programas acuáticos
4. Normas básicas:
In order to allow a close comparison of the results for bonds with the ones obtained originally by Heston and Rouwenhorst (1994) and ensuing studies using their standard decomposition model for equity returns, I will first follow their model and approach as closely as possible. This is the main model in Section 4.1. In the second instance, I propose a Varotto (2003) style extension based on what the information in my data set allows. This is the extended model in Section 4.2.
4.1. The main model
Suppose we have K countries and J industries. Furthermore, we have n = 1, … , N eurobond returns which are measured over the period t = 1, … , T. Note that I do not have a complete panel of eurobond returns as not all eurobonds n are traded over all time periods t . Let 789(t) be the time t return on eurobond n that is related to industry j = 1 ,.. , J and country k = 1, … , K. The basic cross-sectional decomposition that Heston and Rouwenhorst (1994) propose can be written as:
7 = α + ∑;8φ8:8 + ∑=9ψ9<9 + ε (3)
where the dependence of time is suppressed and where the vector 7 consists of all eurobonds 789. :8 and <9 are dummy variables defined as
3 Note that in this chapter both the standard and the extended decomposition is performed on outright returns. Heston and Rouwenhorst (1994) use the term ‘excess returns’, but in their case it refers to the return relative to the average market but decomposition is performed on outright (equity) returns. Varotto (2003) uses excess returns instead of outright (bond) returns as the data input for his extended decomposition model. These excess returns are derived from the contractual cash flows of the bond in question discounted by the risk-free rates derived from its zero government benchmark curve. Whenever the term ‘excess returns’ is used in this chapter, it has the meaning Heston and Rouwenhorst assign to it. Empirical results from the decomposition based on excess returns as the data input, calculated from the 1-month USD deposit rate, are very similar to results obtained from outright returns. These results are not shown in this chapter but can be provided upon request.
:8> ?1, if bond G belongs to industry P0, otherwise T and
<9> ?1, if bond G belongs to country V0, otherwise T
This decomposition needs to be performed for every time period t = 1, … , T. The coefficients φ8
and ψ9 capture the returns that can be assigned to specific industries and countries, respectively.
The decomposition in Eq. (3) shows that a eurobond return 7 can be decomposed into a general global component α, industry components φ8(j = 1 ,.. , J), country components ψ9 (k = 1, … , K), and an idiosyncratic term ε89. Note that the coefficients φ8and ψ9 are not identified, unless additional
restrictions are imposed. Heston and Rouwenhorst add the following restrictions:
∑;8W8φ8 = 0 (4a)
∑=9X9ψ9 = 0 (4b)
where W8 #X91 are the value-weights of industry j (country k) in the total universe of eurobonds.4 All the weights sum to unity:
∑;8W8 = ∑=9X9 = 1
The USD-equivalent of the amount issued is used as an indicator for the market value weight of each eurobond.5
The cross-sectional regressions subject to its restrictions are performed over all eurobonds that are present at time t. The industry and country coefficients, φ8 and ψ9, do not depend on the individual eurobonds n. Rather, the systemic part of the returns that can be assigned to these effects is obtained from the fitted values of the returns from the regressions and represented by the resulting estimated
coefficients φZ and Y ψ[. 9
This estimation procedure allows a decomposition into country and industry indexes in the following way (see Appendix A for the derivation). Let’s focus on the country indexes firstintroducing
4 By construction all individual weights are larger than or equal to zero: W
8 ≥ 0 and X9 ≥ 0.
5 The discussion focuses on value-weighting the returns. The same logic can be applied to the case of equal-weighting the returns. The latter can be achieved by giving each eurobond an equal weight in the computations.
weight \] that is the weight a particular eurobond n has in country ] from set k = 1, … , K, then the sum over the eurobonds results in:
]^ α_ + ∑;8φZY∑ \]:8 + ψ[ ] (5)
The value-weighted index return of country ] can be decomposed into a component that is similar to all countries,α_ , the average of the industry effects of the eurobonds that make up its index, and its
country-specific component, ψ[ . ]
For the industry indexes, a similar decomposition can be made if \` is the weight a particular eurobond n has in industry ` from set j = 1, … , J and a summation over the eurobonds yields:
`^ α_ + φa b ∑` ;8ψ[9∑\`<9 (6)
The construction of the decompositions in Eqs. (5) and (6) is repeated for every time period
t = 1, … , T, giving indexes 9#c1 and 8#c1 for countries and industries respectively on which the underlying
sources of variation can be determined.
To investigate whether the country effects are in part induced by the conversion of local currency returns into common currency, affecting all eurobonds of that country equally, the methodology proposed by Heston and Rouwenhorst (1994) is followed. Suppressing time dependency, the currency components of common currency returns on the value-weighted country indexes of country ] from set k = 1, … , K relative to the total market, denoted FX], is given by:
FX] = S] – ∑=9X9d9 , (7)
where d] is the percentage change of the local currency of country ] vis-à-vis the common currency and
∑= X9
9 = 1. ∑=9X9d9 is the weighted-average change of all local currencies that make up the total
market (including the local currency of country ]) to the common currency (a sort of ‘basket’), weighted by the size of their component in the total market. The calculation of the currency component through Eq. (7) is repeated for all t in the time period and for all countries k (where vk varies at each t) so as to obtain a
time series for each, ef]#c1, which is then regressed on the estimated country effects obtained earlier,
ψ[ #c1 in the following manner: ]
The null hypothesis H0: ] = 1 is accepted for those currency components and country effect pairs
that are fully correlated. The ]h of the regression for each country ] further indicates how much of the variance of country effects is explained by currency movements. The interpretation of this analysis is that it seeks out the part of the country effect that can be attributed to the fluctuation of the currency of that country to the common currency that has affected all businesses in that country equally, thereby leading to a common bond price move of entities located in that country. If this is the case then the macroeconomic situation and/or policy decisions in countries induce a strong correlation between eurobond returns and exchange rates beyond a mere currency conversion effect.
4.2. The extended model
Thee major differences between stocks and bonds influence the investment return made on a portfolio of each type of security and ought to be considered in the analysis. First, stocks have an infinite life (with the exception of those that are delisted) and bonds have a finite life (with the exception of perpetual bonds but these are excluded from my data set). The remaining life of the bond at the time of the investment is an important decision for an investor. It determines where along the yield curve one invests and this has a bearing on anticipated return prospects. The time horizon of the investment matters for bond and equity investors alike (as it is well-known in finance that uncertainty and return volatility increase with time), but bonds are by their nature more sensitive to the term structure of interest rates. Varotto (2003) finds a significant effect for maturity as a separate strategic portfolio investment allocation decision for corporate eurobonds that is more important even than industry diversification. My data set allows for the separate testing of the maturity effect in a Varotto-style extension of the Heston and Rouwenhorst model. The second important difference between stocks and bonds is that debt holders in general and bond holders among them rank above equity holders in terms of priority for repayment in case of the bankruptcy of a company. Where risk distribution of a company’s default probability is virtually binary in the case of equities, it is more graded for bonds. In order to assist bond holders in the assessment of default risk, companies as issuers of bonds and their individual bonds are often credit rated. This issuer and bond credit rating indicates the probability that a corporate issuer will make a timely and full payment on its outstanding debt liabilities under the contractual obligations of the bond in question. The credit rating, in conjunction with an investor’s own assessment of an issuer’s default risk, may change during the life of the bond but is at all times reflected in its market price and thereby its investment return prospects. Credit rating is therefore a contributing strategic investment decision for the composition of corporate eurobond portfolios. Varotto finds a significant effect for credit rating in eurobond returns, though not as significant as maturity but again more significant than industry sector as a means of risk diversification. Though it
would be interesting to separately test for a credit rating effect, my data set does unfortunately not allow for it. The credit rating information on the individual eurobonds is static (recorded at the issue date) and not dynamic as with Varotto’s database and is above all incomplete. Related conditions of the bond, such as its seniority, have a bearing on the return prospects in case of a default situation because the level of seniority among different types of bond issues determines the priority repayment privilege the respective holders have. As the eurobonds are pre-selected on the basis that they are senior unsecured, my database is not able to pick up on the point of seniority as a separate means of risk diversification. This less worrying though, as Varotto finds a very small effect for seniority, the least significant of all.
The third important difference between stocks and bonds concerns liquidity. Companies generally list only on one stock exchange so there is one unique price record for one stock from one company in the market place. Companies tend to issue a multiple of bonds which are not exchange traded but trade over- the-counter (OTC), resulting in multiple price records in different places in the market for multiple bonds from one company. This is the basic reason why liquidity differences are greater for corporate bonds than for equity, and hence matter more as an investment decision in the case of eurobonds. Varotto
acknowledges the importance of liquidity differences for bonds but decides against picking this up as a separate strategic diversification choice on the basis that liquidity is indirectly accounted for in the weighted-least squares estimation. In line with recent research (see e.g., Lin, H., Liu, S., Wu, C., 2009; Fontaine, J., Garcia, R., 2008; De Jong, F., Driessen, J., 2007) that liquidity premiums are a significant element in the determination of credit bond yield spreads, the liquidity effect is included in the extended Heston and Rouwenhorst model.
Based on the above discussion, the following modifications of the model defined under Eq. (3) are adopted:
7 = α + ∑;8φ8:8 + ∑=9ψ9<9 + ∑ i// j/ + ∑l%k%f% + m (9)
where dummy variables :8 and <9 remain as before and new dummy variables are incorporated to capture the liquidity effect, j/ for l = 1, …, L, and remaining life-to-maturity effect , % for m = 1, … , M, which are defined as
j/> ?1, if bond G belongs to liquidity bracket q0, otherwise T and
f%> ?1, if bond G belongs to maturity bracket s0, otherwise T
Additional restrictions are incorporated to define the model, where t/ and u% are the value weights of liquidity type l and remaining maturity type m in the total value-weight market.
∑;8W8φ8 = 0 (10a) ∑=9X9ψ9 = 0 (10b) ∑ t/i/ / = 0 (10c) ∑l u%k% % = 0 (10d) and ∑;8W8 = ∑9= X9 = ∑ t// = ∑l%u% = 1
Similar to Eqs. (5) and (6), the value-weighted index excess returns for the portfolios selected along the two main dimensions of country and industry sector are each decomposed as follows6:
]^ α_ +∑;8φZY∑\]:8+∑ i//Z∑\]jv+∑l%k%[ ∑\]f%+ψ[ ] (11) `^ α_ b ∑;8ψ[9∑\`<9+∑ i//Z∑\`jv+∑l%k%[∑\`f%+φa ` (12)
whereby \v and \w are the weights of each bond n in liquidity sector x from l = 1, … , L and maturity sector y from m = 1, … , M. Terms ψ[ and ] φa continue to represent the pure country and industry effects. `
In the country index decomposition, the term ∑;8φZY∑\]:8 continues to represent the value- weighted sum of industry effects in the portfolio of country ] and is added to by the value-weighted sum of its liquidity (∑ i//Z ∑\]jv) and maturity (∑l%k%[∑\]f%) structure. Similarly for the industry sector portfolios, `. The repeated estimation of Eqs. (11) and (12) gives time series for these effects.