International Bond Pricing Homework

Homework 5Vikas Kumar Singh

International Bond Pricing HomeworkThe purpose of this assignment is to develop your knowledge of asset pricing models in an international context. In particular you will to investigate if the law and finance factors are important in pricing of individual securities. In addition, you will get hands-on exposure to corporate bond pricing models and re-enforce your knowledge of spreadsheet (or regression package) modeling.

The Miller Investment Trust is the manager of a large, privately held stock and bond portfolio. The board of directors has recently had decided that in order to diversify, it should contemplate the purchase of some international bonds. Currently, all the corporate bonds it holds are from U.S. based firms. In particular, the fund is contemplating corporate bonds issued by non-U.S. companies and therefore needs to develop a model that will help identify the factors that are important to pricing foreign corporate bonds. They have given this assignment to the bond portfolio manager (your mentor), who has in-turn given it to you. You will present your findings to the board, so your boss has asked you to answer the following questions to get you ready. Specifically, your boss asked you to address the following questions:1. Are the factors the firm currently uses to price U.S. corporate bonds useful in explaining non-U.S. corporate bonds?In order to answer this question, you should the run firms current U.S. bond pricing model on a sample of foreign corporate issues provided.As per the current method of pricing the bonds, the regression analysis is as follow:SUMMARY OUTPUT

Regression Statistics

Multiple R0.898846073

R Square0.807924262

Adjusted R Square0.798592648

Standard Error0.663662434

Observations260

ANOVA

dfSSMSFSignificance F

Regression12457.60438.13486.5790.000

Residual247108.7910.440

Total259566.394

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept1.47270.61692.38710.01770.25762.68780.25762.6878

rating10.11870.35750.33220.7400-0.58530.8228-0.58530.8228

rating20.36130.25191.43410.1528-0.13490.8574-0.13490.8574

rating30.60820.25002.43310.01570.11591.10050.11591.1005

rating42.33140.27618.44310.00001.78752.87521.78752.8752

rating53.72910.294612.65700.00003.14884.30933.14884.3093

lnnetpro-0.23600.0775-3.04500.0026-0.3887-0.0834-0.3887-0.0834

lnyfmat-0.08370.0860-0.97350.3312-0.25320.0857-0.25320.0857

default0.85140.36002.36520.01880.14241.56030.14241.5603

utildum-0.08220.1187-0.69290.4890-0.31600.1515-0.31600.1515

calldum0.32740.11102.95030.00350.10880.54610.10880.5461

sinkdum0.74650.31322.38370.01790.12971.36330.12971.3633

subdum0.53820.22992.34110.02000.08540.99100.08540.9910

It can be seen from the adjusted r-squared value which is 0.799, that this model explains 79.9% the movement of prices of all the non-US bonds. And it can be seen from above model that most of the parameters except rating1, rating2, innetprp, infymat and utildum have t-statistics over 2 hence all those parameters are statistically significant and hence there is 95% probability that the parameters with a t-statistics over 2 are having the yield spread within 2 standard deviations. 2. Are the signs of the each of the coefficients what you expected from the U.S. market? (go through each one individually)There are few parameters which are not statistically significant and most of the parameters are significant such as

Intercept Coefficient:- 1.4727 and t-stat:- 2.3871

This is positive and it should be positive since the other markets will take this as base and hence will increase the yield because of the other constraint or parameters.

Rating 1

Coefficient:- 0.1187 and t-stat:- 0.3322

The yield spread is dependent on the the yield of US treasury bond so higher the bond rating the lower would the yield spread be and since this rating is for other markets, it would have a positive sign and higher the rating coefficient, the higher the yield spread will be. And the low t-stat indicates that this rating may not be as accurate in pricing the bonds.

Rating 2

Coefficient:- 0.3613 and t-stat:- 1.4341

As explained in rating 1, the same goes for rating 2 and the t-stat is not significant enough for this rating as well.Rating 3

Coefficient:- 0.6082 and t-stat:- 2.4331

As explained in rating 1, the same goes for rating 3 and the t-stat is significant enough for this rating as it is more than 2 and hence it has 95% probability that it will be in 2 standard error.

Rating 4

Coefficient:- 2.3314 and t-stat:- 8.4431

As explained in rating 1, the same goes for rating 4 and the t-stat is significant enough for this rating as it is more than 2 and hence it has 95% probability that it will be in 2 standard error.

Rating 5

Coefficient:- 3.7291 and t-stat:- 12.6570

As explained in rating 1, the same goes for rating 4 and the t-stat is significant enough for this rating as it is more than 2 and hence it has 95% probability that it will be in 2 standard error.

Bond Maturity (lnyfmat)

Coefficient:- -0.0837 and t-stat:- -0.9735

The more the bond maturity period the lesser the price of the bond has to be. So this rating would act as negative parameter and hence it has negative coefficient and the t-stat for this parameter is not statistically significant.Issue Size (lnnetpro)

Coefficient:- -0.2360 and t-stat:- -3.0450The more the size of the bond will be the debt offering will be more stabe and hence the yield of the bond would be lower. So the coefficient for this has to be negative and hence it is as shown in the regression analysis.

Market Conditions (default)

Coefficient:- 0.8514 and t-stat:- 0.3600

The price of the bond hugely depends on the market conditions so the better the market, the more priced the bond will and hence the coefficient of this bond has to positive and close to 1.

Covenant provisions (calldum,subdum,sinkdum)

Calldum- Coefficient:- 0.3274 and t-stat:- 2.9503

Subdum- Coefficient:- 0.5382 and t-stat:- 2.3411Sinkdum- Coefficient:- 0.7465 and t-stat:- 2.3837

The more liquid the bond is and it has more flexibility the bond price would be more and hence the coefficient of this parameter would be positive.

Industry (utildum)

Coefficient:- -0.0822 and t-stat:- -0.6929

This indicator denotes if the firm is a utility, otherwise an industrial firm. And Utilities would be expected to be relatively stable in comparison to other industries.3. Are there additional factors that the market uses to price foreign corporate bonds? Specifically, he wants to know if the volatility of the exchange rate and the firms location are important. To answer this, add to the U.S. model the variables for Volatility, Rule of Law and Creditor rights. What do you find, what does it mean? With the addition of the three new factors in the decision pricing model, the analysis is as follows: SUMMARY OUTPUT

Regression Statistics

Multiple R0.903139801

R Square0.815661501

Adjusted R Square0.804329216

Standard Error0.654142803

Observations260

ANOVA

dfSSMSFSignificance F

Regression15461.986130.799171.97680.0000

Residual244104.40830.4279

Total259566.3944

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept2.322500.695143.341070.000970.953273.691740.953273.69174

rating10.011680.355020.032890.97379-0.687610.71097-0.687610.71097

rating20.330360.251271.314760.18983-0.164580.82530-0.164580.82530

rating30.607810.247292.457920.014670.120721.094890.120721.09489

rating42.203330.276227.976660.000001.659252.747421.659252.74742

rating53.635220.2955812.298440.000003.053004.217443.053004.21744

lnnetpro-0.250030.07811-3.201150.00155-0.40388-0.09618-0.40388-0.09618

lnyfmat-0.070050.08540-0.820220.41289-0.238260.09817-0.238260.09817

default0.750640.358362.094660.037230.044771.456510.044771.45651

utildum-0.087890.12284-0.715490.47499-0.329850.15407-0.329850.15407

calldum0.425370.114683.709250.000260.199490.651260.199490.65126

sinkdum0.723760.309532.338230.020180.114061.333460.114061.33346

subdum0.546950.229322.385100.017840.095250.998650.095250.99865

fxvoliti40.6533922.822001.781330.07610-4.2998785.60666-4.2998785.60666

credrgts-0.088610.04636-1.911130.05716-0.179930.00272-0.179930.00272

ruleofla-0.080860.03055-2.646820.00865-0.14104-0.02069-0.14104-0.02069

It can be seen from the adjusted r-squared value which is 0.804, that this model explains 80.4% the movement of prices of all the non-US bonds. And it can be seen from above model that most of the parameters except rating1, rating2, innetprp, infymat and utildum have t-statistics over 2 hence all those parameters are statistically significant and hence there is 95% probability that the parameters with a t-statistics over 2 are having the yield spread within 2 standard deviations.Rule of Law (ruleofla)

Coefficient:- -0.08086 and t-stat :- -2.64682

The index of the law and order tradition of the country. It is scaled from 0 to 10, with higher scores for counties with more tradition for law and order. So more better the laws would be the more rating a country has so this factor should be negatively correlated with a negative coefficient.

Creditor Rights (credrgts)

Coefficient:- -0.08861 and t-stat :- -1.91113

This is an index aggregating different creditor rights a particular country provides. This should be negatively correlated as the higher the chances of default higher would be the yield spread.

FX Volatility (fxvoliti)

Coefficient:- 40.65339 and t-stat :- 1.78133

The greater the volatility, the greater would be the yield spread of a given bond. But this factor is statistically not significant since the t-stat value is less than 2.

Miller Investment Trust U.S. Bond Pricing Model

Yield Spread = constant + B1(Rating1) + + B5(Rating5) + B6(Bond Maturity) + B7(Issue Size) + B8(Market Conditions) +B9(Call Indicator) +B10(Sinking Fund Indicator) +B11(Subordinated Indicator) + B12(Industry Indicator)

whereYield Spread = Difference between the Yield-to-Maturity for the bond minus the yield of a Treasury bond with similar maturity (variable name in dataset: ysprd)Bond Ratings: The company uses 6 ratings classifications that correspond to Moodys rating of the bond issue. Rating 0 denotes if the bond was rated Aaa, Rating 1denotes if the bond was rated Aa1, Aa2, or Aa3, Rating 2 denotes if the bond was rated A1,A2,A3, and so on. Note: Rating 0 is not included in the dataset to overcome the dummy variable trap. Therefore, the estimated beta coefficient is going to be marginal affect of the rating over Aaa. For example if you find the B1 is .1, that means the Bonds with Aa1 ratings rating have a.1% greater interest rate then AAA bonds.Bond Maturity: The natural logarithm of the issues maturity in years (variable name in dataset: lnyfmat)Issue Size: The natural Logarithm of the dollar size of the net proceeds of the bond issue in USD millions (variable name in dataset: lnnetpro)Market Conditions: The difference between the Moodys Aaa seasoned corporate bond yield index and the composite Treasury yield on the offer date. This measure is the average risk premium for corporate bonds.(variable name in dataset: default)Convent Provisions: Indicators to denote the if the bond is Callable, has a Sinking fund provision, or is Subordinated. (variable name in dataset: calldum,subdum,sinkdum)

Industry: Indicator to denote if the firm is a utility, otherwise an industrial firm. (variable name in dataset: utildum)Proposed Additional FactorsRule of Law: The index of the law and order tradition of the country. It is scaled from 0 to 10, with higher scores for counties with more tradition for law and order. From LLSV (1998) (variable name in dataset: ruleofla)Creditor Rights: is an index aggregating different creditor rights a particular country provides. The index ranges from 0 to 4, with 4 representing the highest protection. One point is added if there is no automatic stay on assets, secured creditors get paid first, there are restrictions on reorganizations, and if management does not stay in reorganizations. From LLSV (1998).(variable name in dataset: credrgts)FX Volatility: The 30-day historical volatility of the U.S. to home country currency exchange rate(variable name in dataset: fxvol)

The Data

The spreadsheet, [bond case data], contains data on 260 corporate bonds issued by foreign firms in the U.S. over the period 1987-1998.