Liquidity Risk

First, we need to have more information about the situations of convertible bonds in Taiwan market. In figure 1, we can see the total volume of convertible bonds in Taiwan from 1997 to 2013.

Figure 3-1. Total trading volumes of convertible bonds in Taiwan market

Asia financial crisis occurred in 1997, and there were a lot of companies with financial crisis at that time. The credit risk of the financial products which relate to those companies were higher and higher, leading to the price of these financial products lower and lower. Since the investors were afraid that those companies would default, they would not buy these financial products. We can see that the total volume of convertible bond is just around 21.5 million dollars in 1997, and the total volumes are increasing during 1997 to 2004. The biggest total volume of convertible bonds is in 2007, and then the total volumes are decreasing during 2007 to 2010 because there was another financial crisis during 2008.

Compared to the government bonds, the total volumes of government bonds are almost 200 times greater than the total volumes of convertible bonds in figure 2.

Clearly, the total volumes in the convertible bonds market are really small in Taiwan, so the liquidity risk of convertible bonds in Taiwan market is important.

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Figure 3-2. Total trading volumes of

government bonds and convertible bonds in Taiwan in 2013

There are some common indicators to see the liquidity of the market, we are going to introduce them as follows:

(1) The Depth of the Market:

It indicates the volume of the financial products. If the volume is large at the specific price, the liquidity of the product will be perceived as good. Otherwise, the liquidity will be perceived as not good in the market.

(2) The Width of the Market:

It indicates the bid-ask spread of the financial product. If the bid-ask spread is large, it means the willing to pay of the buyer is much lower than the willing to pay of the seller. So if they want to trade to each other, the willing to pay of the buyer should increase a lot or the willing to pay of the seller should decrease a lot.

Then the trade could be done. Since they have to make a larger concession for the deal to be done, so the bid-ask spread is larger, the product in the market is less liquidity.

(3) Immediacy of Trade:

It indicates the time to make trade be done. If the trade could be done in a short time, which means the market is liquidity. The longer the time for trade is, the less liquidity the market is.

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There is a widely used illiquidity measurement proposed by Amihud (2002), the ratio gives the absolute (percentage) price change per dollar of daily trading volume, or the daily price impact of the order flow. It can be written as follows:

ILLIQ_iy = ¹ use this measurement with Fama-French model to do the regression and estimate the liquidity to price assets in US water transportation.

It is difficult to put this model into our model to estimate liquidity risk directly since we will face some problems as follows:

(1) We do not have the data about the future volumes of the convertible bond on the pricing date. And simulate them is not a reasonable method when we estimate the liquidity risk because volumes should be fact rather than fake.

(2) Compare with other bonds, the volume of the convertible bond is so small that will make the illiquidity measurement become too large.

(3) It is impossible to know the number of the trading day of future years.

To solve these problems about volume, we use another two methods to estimate the liquidity risk as follows:

a. Volume Method

We construct a system to solve these problems. First, calculate the proportion of the trading volume of the convertible bond to all trading volumes of convertible bonds.

Let W_i = 𝑇𝑟𝑠𝑑𝑇𝑙𝑇 𝑉𝑉𝑙𝑑𝑉𝑠_𝑖

𝑇𝑉𝑡𝑠𝑙 𝑇𝑟𝑠𝑑𝑇𝑙𝑇 𝑉𝑉𝑙𝑑𝑉𝑠 ………..……… (11)

where Trading Volume_i is the trading volume of convertible bond of company I, and Total Trading Volume is the trading volumes of all convertible bonds in the market

Second, we put each proportion into nine groups which are [0, 0.02), [0.02, 0.04), [0.04, 0.06), [0.06, 0.08), [0.08, 0.010), [0.10, 0.12), [0.12, 0.14), [0.14, 0.16), and [0.16, 1). Then we need to find the liquidity factors to correspond to these groups.

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According to liquidity preference theory, market participants need to be compensated for the interest rate risk associated with holding longer-term bonds. We can see this situation in figure 4.

Figure 3-3. Term Structure

So we choose to use the difference between the interest rate of the 10-year government bond and the interest rate of the 1-year government bond to estimate the liquidity risk.

Let d = interest rate₁₀ – interest rate₀₁

where interest rate10 is the interest rate of 10-year government bond, and interest rate01

is the interest rate of 1-year government bond.

d^* = 𝑇𝑙𝑡𝑠𝑟𝑠𝜆𝑡 𝑟𝑠𝑡𝑠₁₀− 𝑇𝑙𝑡𝑠𝑟𝑠𝜆𝑡 𝑟𝑠𝑡𝑠₀₁

𝑙𝑑𝑉𝑛𝑠𝑟 𝑉𝑜 𝑇𝑟𝑉𝑑𝑠𝜆 ………(12).

= 𝑇𝑙𝑡𝑠𝑟𝑠𝜆𝑡 𝑟𝑠𝑡𝑠₁₀− 𝑇𝑙𝑡𝑠𝑟𝑠𝜆𝑡 𝑟𝑠𝑡𝑠₀₁

9 , since we have 9 groups.

So we can get the liquidity factor table as follows:

Table 3-1. Liquidity Factor Table Weight (W_i) Liquidity Factor 0.02↓ 8d^* + d^*

0.02~0.04 7d^* + d^* 0.04~0.06 6d^* + d^*

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Obviously, after we find the weight of the volume of the convertible bond, we will have the correspondent liquidity factor. We can write the liquidity factor function as follows:

On the other hand, we also can use bid-ask spread to estimate the liquidity risk. We already know that the width of the market indicates the bid-ask spread. The bid-ask spread is larger, the convertible bond in the market is less liquidity. In this method, we use the average bid-ask spread over the average convertible bond price as liquidity factor directly. We can write it down as follows:

LIQ = 𝑠𝑎𝑠𝑟𝑠𝑇𝑠 𝑛𝑇𝑑−𝑠𝜆𝑎 𝜆𝑠𝑟𝑠𝑠𝑑

𝑠𝑎𝑠𝑟𝑠𝑇𝑠 𝑐𝑉𝑙𝑎𝑠𝑟𝑡𝑇𝑛𝑙𝑠 𝑛𝑉𝑙𝑑 𝑠𝑟𝑇𝑐𝑠 ………(13)

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