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Rwanda’s involvement in Eastern DRC: A criminal real options approach

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Abstract

This paper applies an alternative model to analyze criminal behaviour by countries based on real option models. Criminal options incorporate a richer framework than traditional cost-benefit models and allow examining the optimal timing of a crime as criminals have the possibility but not the obligation to commit a crime in the near future. From the model, we show how criminal states can actively manage their criminal options. More importantly, we show how the international community can optimally intervene pro-actively, by reducing the incentives for criminal states to execute their criminal options. These novel insights are then applied to two episodes of criminal behaviour by Rwanda in the Democratic Republic of Congo (DRC): the massive killing of Hutu refugees by the Rwanda Patriotic Army (RPA) in late 1996-early 1997 and the illegal exploitation of Congolese resources from August 1998 onwards. This article describes and assesses these activities from this real option perspective.

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Notes

  1. We use the expression “so-called”, because the “international community” does not really exist. Is it its institutional translation, namely the United Nations? Or does it refer to specific countries with a particular interest in a given situation or the press or vocal NGOs attempting to influence international public opinion? The international community is all of the above, and the notion lacks clarity and allows the actors to escape their responsibilities. However, after this caveat, the expression will be used throughout this article.

  2. More formally, a criminal will maximize the following expected utility function [5]: \( EU=pU\left( {Y-f} \right)+\left( {1-p} \right)U(Y) \), with EU expected utility, p the probability of punishment, U the criminal’s utility function, f the severity of punishment, Y the income if undetected, and Y-f the income if punished.

  3. The time value of an option is the difference between the market value of the option and the intrinsic value.

  4. This is analogous to holding an American call option alive before the maturity date despite the fact that it can be exercised on any moment.

  5. Real-life real option modeling often requires more sophisticated models such as compound option models [8, 9], or numerical approaches. An overview of such models is beyond the scope of the article.

  6. The sixth lever (the risk-free interest rate) is largely exogenous and will be left out of consideration.

  7. The previous footnote also applies here.

  8. It should be noted that this threat also affects persons other than those occupying state functions, such as rebel leaders.

  9. The EU Special Representative for the Great Lakes Region Aldo Ajello has confirmed this information.

  10. According to the then U.S. Ambassador to Kigali Robert Gribbin, already in March 1996 Kagame told him that “if Zaire continues to support the ex-FAR/Interahamwe against Rwanda, Rwanda in turn could find anti-Mobutu elements to support”, adding that “if the international community could not help improve security in the region, the RPA might be compelled to act alone” [18]: 144–145.

  11. The existence of this project was later confirmed by documents discovered in November 1996 in Mugunga refugee camp, where many ex-FAR had regrouped.

  12. U.S. Ambassador in Kigali Gribbin believes that Kagame’s August 1996 visit to Washington ended in a misunderstanding: “Kagame judged that he was honest about Rwanda’s intent to dismantle the camps in the absence of an international undertaking to do so. In turn Secretary of Defense William Perry thought he laid down a clear marker that unilateral action was not advisable. Kagame thought he got an okay. Perry thought he had quashed the idea. Each went away happy” [18]: 175–176.

  13. As we shall see later, it (unsuccessfully) did during the second war.

  14. The report does not just point an accusing finger at Rwanda, but at other players (such as the armies of the DRC, Angola and Uganda, and nonstate armed groups) as well. However, the crimes committed by the Rwandan army were the most serious and widespread.

  15. Thus, for example, did The Washington Post of 3 October 2008 carry a story about the support of the US for the renewal of the contract of one of the indicted officers as deputy commander of the peacekeeping force in Darfur. The article argues that this support was in breach of US legislation outlawing “assistance to human rights violators”. The executive director of Human Rights Watch is quoted as stating that the US position prevents “any effort to hold a senior Rwandan officer accountable for serious atrocities”. Obviously, for Washington this sort of debate raises the issue of the political price it is willing to pay for its support for the Kigali regime.

  16. During the period 2003–2008 period, on average ODA amounted to 26 % of GDP and slightly more than 50 % of the state budget. Of total ODA, budget support type of aid interventions (sector and general budget support as well as HIPC debt relief funds) amounted to slightly more that 40 % on average. For details, see ODI/Mokoro [35].

  17. This section builds upon Reyntjens [39] where more details can be found.

  18. The Panel produced another “Final Report” in October 2003 (see infra).

  19. After Bout’s companies started providing logistical support to US forces in Iraq, he disappeared from the radar screen. Under US pressure, his name was taken off a draft UN list of mercenaries and arms dealers [17]. Cynically enough, Bout was arrested in Thailand in March 2008, on the basis of a US warrant issued for weapons deals with the Colombian FARC rebels.

  20. Aircraft owned by Bout and his frontmen continued to operate in the region during 2004 [52], paras 67, 69, 73, 151.

  21. Several reports point to the direct link between the exploitation of resources and the continuation of the conflict. The UN Panel notes that the control of mineral-rich areas “could be seen primarily as an economic and financial objective rather than a security objective for Rwanda” [49], para. 175; “Most of the fights between Rwandan soldiers and mai-mai have occurred in the so-called ‘coltan belt’” (idem, para. 176). Under the title “Rwanda’s unusual tactics”, the Panel found that “attacks (by the RPA) seem to coincide with the period when coltan has been extracted and put in bags for evacuation by the mai-mai. Attacked, the mai-mai abandon their coltan, which is then taken away by small aircraft” (idem, para. 177).

  22. In 2003, Rwanda produced about 120 metric tonnes of columbite-tantalite concentrates, 284 metric tons of cassiterite, and 109 metric tons of wolframite. These are very small volumes. However, exports amounted to 861, 3,553 and 156 metric tons respectively, still quite small figures, but showing the gap between production and (re-)export (US Geological Survey Minerals Yearbook 2004).

  23. This may seem a modest figure, but in light of the structure of the Rwandan economy, it is gigantic. Indeed in that same year, the production of export crops (mainly coffee and tea) only accounted for 0.4 % of GDP [23]: 80.

  24. Of course, it was not really invisible, but the international community preferred to turn a blind eye to these practices.

  25. This is a very clear example of what in option theory is called a growth option, i.e. an option to do a crime that, once committed, may give rise to other criminal options with additional potential net returns.

  26. Marysse [31] added that “as military spending … was limited as a condition for access to financial flows provided by the Bretton Woods institutions, … wartime plunder has helped finance the conflict”. He denounced the “ostrich policy” of a number of bilateral donors and the International Financial Institutions which, by continuing to fund the invading countries (Rwanda and Uganda) in the knowledge that their aid is fungible, indirectly supported the continuation of the war.

  27. The UN “Panel of experts on the illegal exploitation of natural resources and other forms of wealth in the Democratic Republic of the Congo”, also known as the “Kassem Panel”, has been criticised on account of its methodology and even political bias. However, the facts mentioned in this article are established beyond reasonable doubt and corroborated by several other sources (see e.g., [16, 26]).

  28. The “Congo Desk” had an office called “Production” which oversaw the economic aspects of Rwandan operations in the DRC.

  29. Many civil society sources in North and South Kivu reported Rwandan troop movements, and MONUC openly suspected the presence of the Rwandan army on Congolese soil (see, for instance, [24]).

  30. This unpublished Section V of the report is on file with the editors of this journal.

  31. Letter dated 20 October 2003 from Mahmoud Kassem, chairman of the Panel, to UN Secretary General Kofi Annan. Also this letter is on file with the editors of this journal.

  32. A few examples among many: the already mentioned unit with the telling name “Production” within the Congo Desk of the Rwandan External Security Organisation; the fact that Congolese minerals were exported by Rwanda Metals and Grands Lacs Metals, two companies controlled by the RPF/RPA and that foreign clients were contacted directly by the Congo Desk ([57]: 44); and the fact that the Rwandan embassy in Brussels contacted potential buyers for 32 tons of Papaine looted in the DRC [56]: 137.

  33. This was a structural feature, not linked to the decline as a result of war and genocide in 1990–1994. In 1989, the year before the war started, coffee accounted for US$ 59 million out of total exports worth US$ 97 million.

  34. For an analysis of these and other figures on the mineral trade, see Willum [57].

  35. The UN Panel of Experts adopts a broad interpretation of the concept of illegality. This included all or some of the following: violation of sovereignty, of regulatory frameworks, of widely accepted practices in trade and business, and of international law including “soft law” [49]: para. 15.

  36. “Foreign Troops in Congo Fighting, Rwanda Levels Genocide Charges”, DPA, 28 August 1998, quoted by [30]: 131. In this short sentence, Mazimhaka manages to lie twice: the Rwandan army was already in the DRC and the anti-Tutsi pogroms started after the beginning of the war, and indeed as a reaction to it.

  37. Uganda was less fortunate. It accepted the ICJ’s jurisdiction in a similar case and was found guilty of violating its obligations under a number of international legal instruments, and condemned to making reparations to the DRC [20].

  38. Right at the beginning, it even involved a daring airborne operation in the Bas-Congo, west of Kinshasa, over 1,500 km from Rwanda.

  39. “Congo rebels declare ceasefire, gunfire goes on”, Goma, Reuters, 29 October 2008.

  40. “UN says Rwanda fired tanks at Congo”, Goma, AP, 3 November 2008.

  41. Thus Richard Dowden, the director of the Royal African Society, published an op-ed in The Independent of 15 December 2008 under the title “Britain should cease its one-sided support for Rwanda”. Early March 2009, Canada announced that Rwanda was removed from its list of bilateral beneficiaries (it did not however explicitly link this decision to the UN report).

  42. See also Human Rights Watch, DR Congo: Rwanda Should Stop Aiding War Crimes Suspect. Congolese Renegade General Bosco Ntaganda Receives Recruits and Weapons from Rwanda, Goma, 4 June 2012.

  43. “Rwanda’s Paul Kagame warned he may be charged with aiding war crimes”, The Guardian, 25 July 2012.

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Authors and Affiliations

  1. Institute of Development Policy and Management (IOB), University of Antwerp, Antwerpen, Belgium

    Danny Cassimon & Filip Reyntjens

  2. School of Economics, Utrecht University, Utrecht, the Netherlands

    Peter-Jan Engelen

Authors
  1. Danny Cassimon
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  2. Peter-Jan Engelen
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  3. Filip Reyntjens
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Correspondence to Danny Cassimon.

Appendix 1: The Black-Scholes formula for call option valuation

Appendix 1: The Black-Scholes formula for call option valuation

The value of a criminal call option according to the Black-Scholes model can be calculated as:

$$ C=V\,{e^{{-\delta \left( {T-t} \right)}}}\,N\left( {d_1 } \right)-I\,{e^{{-{r_c}\left( {T-t} \right)}}}\,N\left( {d_2 } \right), $$
(A.1)

Where

$$ {d_1}=\frac{{\ln \left( {\frac{V}{I}} \right)+\left( {r_c -\delta +\frac{1}{2}{\sigma^2}} \right)\left( {T-t} \right)}}{{\sigma \sqrt{T-t }}} $$
(A.2)
$$ {d_2}=\frac{{\ln \left( {\frac{V}{I}} \right)+\left( {r_c -\delta -\frac{1}{2}{\sigma^2}} \right)\left( {T-t} \right)}}{{\sigma \sqrt{T-t }}}={d_1}-\sigma \sqrt{T-t }, $$
(A.3)

with

C:

value of a call-option

V:

present value of the expected proceeds of the crime (Y)

I:

expected cost of the crime (p.f)

T-t:

time to expiration (expressed in terms of years)

σ:

annualized standard deviation of the criminal return

rc :

continuous risk-free interest rate

δ:

opportunity cost (expressed in terms of years), and

N(d):

value of d under the cumulative normal probability density function.

The effect of a change in one of the parameters on the value of the call option (the so-called Greeks), i.e., the first derivative, is calculated as follows

Sensitivity of C to:

Name and symbol

Formula and sign of impact on C

Benefits of the crime (Y)

Delta

Δ

\( {e^{{-\delta \,\left( {T-t} \right)}}}\,N\left( {d_1 } \right) > 0 \)

Cost of the crime (p.f)

Psi

Ψ

\( -{e^{{-r\,\left( {T-t} \right)}}}\,N\left( {d_2 } \right) < 0 \)

Lifetime (T-t)

Theta

Θ

\( \begin{array}{*{20}{c}} {\frac{{-Y\:n\left( {{{d}_{1}}} \right)\:\sigma \:{{e}^{{-\delta \:\left( {T-t} \right)}}}}}{{2\:\sqrt{{T-t}}}}-r\:\left( {p.f} \right)\:{{e}^{{-r\:\left( {T-t} \right)}}}\:N\left( {{{d}_{2}}} \right)} \hfill \\ {+\delta \:Y\:N\left( {{{d}_{1}}} \right)\:{{e}^{{-\delta \:\left( {T-t} \right)}}}} \hfill \\ \end{array}>0 \)

Risk-free interest rate (r)

Rho

ρ

\( \left( {p.f} \right)\,\left( {T-t} \right)\,{e^{{-r\,\left( {T-t} \right)}}}\,N\left( {d_2 } \right) > 0 \)

Volatility (σ)

Vega

ν

\( Y\,\sqrt{T-t}\,n\left( {d_1 } \right)\,{e^{{-\delta \,\left( {T-t} \right)}}} > 0 \)

Opportunity cost (δ)

Ksi

Ξ

\( -Y\,\left( {T-t} \right)\,{e^{{-\delta \left( {T-t} \right)}}}\,N\left( {d_1 } \right) < 0 \)

The value N(d1) is the derivative of the standard normal distribution function with respect to d1

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Cassimon, D., Engelen, PJ. & Reyntjens, F. Rwanda’s involvement in Eastern DRC: A criminal real options approach. Crime Law Soc Change 59, 39–62 (2013). https://doi.org/10.1007/s10611-012-9397-7

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