Thus, according to Kautilya, a king’s utility depended on his wealth relative to that of his enemy. That is, U = U (R) Where R = W1/W2, W1 = a king’s own wealth and W2 = enemy’s wealth.
According to Kautilya’s hypothesis, only the relative standing was relevant and not the marginal changes in one’s own wealth.3 The utility function may be highly concave in the relative assets and could have a kink if the value of R was less than one.4 Since in that case, any adverse change in R could affect the survival of a king, therefore, such a reference point is justified. But in general, one has to explain how an individual determines a reference point, how it shifts and how much time he takes to assign it the status of a reference point.5 The current assets are unlikely to be a reference point unless linked to something intrinsic. The loss-aversion hypothesis, at best, in its current form, seems to be incomplete since it does not answer such questions satisfactorily.
18.4 KAUTILYA ON INVARIANCE HYPOTHESIS Prosperity and Shift in the Utility Function: Machina (1982) discusses the Markowitz’s ‘invariance hypothesis’ at length. Markowitz observed that both poor and rich individuals play lotteries and buy insurance policies. A fixed utility function cannot explain this invariance. Therefore, according to Markowitz, as the wealth of a person increases, his utility function shifts horizontally. Kautilya (p 624) stated, ‘The king may face dangers even from a trusted king of equal power, when the latter has achieved his objective. Even an equally powerful king tends to become stronger after the task is accomplished and, when his power has increased, becomes untrustworthy. Prosperity changes peoples’ minds (7.5).’ According to Kautilya, a king might become less risk-averse, implying that the utility function was concave for R≤1 but became almost linear for R>1. That is, utility function’s shape might change significantly. Thus, according to Kautilya, the invariance hypothesis was not valid. It seems that the invariance hypothesis is incompatible with loss-aversion hypothesis.
It may be emphasized that Kautilya was very critical of gambling, and considered it as a zero-sum game and gamblers as irrational, implying that a rational investor would not have any convexity in his utility function. According to him (p 138-139), ‘Of the two parties [in gambling], one has to lose as we know from the stories of Nala and Yudhishtira. The same wager won by one is, to the loser, a fish-hook which becomes a source of enmity. A gambler never knows how much wealth he has got, tries to enjoy wealth which he has not got and loses it before he can enjoy it. Being irregular in his habits, he contracts stomach, urinary and bowel disorders’. He (p 140) continued, ‘Gambling is the most evil among vices, because it destroys the ruling class by depriving them their ability to govern (8.3)’. However, he considered some limited but highly controlled gambling to raise revenue for the state. He recommended a five per cent tax on winnings. He (p 355) suggested, ‘The Chief Controller shall be responsible for ensuring that gambling is carried out [only] in designated places under the supervision of honest gambling masters, in order to detect men who follow secret activities [like spying] (3.20).’
18.5 KAUTILYA’S HYPOTHESIS: POWER BREEDS MORE POWER Kautilya believed as the relative asset ratio R increased, the probability distribution of returns changed. He listed three sources of such a change.
• Acquisition of Additional Wealth with Every Conquest: He (p 259) stated, ‘With increased wealth and a powerful army, more territory can be acquired, thereby further increasing the wealth of the state (2.12).’
• A Stronger King Secured a Favourable Treaty: He (p 587) observed, ‘An equal treaty is one in which the stronger king gets a larger share, an equally powerful king an equal share and a weaker king a smaller share. An unequal treaty is one in which a strong, equal or weak king does not get a share according to his power (7.8).’
• Strength Won Support: He mentioned that ‘a mighty king can get the help of another energetic one or he can hire or buy heroic fighters’ (9.1). That is, it was easier for a powerful king to win the support of other kings.
Now-a-days, rich clients are treated differently by brokerage firms (they are designated as premium accounts) and face a more favourable efficiency frontier. A small investor cannot participate in the hedge funds or buy even one share of Berkshire Hathaway. Big investors also have informational advantage and sometimes benefit from after hour trading, implying that financial markets may be segmented. That implies that the separation theorem may not hold.
SUMMARY It is not claimed that Kautilya understood the vertical summation of individual demands curves or the concept of deadweight loss or developed demand revealing mechanisms. However, he appears to understand the non-rivalry nature of public goods. A foreign ruler deprives the country of its culture and prosperity. Kautilya advised the king to protect national freedom by every available means and at every cost.
The Arthashastra contains a detailed discussion on the organizational structure of the defence services and the responsibilities and salaries of the key officials. Kautilya also stressed the war-readiness of both mammals and equipment. For example, he (p 693) wrote, ‘The horses shall be bathed twice a day and decorated with garlands and perfumes (2.30).’ Roger Boesche (2002, p 105) comments, ‘In this, Kautilya makes us pause in surprise. Do we want a state this intrusive? Does the state really need to command us to bathe horses twice a day, to wash clothes only on smooth stones, to prescribe penalties for tossing dirt in the road or for harming bushes, and to tell us at what time we must cover our windows at night?’ Boesche is not paying attention. Kautilya was not giving any command to private individuals as to how they took care of their horses. Kautilya was talking about horses in the king’s stable, which were going to be used in a battle. Keeping them clean was critical to protect them against diseases. This instruction was for a state employee who was responsible for their readiness for a battle.6 We might take it illustratively–as a small example–signifying his concern for all time defence preparedness.
19
Risk-return Analysis of Campaigns
Markowitz has been rightfully acknowledged as the founder of the modern portfolio theory. His (1952) seminal contribution showed how to construct a diversified portfolio.1 He (1999) provides a historical review of the contributions of several writers, including Shakespeare, from 1600 onwards to the portfolio theory. Rubinstein (2002) adds a few more contributions, including Bernoulli’s (1738), on the desirability of diversification, which was left out of Markowitz’s list of contributions. Varian (1993) describes the pre-Markowitz state of portfolio theory, ‘The fact that investors should care about both, the risk and the return of their investments is so commonplace today that it is hard to believe that this view was not appreciated in 1952.’2 All these historical reviews regarding the developments in the portfolio theory have been limited to Europe and only to the last four hundred years. It is remarkable that Kautilya, two thousand years earlier than Bernoulli (or Shakespeare), considered risk-return tradeoffs in making choices involving risky situations. Although he was not aware of the terms, such as portfolio balancing, diversification, meanvariance approach, the relative risk-aversion, absolute risk-aversion, risk premium, and expected or non-expected utility theory, he did use some of these concepts in making various choices.
Kautilya’s goal was to bring the whole Indian sub-continent under one rule but he pursued it very cautiously. He is the first known economist, who explicitly used the risk-return trade-offs in making alliances for joint campaigns. This is discussed in Section 19.1. Similarly, Kautilya used the risk-return trade-off in the acquisition of land and its location. This analysis is presented in Section 19.2. He suggested diversification to reduce risk and a few applications of the principle of diversification are discussed in Section 19.3. Section 19.4 presents his unique insight in analyzing the complementary nature of variables, which were considered relevant in the determination of success of a campaign.
19.1 RISK-RETURN TRADE-OFF IN MAKING ALLIANCES Machina (1987) remarks, ‘During the development of modern probability theory in t
he 17th century, mathematicians such as Blaise Pascal and Pierre de Fermant assumed that the attractiveness of a gamble offering the payoffs (x1…xn) with probabilities (p1…pn) was given by its expected value x—= Σxipi’. Pascal-Fermant correspondence was concerned with making sure that there was equity in sharing the winnings from gambling. Nicholas Bernoulli (1713) produced the St Petersburg paradox to show the inadequacy of the expected value in ensuring equity, and also challenged something very fundamental: a belief prevailing at the time that there was no tension between reasonableness and prudence.3 Daniel Bernoulli (1731/1738) proposed the replacement of the expected value by expected utility, which he called ‘moral expectation’. He proposed a logarithmic utility function to resolve the St Petersburg paradox and used it to justify the desirability of diversification.
Kautilya considered choices involving risky situations as an important part of economics.4 In fact, Kautilya applied the risk-return trade-off in all kinds of activities, that is, whether it was an acquisition of an asset, the selection of an ally or waging a war. A few applications of such trade-offs are provided below. It is not claimed that Kautilya had a fully developed theory of portfolio balancing. Rather, the claim is that he was aware of the relevance of both risk and return in making choices under situations involving risk.
Kautilya (p 634) asserted, ‘A small revolt in the rear outweighs a large gain in the front; for, when the king is not there, a small revolt in the rear may be worsened by the anger of the people or by traitors, enemies and jungle tribes. If this happens, a large gain in front, even if actually obtained, will be eaten up by the subjects, allies, losses and expenses. Therefore, a king shall not undertake a campaign when the gain in front is [less than] a thousand times the likely loss due to a revolt in the rear or, at least, a hundred times the loss. A well-known proverb is: ‘Misfortunes are, [in the beginning] not longer than the point of a needle’ (9.3).’ He continued, ‘The king shall undertake a march when the expected gain outweighs the losses and expenses (9.4).’
It is significant that Kautilya explicitly stated that a king should go on a campaign only if the expected gain was larger than the expected loss (of trained men and animals and reduction in wealth and grains). He specified this as a necessary condition for undertaking a project. If the above statement is interpreted in an overall context, it has two salient features: (i) display of a highly risk-averse behavior. That is, the king should not start a campaign unless the expected gain was several times the expected loss. (ii) He wanted to make sure that all the losses were added up so that an appropriate decision could be made.5
Kautilya on Risk-return Trade-off: He (p 608) asserted, ‘When there is a choice between two possible allies, both in difficulties, of whom one is constant but not amenable to control and the other is temporary but controllable, which one should be preferred? Some teachers say that the constant friend, though not controllable, is to be preferred because, even if he cannot help, he can do no harm. Kautilya disagrees. The one amenable to control, though a temporary ally, is preferable because he remains an ally only as long as he helps. The real characteristic of friendship is giving help (7.9).’ He (p 608) continued, ‘When there
Figure 19.1: U0,U1 and U2 are the indifference curves showing risk-return preferences. Points A, B, D and O represent available choices related to risk and return (help). is a choice between two possible allies, both amenable to control, of whom one can give substantial but temporary help and the other a constant help but only a little, which one should be preferred? Some teachers say that a temporary friend giving substantial help shall be chosen because such a friend, by giving a lot of help in a short time, helps to meet a large outlay. Kautilya disagrees. The constant ally giving smaller help shall be preferred. The temporary friend giving substantial help is likely to withdraw for fear of having to give more or, even if he actually provides the help, will expect it to be repaid. The constant ally, giving a small help continuously, does, in fact, give great help over a period of time (7.9)’. Figure 19.1 captures his reasoning.
Kautilya considered four types of allies: (i) (reliable, no help) represented by point O; (ii) (not reliable, some help) indicated by point A; (iii) (not reliable, large help) indicated by point D and (iv) (reliable, small help) given by point B (this is like a return on a safe asset). First, he compared point O to point A and according to him, point A should be preferred and then, he compared point D to point B and he preferred point B to point D. Additionally a reliable friend ‘giving a small help continuously’ would have resulted in a shift of the indifference curve U2 upward and, therefore, even more desirable.
19.2 RISK-RETURN TRADE-OFF IN ACQUIRING LAND Type of Land: During the fourth century BCE, there was no stock market, a market for bonds or even paper money and there were no financial institutions or financial derivatives. The only assets available were the different types of land, precious metals like gold and silver, and precious stones like diamonds. Yet, it is remarkable that Kautilya considered the expected return and risk of an asset as critical factors in its acquisition. He (p 619) stated, ‘As between land dependent on rain and land with flowing water [ie. a river], a smaller tract with flowing water is preferable to a larger drier one because with flowing water, which is always available, the production of crops is assured. As between two irrigated tracts, one on which cereals can be grown is preferable. [However], if one of them is larger, the larger one unsuitable to the cultivation of cereals is preferable to the smaller one, which is suitable. For, not only can different types of wet crops, dry crops and medicinal plants be grown in [different parts of ] a large area but also many forts and defensive works can be built. The value of land is what man makes of it (7.11).’
The above statement by Kautilya contains three comparisons. Let us compare them separately.
The first one involves comparing an irrigated tract of land, which might provide lower but more ‘assured’ yield to a dry tract of land, which might provide a higher but less certain yield. Figure 19.2 is used to capture this comparison.
The risk-return trade-off for the irrigated tract is represented by point B and that for the dry tract of land is represented by point A. Kautilya preferred Point B to point A, despite the fact that the expected return at point B was lower than that at point A because the risk was also lower at point B. He displayed a risk-averse behavior.
Between two irrigated tracts of land, the one, which was suitable for growing cereals, was preferred,since both the tracts were irrigated implying that risk was the same. However, it seems that the return from cereals was higher than that from non-cereals. Therefore, point B, which represents the cereal production, was preferred to point A.
Between two irrigated tracts of land, the one, which was larger
Figure 19.2: U0 and U1 are the indifference curves showing risk-return preferences. Points A, and B represent available choices related to risk and expected return.
Figure 19.3: U0 and U1 are the indifference curves showing risk-return preferences. Points A, and B represent available choices related to risk and expected return. and unsuitable for growing cereals, was preferred to the one, which was smaller but suitable for growing cereals. He offered several possible explanations for this choice. According to him, a larger tract was likely to offer a larger number of choices. This would be because potentially, a larger variety of crops and plants could be grown to satisfy diverse consumption and medicinal needs. Also, it might have provided suitable sites to build forts and other defense works to enhance national security. Thus, the total expected return from a larger tract might be much higher than that from a smaller tract on which cereals could be grown (both tracts were irrigated implying the same degree of risk). It is apparent that he considered both return and risk in making a selection (figure similar to Figure 19.3 could be used in this case).
Risk-return Trade-off in Deciding on the Location of the Land: Kautilya, in addition to the economic risk, considered a political risk also in acquiring a piece of land. He (p 61
8) asked, ‘Which is better—a rich land with permanent enemies or poor land without permanent enemies?’ He answered it as follows: ‘Some teachers say that, because a rich land enables one to get wealth and an army with which to destroy the enemies, a rich land with permanent enemies is preferable. Kautilya disagrees. Acquiring land with such enemies, one only adds to one’s number of enemies; and an enemy remains an enemy whether he is helped or harmed: on the other hand, a temporary enemy can be made to be quiet through favours or at least by not harming him (7.10).’ He was comparing the risk and return from this choice, which may be expressed by Figure 19.4.
Point A indicates a higher expected rate of return and a higher risk as well (rich land with permanent enemies) compared to those indicated by point B (not as fertile but without permanent enemies). Thus he would prefer point B on the higher indifference curve U1 to Point A on a lower indifference curve U0.
Figure 19.4: U0 and U1 are the indifference curves showing risk-return preferences. Points A, and B represent available choices related to risk and expected return. 19.3 RISK REDUCTION THROUGH DIVERSIFICATION Nobel Laureate James Tobin (1958) provided a formal analysis in justification of the ancient maxim. Not to put all your eggs into one basket. The modern concepts of variances and co-variances were not available to Kautilya, but his insights on risk reduction through diversification are quite modern.6 He proposed its application in several economic and non-economic situations. A few of them are presented below.
Not to Keep All Soldiers in one Place: According to Kautilya (p 561), if a king ‘Perceives [that it will be of advantage to him] he may [in the following situations] wish power and happiness even to his enemy. If a powerful enemy is likely to antagonize his subjects by harming them verbally or physically or destroying their property or if an enemy enjoying his success is to become negligent or weak due to [excessive] indulgence in hunting, gambling, women or drink, it will be easy to overpower him. If an enemy, when attacked, is likely to be found with all his troops in one place other than his fort, he will be easily overpowered, being friendless and unprotected by his fort (6.2).’
Kautilya- the True Founder of Economics Page 32