Viewing the Lassonde Curve Through the Prism of Uncertainty & Risk

Introduction

The classic Lassonde curve showing project value vs project stage for exploration is a staple of the exploration finance community. In its classic form it shows an appreciating value leading up to ‘Discovery’ (what constitutes ‘Discovery’ is a subject worthy of debate) which falls back as the excitement abates, reality sets in, and news-flow dries up. Value then picks up again prior to first production after which there is a steady drop as the reserve depletes. What lies at the heart of the movements prior to mining is essentially changes in our perception of uncertainty and risk.

Figure 1 - The Lassonde Exploration Project Value Curve

Risk vs Uncertainty

It is important to define exactly what constitutes uncertainty and risk, as the two can be confused. Uncertainty pertains to the range of unknown possible outcomes and in exploration this is dominated by the uncertainty of reserve/resource size that can range from zero to very large numbers indeed. I’ve yet to come across a unified definition of risk in the exploration/mining industry but I favour the definition that it is the range of possible uncertain scenarios that result in loss to the company. In the context of an early stage exploration programme this means a programme that doesn’t result in any meaningful Discovery but still costs money to acquire, explore and maintain. So, in the frequency distribution chart below, the risk may be interpreted as the blue portion that represents scenarios of no Discovery. I also exclude from the risk section projects that though do not reach a Discovery but do uncover ‘Sub-Discovery’ mineralised bodies, these are projects where there is enough ‘smoke’ for the project to be sold on to another operator and for exploration costs to be recouped, even if no profit is made. The blue portion therefore extends from no mineralisation to somewhere between ‘Mineralised Body’ and ‘Discovery’. We can calculate a risk probability from the ratio of scenarios in the risk portion to those outside.

Figure 2 - Resource/Reserve Uncertainty and Risk

At this stage, it is also important to emphasize that risk has another dimension and that is its magnitude, which is often very contextual. For a junior explorer with 2 or 3 projects, their flagship project failing may be catastrophic, whereas for a major miner any single exploration project failing is very insignificant, at least at a pre-Discovery stage. This magnitude is important when thinking about overall risk and we may imply that exploration for junior exploration companies is very high overall risk but relatively low overall risk for a major. A nomenclature of risk probability, risk magnitude and overall risk can be used to distinguish between the different elements of risk.

The Evolution of Risk and Uncertainty Post Discovery

Using a definition of Discovery as a positive pre-feasibility study, the post Discovery period coincides with feasibility work comprising further technical studies such as metallurgy, resource/reserve definition, geotechnics, etc as well as other important studies in the spheres of environmental impact, social impact and permitting. Ultimately this leads to the definition of mineable ‘Reserves’, the portions of an ore body that can with relative certainty, be profitably mined after taking account of all the technical, environmental, social, political and economic factors. Note some deposits that are commonly termed ‘Discoveries’ never really produce reserves in this sense, often due to some fatal flaw such as metallurgical difficulties or an unworkable national mining code. During the post Discovery period, subsurface uncertainty the pre-eminent source of deposit size uncertainty, reduces dramatically as further exploration work is conducted. The reduction of uncertainty may often also be negatively skewed as during the exploration stage you may be extending the mineralisation out from the heart of the deposit, whereas post Discovery it may be more likely you are closing off mineralisation and thereby making the range of possible scenarios smaller by removing the most favourable scenarios to the right of figure 2. The possible scenarios envisaged have been narrowed at least to the small unshaded portion to the right of the figure 2 and theoretically by the end of feasibility this uncertainty should be negligible and the deposit size known with relative certainty. Certain types of deposits may have feasibility studies where the extent of the deposit is known only to a level that there are reserves sufficient for an initial production period, but these can still be considered to be ‘de-risked’ in the sense of deposit uncertainty, retaining this degree of uncertainty may be adding value.

Conversely, post-Discovery above surface uncertainty often increases as governments, financial institutions and NGO’s start to look closer at new possible mines. However, the uncertain range of possible outcomes is still much smaller than that resulting from the previous period of subsurface uncertainty and tends to be binary in nature, such as the granting of a mining licence or success in gaining adequate finance. The combined effect of the dramatic reduction of subsurface uncertainty and modest rise in above surface uncertainty results in a reduction of the range of uncertainty overall. In addition to the reduction of uncertainty there is also a corresponding reduction in risk probability as a large proportion of discoveries go on to be mined. Conversely the risk magnitude increases during this period as increasingly large sums are spent on the project and therefore the impact of failure becomes more significant. The level of overall risk in this period varies from project to project but may well remain static or even increase despite the reduction of uncertainty and risk probability.

It’s worth considering if the supposition that uncertainty ranges are increasing or decreasing in the manner described in the previous paragraphs, owing to the sequential nature of exploration. For instance, even though a small exploration company might find an above ground uncertainty such as the overall risk of nationalisation rather small, a successful exploration project would have to pass through the mine development phase to come to fruition, thereby passing through the later stages where overall risk of nationalisation is high. It can be argued that we should therefore include a high nationalisation risk probability in early stage exploration. However, because the companies & investors who develop the mines are often different from those exploring the projects and the staged nature of exploration and project development, the approach of dynamic changing uncertainty with development stage is not only conceptually accurate, but also practical.

The Value of Uncertainty

It is important to remember that during exploration a high degree of uncertainty is favourable, as long as it is not negatively skewed. The large range of uncertainty includes the possibility that your tenement may host a world class deposit (or merely a small modestly profitable mine) and it is this that gives an exploration project value. At this juncture, we should reflect on the importance of world class deposits on exploration. World class deposits make up the long tail of the deposit frequency distribution but this tail is extremely important. A disproportionate of the worlds minerals are mined from world class deposits and their possible existence is what drives global exploration. If exploration could only yield modest deposits at best, it would not be worthwhile, even though the Discovery of a modest deposit for an individual project is a success. 

A useful proof of the value of uncertainty is the economic similarity of exploration to a financial option, as exploration gives the option but not obligation to do further exploration and eventually build a mine at the end of a period of time. I have covered this on previous blogs where I have compared exploration to a compound option with each exploration stage an option on the next (see series of blogs: Exploration Risks and Decisions). In this blog it should suffice to say that when using an option model, resource/reserve uncertainty is akin to underlying price volatility in a financial option. Financial options in which the underlying has a high volatility have a comparatively higher valuation.

Risk, Uncertainty and The Lassonde Curve

The Lassonde curve only considers the average trajectory of successful projects, in fact it would be fascinating to view a graph that averaged all projects globally and see if it had some of the same characteristics of the Lassonde curve. You would expect such a graph to move in line with cumulative expenditure over the stages but perhaps it would reveal long standing arbitrages where risk is not being appropriately priced? Returning to the classic Lassonde curve, let us analyse the parts within the uncertainty and risk framework outlined.

As early stage exploration progresses with successful results, project value increases exponentially due to the range of possible scenarios becoming progressively restricted to the right-hand side of the frequency distribution. To take the example of gold exploration, after the initial phases of exploration we may have arrived at a point where we have scout drilled ore grade intersections at shallow depths, such it could be said with reasonable certainty that there is at least 200,000oz. This would rule out the possibility that resources are nil or perhaps even that they are less than 200,000oz but importantly not eradicated the possibility that there is a world class deposit at depth or along strike, so that our updated expectations are skewed positively but still contain a large range of uncertainty. It is this elimination of negative scenarios whilst retaining reasonable levels of uncertainty, skewed towards positive outcomes at least for successful projects, that drives this period of value appreciation.

One of the key factors which shapes the Lassonde curve is the removal of subsurface uncertainty as exploration continues to Discovery phase and you begin to realise that your deposit is merely ordinary rather than potentially world class. Or if your deposit is world class then it is the realisation that your project is merely world class and not one of the freak deposits like Grasberg or Muruntau! It is this which drives the downward inflection of the curve post Discovery. This is compounded by a possibly static or increasing level of overall risk, and the fact that the new above ground uncertainty introduced, is large in magnitude and heavily skewed to negative outcomes. After all the government can’t increase the size of your deposit but can certainly minimize its value, possibly to nil. Though this is known beforehand, I suspect the above surface uncertainty isn’t fully accounted for in the pre-Discovery stage, compounding the downward trajectory post Discovery.

The downward trajectory continues until the mine begins to head to first production when there is an upwards inflection in value. This upwards inflection is due to the removal of the negatively skewed above surface uncertainty as mining licences & environmental permits are granted and financing secured. Although the gradient on the curve may be similar, because you are starting from a higher value initially the return is much lower in this phase than pre-Discovery. There is after all little subsurface uncertainty to fuel exponential gains.

Implications for Investors

Investors should keep in mind the effects of uncertainty and risk on the Lassonde curve when investing. It is possible to invest in early stage exploration projects with reduced ranges of uncertainty, such as investing into a mature well explored terrane where there are perhaps no undiscovered world class deposits which tend to be discovered early in the course of a regions exploration lifetime. With such investments, you can expect the gradient of the Lassonde curve to be correspondingly lower than frontier exploration in the pre-Discovery phase as the uncertainty is so much lower. Investing post Discovery may seem unappealing, however if you can identify deposits where the overall risk from above subsurface is mitigated, for example due to an already granted mining licence, then an investment maybe worthwhile. Similarly, a post Discovery project which still has a large degree of uncertainty due to mineralisation which is still open at depth or along strike or has possible satellite deposits then again investment may be warranted. Investors should be mindful of the positive effects of uncertainty which is not negatively skewed such as subsurface uncertainty (in fact it can be argued that subsurface uncertainty is heavily positive skewed given that an exploration project starts with nothing and tends to gradually add resources), on exploration value. With risk, investors should understand the two components of both probability and magnitude to make informed decisions of overall risk. 

The old risk = reward adage is only true if the overall risk has been adequately priced in, and abnormal returns are only possible if risk has been overpriced. What is perhaps a better adage for exploration investors is uncertainty = reward, so long as the uncertainty isn’t negatively skewed, which due to the nature of exploration is rarely the case. Conversely, increased risk on the project level is value destructive. Neither risk nor uncertainty in themselves leads to great investment opportunities, as always in investing the key is using a greater insight into these factors to identify mispricing by the market. Smart investing in exploration means identifying projects where the value of the uncertainty has not been priced in sufficiently, or the discounts arising from risk have not been properly priced.