempt to outperform the benchmark by holding different compositions to that of the benchmark. In other words, managers are typically concerned with their performance relative to a benchmark.
In our diagram this relative risk can be viewed by looking up the 45 degree line from the bottom left and noting the dispersion around this line (ie, departures from the benchmark). The dispersion around this 45 degree line is also commonly referred as the tracking error or relative risk.
We contend that this relative risk is ultimately the manager's risk, as it can only be incurred when managers hold a different component mix to that of the benchmark in an attempt to outperform it. In Figure 1 there's no dispersion around the 45 degree line because the figure depicts a perfect tracker fund.
However, in Figure 2 we've demonstrated how the relative risk (or tracking error) is increased when managers hold a different mix of stocks to that of the benchmark in an attempt to outperform it (ie, take on stock selection bets/risk).
From Figure 2 it's evident that the manager's risk increases significantly as managers take on more aggressive stock selection bets. In considering the effect of increasing selection bets on the other components of risk - namely, absolute risk and the risk of the benchmark - it's evident from the comparison of Figures 1 and 2 that, with increased selection activity, there's a small increase in the absolute (or investor's risk) but no change to the benchmark (or trustee's) risk.
Typically, in the fund management industry in SA absolute risk is of a larger magnitude than relative risk, hence stock selection activity has a greater effect on relative risk than absolute risk (apparent in Figure 2).
Bearing in mind that tracking error arises from any departure from the 45 degree line depicted in the figures, it's evident that changing the market exposure of a fund will also affect the relative risk (or tracking error). The market exposure of the fund is measured by the beta coefficient of the fund and can typically be changed by changing the equity/cash mix.
Figure 3 depicts how lowering the market exposure (and hence the fund beta) affects both the absolute (investor's) risk and the relative (manager's) risk.
It's evident from Figure 3 that lowering the market exposure effectively lowers the fund's exposure to risky assets. It's clear that less exposure to risky assets significantly lowers the investor's (or absolute) risk but substantially increases the manager's risk (tracking error).
Clearly, if the market rises when managers have relatively more cash than their peers, these managers will significantly underperform their peers, hence increasing the manager's risk.
However, any departure from the 45 degree line translates into tracking error risk. As we've demonstrated, departures from the 45 degree line can be caused either by selection activity (Figure 2) or changes in market exposure (Figure 3).
Figure 4 on the other hand, shows how an increase in the market exposure (by increasing the beta) of a fund impacts on the risks of the players. A fund having a greater proportion of funds invested in equity than that of the benchmark will typically have a beta (relative to the benchmark) greater than one as portrayed in Figure 4.
Most significant in Figure 4 is the substantial increase in the investor's (absolute) risk when the market exposure is increased. Clearly, an increase in market exposure implies that the investor is exposed to a larger component of risky assets - hence the increased investor or absolute risk.
Also notice how the manager's (relative) risk also increases. As discussed above, any departure of the fund's beta from one - up (as in Figure 4) or down (as in Figure 3) - will increase the tracking error (via the relative benchmark exposure). In neither of the diagrams does the benchmark risk, of course, change.
When comparing tracking error (or manager) risks taken on in the unit trust and pension fund industries we note that the average tracking error of the general equity category of unit trusts turned out to be 4%/year in contrast to that of the top 10 pension funds of only 2,8%/year. (See Table 1).
Why is it that that non-professionals (at investments), such as trustees, should be responsible for the lion's share of the risk (benchmark risk) while the professional asset managers should only be responsible for the substantially smaller component of tracking error risk of the fund?
The reason for that split is that the large benchmark portion of risk is attributable to the benchmark or market - that portion is expected to be rewarded unconditionally. Suggesting that, one expects to be compensated for bearing that component of risk by simply being invested in the market in the long term - without any particular application of skill.
However, to be rewarded over and above that (conditionally) requires the skill of the manager - who typically uses the relatively smaller tracking error component to attempt to actively outperform the benchmark.
Professor Dave Bradfield
Bradfield is head of research at Cadiz. He has a BSc (Hons), HED (Unisa), MSc and PhD (UCT) and has lectured at UCT's department of mathematical statistics.
He's won awards for research publications in the journal De Ratione and was awarded the first "best research paper" award by the Investment Analysts Society.
He's an associate editor of the multinational Finance Journal and a member of the Euro working group in financial modelling and the Southern African Finance Association.
