We define liquidity as the measure of the ease with which we can buy (and even more, sell) a financial instrument. The best measure of liquidity is the bid-offer spread, the difference between the price at which one is willing to buy and the price at which one is willing to sell.

The bid-offer spread is a proxy of the knowledge we possess of a particular market. If someone asked us the prices at which we would buy and sell a pint of milk we might not be able to exactly remember how much we paid last time we went shopping, but we would give two numbers fairly close to each other (and bracketing the average market value). If the same question was about a vintage sports car, we would not, except for the most fortunate among us, be able to show the same level of confidence, and the two prices would be much, much farther apart (and possibly not even bracketing the average market value). This is because knowledge is linked to the frequency with which an item is bought and sold, which in itself is a definition of liquidity.

Previously, we mentioned how even more important than the price at which we buy a financial instrument is the price at which we can sell it. Let us imagine that we would like to purchase a security and let us assume that we are told that there is going to be a certain amount of time in which we will not be able to find a buyer should we wish to sell it. What would be the relationship between the amount of time and the price we are willing to pay for the security? Financial common sense dictates that the longer the amount of time in which we would be unable to sell it, the lower the price we will be willing to pay for it. Similarly, let us assume that we want to sell a security but we are told that we won't be able to purchase the same or a similar one for a certain amount of time. Again, the longer the amount of time, the higher the price we are going to sell it for. Combining the two, the longer the uncertainty to find a buyer/seller, the lower/higher our bid-offer prices and hence the wider the bid-offer spread. The fact that the price at which we wish to sell is probably slightly more important is due to the fact that, in general, and this might be a gross generalization, the market is more risk averse in nature.^{[1]}

Emerging markets are characterized by considerably lower levels of liquidity when compared to developed markets. This is due to general uncertainty and to a certain volatility of interest by which we mean that

FIGURE 4.1 A comparison between developed and emerging markets bid-offer spreads, a) Developed markets: USD and EUR five-year interest rate swap rates; b) advanced emerging markets: ILS (Israeli Shekel) and CZK (Czech Krone) five-year swap rate as of September 6, 2011. Source: Thomson Reuters Eikon.

the appetite for investment is particularly sensitive to news and information. On the back of current news there might be more or less appetite at unpredictable moments to an extent far larger than in the case of developed markets where appetite is driven perhaps by wider and less explicit considerations. Another important factor driving liquidity and lack thereof is the fact that the volume traded in emerging markets and its frequency are considerably smaller.

Figures 4.1 and 4.2 show a set of quotes for the five-year interest rate swap rates for a certain number of developed and emerging countries. The goal of the figure is to show the widening bid-offer spread. Figure 4.1a shows the quote for EUR and USD, the two most liquid currencies in the world: the bid-offer is less than 2 bps. Figure 4.1b shows two advanced emerging markets, Israel and the Czech Republic: the quote for the same maturity of the same instrument is now in the order of 5 bps. Figure 4.2a shows the same quote for two middle-ranking emerging markets, South Africa and Hungary: the bid-offer is now 10 bps. Finally Figure 4.2b shows the five-year swap rate for two emerging markets belonging to the least developed ones, Turkey and the Philippines: the bid-offer is now 30 bps and 55 bps respectively.

We have shown quotes for interest rate swaps because we wanted to show the difference in bid-offer spreads between developed and emerging market currencies: in developed markets, interest rate swaps are among the most common instruments. This, however, could be a bit misleading since a swap might not necessarily be the most common instrument in all markets. We said in Section 2.2.3 that in some emerging markets FX forwards are the

FIGURE 4.2 A comparison between developed and emerging markets bid-offer spreads, a) Mid-development emerging markets: ZAR (South African Rand) and HUF (Hungarian Florin) five-year swap rates; b) low-development emerging markets: TRY (Turkish Lira) and PHP (Philippine Pesos) five-year swap rate as of September 6, 2011. Source: Thomson Reuters Eikon.

most liquid instrument type, more so than interest rate swaps. In the case of Turkey we see that the bid-offer is quite wide for swaps; it could be that for FX forwards it might not be so wide. To test this we are going to use the

information shown in Figure 4.3a.

Let us remind ourselves of what we have discussed in the chapter about curve construction. If we want to obtain the discount factor at time T in TRY using FX forwards (see Equation 2.3), we need to use

from which we can obtain the zero rate equivalent (which we have defined in Section 2.4.3 as a nontraded value useful for illustration purposes) by doing

in case of linear compounding or

FIGURE 4.3 FX forward rates for a) Turkish Lira (TRY); b) a selection of African currencies as of September 7, 2011. Source: Thomson Reuters Eikon.

in case of continuous compounding. We show both types of compounding since a zero rate is not an officially traded quantity with specified characteristics: both could be valid. The same calculation applies, of course, to bid and offer prices.

From Figure 4.3 we see that the bid-spot FX rate is 1.7618 Turkish Liras for one U.S. Dollar and the offer FX rate is 1.7644. We are going to calculate the zero rate equivalent for a maturity of three years (the farthest available). The bid pips are 2,837 and the offer pips are 2,956. Assuming the USD discount factor (which we know is a big assumption, but since our goal is to find a relative measure, i.e., the bid-offer spread, the impact of this assumption is limited), we obtain the discount relative to the bid quote, and the one relative to the offer quote, . Since it is difficult to compare discount factors and get a feel for a market spread, we convert them into zero rates.

The bid and offer zero rates^{[2]} linearly compounded are

and

if continuously compounded. If they seem different from the rates quoted in Figure 4.2b let us not forget that they must be different; those are swap rates (the coupon in Equation 2.4), these are zero rates (the r in Equation 2.2).

If we now calculate the bid-offer spread we see that it is 20 bps in the case of the continuously compounded rate and 23 bps in the case of the linearly compounded rate. This is roughly two-thirds of the bid-offer on the swap rate,^{[3]} that is, it shows a far greater liquidity. Nevertheless, the bid-offer is far from the levels found in a developed market. As an emerging market develops, as different market participants enter into it, as the principal amount of trades increases, the bid-offer tightens.

[1] Shown, for example, by the fact that, at equal distance from current prices, equity put options are more valuable than equity call options.

[2] To be more correct, the calculation is slightly more complicated and can be seen in Appendix A; however, for a feel of the magnitudes involved, these numbers are sufficiently precise.

[3] The three-year quote is not shown in Fig. 4.2b, but its bid-offer was also 30 bps.

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