Visión rememorativa de la retórica monástica.

Suppose, the common belief about the risky asset quality is later discovered, and that its worst payoff is equal toR00whereR00< R0. This is, to some extent, similar to the situation when the credit default swap (CDS) agreements were introduced into the market, and the market prices of mortgages backed the securities being discovered. Observing the sharp drop in the ABX Index in 2007, investors started to lower their valuation of a mortgage-backed security (MBS). Initially, as the investors had little information about a given MBS quality, they needed to rely on ratings provided by CRAs. The ratings were then shown to have been inflated, and, subsequently, these were revised down. As a rating usually indicates the level of risk attached to a given security, we can think of the rating in terms of the worst possible payoff of a risky asset, which could representR in this model.

As shown in Figure 4.5a, the ‘good news’ equilibrium re-allocates the holdings of cash and of risky assets to bew0h and y0h, respectively. As a result, the demand functions for risky assets, given the arrival of bad news (or the reversal of good news),y00h, could be explained by Eq(4.2), where, w_eh =w0h and y_eh =y0h. We can then show the characterisation of equilibrium below; this is followed by numerical example at the end.

Bad news results in a drop in the risky asset price top00 as, in equilibrium, wealth is being transferred to less optimistic agents,h < h0_m, who previously soldY

given good news. In response to a drop in asset quality and a lower risky asset price, there is a group of optimists who want to reduce their holdings of risky assets, and to supplyY into the market, while a group of less-optimistic agents, who preserve cash given good news ,are willing to acquire moreY. This less-optimistic group finds a drop in price ofY to be an opportunity for investment. The low valuation provided by these less-optimistic buyers exacerbates risky asset prices further in equilibrium. There exists the unique marginal buyerh00_m, who is indifferent between buying and sellingY, that is,y00h00m _=y0h00m_{. From Eq(4.2), it can be shown that the agents’}

wealth after re-distributionw0h+p00y0h is decreasing withhforh∈(h0_s, h0_b). This is because the risky asset demand (and supply) given good newsy0h−yh is increasing (and decreasing) with h. The numerical example of re-distribution of wealth is provided in Figure 4.8. In this case, although the price of Y drops, the marginal buyers shift up further toh00_m because the agents belowh00_m will be buyingY, while the agents aboveh00_m will be reducing their holdings ofY. The agent h0_m< h < h00_m

will be acquiring additionalY.

A similar logical argument, as inAppendix D.2.2, can be applied to show that unanticipated bad news will lower the marginal pessimist to h00_s < h0_s. Intuitively, lower marginal pessimist implies that less-optimistic agents are more willing to hold

Y as, from their point of view, the risky asset is relatively cheap compared to the drop in its worst payoff. However, the marginal optimistsh00_b can be above or below

h0_b depending onp00.

The equilibrium is determined by the system of two equations, Eq(4.10) and Eq(4.11) below. Eq(4.10) demonstrates the market-clearing condition, which equates supply and demand for risky assets. The left-hand side shows aggregate revenue. The first terms represent revenues of agents who were previously extreme optimistsh0_b < h < h00_b,, who become cautious optimists by selling parts of Y. The second term represent cautious optimists h00_m < h < h0_b who are reducing their holding ofY as, in their views, its price is too expensive. The right-hand side shows aggregate expenditure. The first term represents expenditure of cautious optimists

h0_s < h < h00_m, who are increasing their holdings ofY. The second terms represent the expenditures by new cautious optimists h00_s < h < h0_s, who see bad news as an opportunity to acquire additionalY.

Z h00_b h0_b p00(y0−y00)dh+ Z h0_b h00 m p00(y0−y00)dh= Z h00_m h0 s p00(y00−y0)dh+ Z h0_s h00 s p00(y00−y0)dh (4.10) where, h00_b = (p 00_−R00 1−R00 )( 1 p00) h00_s = p 00_−R00 1−R00

Eq(4.11) represents marginal buyer h00_m, who is indifferent between buying and sellingY, and who will not participate in the market because he finds his current holding optimal that isy00h00m =y0h00m. The left-hand side of the equation represents

y00h00m_{, which is given by applying Eq(4.2) to this equilibrium where the marginal}

buyer’s wealth is represented by w0h00m _+p00_y0h00m_{. The right-hand side represents}

y0h00m. (h00_m(1−R00)−(p00−R00)) (1−p00)(p00−R00) (w 0h00m_+p00_y0h00m_{) =} (h 00 m(1−R0)−(p0−R0)) (1−p0)(p0−R0) (w h00m_+p0_yh00m₎ (4.11) which implies h00_m= −R 0_−p00_{(1 +R}0_{(−2 +R}00_{)) +R}00_+p0_(1−p00_R0_{+ (−2 +p}00_+R0_)R00₎ (p0_−p00_{)(−1 +R}0_{)(−1 +R}00₎

From a system of equations above with two equations and two unknowns, we can solve for the risky asset price p00 and the marginal buyerh00_m. We can then determine the marginal optimisth00_b and the marginal pessimisth00_s, accordingly. For

R00 =R = 0.2, we get p00 = 0.565, h00_m = 0.626,h00_b = 0.807, and h00_s = 0.456. Figure 4.7a shows allocation of Y across agents. Figure 4.7b shows consumption plans in

U and Dof all agents. It is also interesting to see the re-distribution of wealth after the good news, as shown in Figure 4.8. Figure 4.9 summarises the distribution of agents in all equilibria of the non-leverage economy.4

The reversal of good news leads to new allocations ofY across agents, and to a drop in the price ofY. The impact on wealth will be perceived most by the agents who bought the risky asset given good news. Indeed, the price ofY becomes even

lower than the price in the initial equilibrium, though the asset quality is reversed to the same quality, as in the initial equilibrium. This amplification mechanism arises mainly from the risk-averse assumption as the downward sloping supply curve is exhibited by the optimists who need to reduce their holdings ofY, even though a lower price will affect their wealth and lessen their incentive to holdY.

(a) Distribution of risky asset holdings (b) Consumption plans in U(Green) and D(Red), and expected consumption (Black)

Figure 4.7: No-leverage economy - a ‘good news’ reversal equilibrium

Figure 4.8: No-leverage economy - wealth re-distribution with ‘good news’ reversal