# questions on bond

#### Lun

I'm studying bond pricing, I have 2 questions now.

Q1
say, the yield for 3yr & 5yr bond are 3% & 5% respectively
then, I buy a 5yr bond, that is with yield 5%

-------- after 2 years --------------------------------------------------
the yield for 3yr & 5yr bond are 2% & 4% respectively
as u know, my bond has 3 more yr to go, which rate (2% or 4%) should be used as the yield to calculate the price ?

Q2
for corporate bond, how the credit spread is determined ?
is it determined by credit rating of that corporate
If two corporates have the same credit rating, then their credit spread are the same ?

Thank you

#### doug reich

##### Some guy
1. You want to use the 3yr and 5yr bonds to back out a rate curve. This is partly done with a model for what the rates are at 1 yr, 2 yr, etc. for which you do not have data. You then use those rates to discount the coupon payments to get the price.

2. The spread is defined as the market's yield above treasuries. You don't get to decide either; it's just a number that represents the market's perception of how much riskier a corporate is than the US Government (traditionally thought of as a riskless bond). Part of the spread is a function of the bond parameters itself, since longer maturities will be higher risk.

Two corporates will not have the same spread necessarily, as factors other than credit rating go into it. Foremost, people don't have to trust the credit rating. However, maturities and liquidity of the issue will also change the spread.

#### Lun

1. It seems that I'm completely in the wrong direction. I don't understand what you mean, can you explain more. You can ignore the data provided, and directly explain how to determine the yield after 2yr. I suppose these data are useful, and that's why I provide these data.

2. Well, I think I should be honest on what's annoying me. I have a portfolio of, say, 3 corporate bonds, how can I calculate the Var (value at risk) ? I really can't think of how to model the price ? by historical data ?

Thank you

#### Yan He

2. Well, I think I should be honest on what's annoying me. I have a portfolio of, say, 3 corporate bonds, how can I calculate the Var (value at risk) ? I really can't think of how to model the price ? by historical data ?

Thank you

You are holding a relatively simple fixed income portfolio, to calculate your VAR, you can calculate your portfolio Dolar Duration and apply the confidentia leve you want.

#### PatM

sort of a big topic

That is sort of a big topic for a chat board. Basically, you take the pricing equation for a bond, and vary the inputs to get an expected distribution for the price of the bond (or portfolio) over some time horizon. For one day horizons, the inputs to vary are the rates in the curve. For longer time horizons, you have to shorten the time to maturity for the bond as you go in the Monte Carlo, and you should consider possible credit deterioration or default. Look at the RiskMetrics web site: www.riskmetrics.com/publications/techdocs/rm2006.html
They have lots of discussion about calculating VaR.

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