Frozen Market
6.5 Trading Voluntarily
6.5.3 Temporarily Frozen Market 2
Afonso (2011, p. 340) suggests “trading halts [...] to slow down trading” as one feasible reaction to a one-sided market. Longstaff (2009) considers a temporarily frozen period that he calls ‘blackout’, during which the illiquid asset cannot be traded.142 I implement both concepts into the aggregate liquidity shock model
140 After 1.05 years, the percentage price change is less than 0.001% per day.
141 There is a special case for this setting: Assume severe aggregate liquidity shocks and trade is only intermediated by market makers, i.e.λ=0. Then, the impact on the bid-ask spread is negligible. It is only a very small parallel shift, compared to a setting without any aggregate shocks. Feldhütter (2010, p. 17) states a comparable result.
142 This blackout period is the only source of illiquidity in the model of Longstaff (2009).
in the following way: Assume that the market is characterized by a seller’s mar-ket a long time after the shock, i.e. µlo(ss) <µhn(ss). Assume further that the shock leads to a buyer’s market, which impliesµlo(0)>µ
hn(0). There is a single intersection time t∗, for which µlo(t∗) = µhn(t∗) with 0<t∗ <∞ holds. I sug-gest a trading stop after the shock if there are no gains from trade. At time t∗, this is when the market returns to a seller’s market again with µlo(t) <µhn(t) for 0<t∗ <t, trade reopens and continues with the constant intensitiesλandρ.
Summarizing all presumptions leads to two definitions for the meeting intensi-tiesλandρ, which are
λ(t) =
0 for 0≤t<t∗
λ fort∗ ≤t (6.14)
and
ρ(t) =
0 for 0≤t <t∗
ρ fort∗ ≤t. (6.15)
The aggregate liquidity shock leads to an elevated amount of potential sellers and a reduced amount of potential buyers—each compared to its steady state.
The only possibility of a type change during a trading halt is an idiosyncratic preference shock with intensitiesλu and λd. As a result, the remaining mass of potential buyers does not soak up the surplus of potential sellers, because trade is impossible. Instead, the mass of potential buyers increases monotonically and the mass of potential sellers decreases monotonically during the frozen period.
The proof for the latter proposition is as follows: The mass dynamics of µhnf (t) andµlof (t)are
˙
µlof(t) =−[λu+λd]µlof (t) +λds, for 0≤t≤t∗, (6.16) µ˙hnf (t) =−[λu+λd]µhnf (t) +λu(1−s), for 0≤t≤t∗, (6.17) where superscript ‘f’ assigns the ODEs (6.16) and (6.17) to the frozen time period 0≤t≤t∗. The solutions to equations (6.16) and (6.17) are
µlof (t) = µlo(0)e−(λu+λd)t+ λds λu+λd
h1−e−(λu+λd)ti, for 0≤t≤t∗, (6.18)
µhnf (t) = µhn(0)e−(λu+λd)t+λu(1−s) λu+λd
h1−e−(λu+λd)ti, for 0 ≤t≤t∗. (6.19)
It is clear from equations (6.18) and (6.19) thatµlof (t)and µhnf (t)converge mono-tonically. Since the relation µlo(ss) <µhn(ss) and µlo(0) >µ
hn(0) hold by as-sumption,µlo(0)>µf
lo(t∗) = µhnf (t∗)>µhn(0) must then hold as well. This con-nection completes the proof.
As soon as µlo(t∗) =µhn(t∗), the market reopens again. At this time, there are equally as many potential buyers as potential sellers in the market. Nearly all potential buyers and potential sellers are rapidly matched to each other, since meeting intensities are relatively high by assumption. The fraction of potential buyers are not close to zero at time t∗. With reference to equations (3.4) and (3.5), type changes due to trading generally dominate type switches then. As a result, a sharp drop of fractions µlo(t) and µhn(t) towards zero can be observed immediately after timet∗. Thereafter, masses start to converge monotonically to their long run values.
The evolution of probabilityπhn(t)reacts on the altered type evolution of poten-tial buyers discussed above. Since µhnf (t) is increasing until time t∗, the proba-bility πhn(t) is greater than zero for 0≤t ≤t∗. Function πhn(t) drops sharply below zero right after time t∗. But this time, it is only a short peak, since µhn(t) immediately starts to increase towards its steady state level after the sharp drop.
Nevertheless, the higher the meeting intensitiesλandρare, the more intense this peak is, because trade takes place quickly.
Example
Figure 6.7 illustrates the effect of this modification on mass dynamics.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Calendar time
µσ(t) µlo(t)µ
hn(t) µho(t) µln(t)
Figure 6.7:Process of mass distribution in a temporarily frozen market.
The pattern is as explained above: The fraction of potential buyers (sellers) in-creases (dein-creases) until the intersection time t∗ =0.48. This intersection time must be the same time as in chapter 5.2, sinceλu, λd, µho(0), and µhn(0)are not affected by the trading halt. At timet∗, the market reopens and buyers and sell-ers are matched quickly. Both fractions drop sharply and finally start to converge towards their long run level.
Prices are shown in the left panel of figure 6.8. No trade takes place during the first 0.48 years after the shock. There are no prices at all. At timet∗, the market reopens and market participants bargain prices. The prices a long time after the shock are only 4.14% lower than steady state prices without aggregate liquidity shocks.143
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 9.45
9.5 9.55
Calendar time
Price
Ps(t) As(t) Bs(t)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.01
0.02 0.03 0.04
Calendar time
Bid−Ask Spread As(t)−Bs(t)
A(ss)−B(ss)
Figure 6.8: Price process (left panel) and bid-ask spread (right panel) in a temporarily frozen market.
The right panel of figure 6.8 depicts the bid-ask spread. There are no bid-ask spreads during the first 0.48 years after the shock as well. The remaining part is similar to figure 5.11 but with higher meeting intensities.
Remark
One drawback of a market freeze is, as Camargo, Kim, and Lester (2013, p. 2) emphasize, that the price discovery process is interrupted. Trading prices do not only indicate the value of an asset for particular buyers and sellers at a particular time but also imply information for other agents. A recent example from the 2007 financial crisis is the impossibility of fair valuation of assets in three BNP Paribas investment funds. BNP Paribas temporarily suspended money withdrawals from these funds, as stated on August 9, 2007: “For some of the securities there are just no prices [...] As there are no prices, we can’t calculate the value of the funds.”144
143 The steady state price without aggregate liquidity shocks is P(ss) =9.9183, compared to Ps(ss) =9.5077 within this modification.
144 Alain Papiasse, head of BNP Paribas’s asset management and services division. See Boyd (2007) and Camargo, Kim, and Lester (2013), p. 2.
Therefore, a temporary market freeze is a suboptimal solution. The next section offers another possibility of controlling for gains from trade in the aggregate liq-uidity shock model.