Effect of Factors on Bonds Metrics

[Delo]

Hi,
I tried to capture the effect of factors on Bond metrics. See below. Can anyone please verify whether following is correct?
Apologies, as exam is nearing I am feeling pressured for time and hence spared to do extensive forum search.

"+" --> Increase "-"--> Decrease

Please mention the quadrant that has problem...

 

[ShaktiRathore]

Hi
Price Vs Time to maturity should be -ve,P(2yr maturity,annual conupon)=5/1.1+105/1.1^2=91.32
P(3yr maturity,annual coupon)=5/1.1+5/1.1^2+105/1.1^3=87.56<91.32
Identical coupon and yield with increasing maturity is decreasing price.
Also price should have + relation to rating,as high rating implies low yield which implies high price.
Dv01 is (ModDurn/10000)*Price so Dv01 shows combined effect of factor on Duration and Price,as Time to maturity and coupon have opposite effects on Duration and price,this complicates the relation of Dv01 to Time to maturity and coupon.
Thanks

 

[ami44]

Hi ckat,

great idea to make this matrix. I already learnt a lot from thinking about it.

I think the relationship between price and time to maturity depends on the yieldcurve, its determined by the fact if the forward rate for the new coupon period is higher or lower than the coupon of the bond.
Shakti, if you use an above par bond in your example, e.g. with a coupon of 12 you will have the contrary effect

Rating should always be the contrary of yield, since a higher rating decreases the bond spread which is part of the yield. Shakti already pointed out the error in the first column.

I think DV01 should always go down, if time to maturity increases,
If we use the following simple form of DV01:
DV01 = - [ Σ ti * CFcoupon * DFi + tn * Nominal * DFn ] / 10000
ti, CFcoupon und DFi are always positive. So adding a new coupon increases the amount of the left sum term. The Nominal term increases also, if tn increases.
So in total the amount increases and DV01 decreases because it's negative.
Of course I'm talking about a long position, for a short position it's the other way around.

In my opinion the other entries are correct, except for convexity, which I'm not sure at the moment.

 

[Bester]

Hi,

I would think that the relationship between convexity and bond yield is negative, therefore the relationship of convexity with price is positive.

Convexity decreases at higher yields because the price-yield curve flattens at higher yields.

 

[ami44]

I think DV01 should always go down, if time to maturity increases,

Ups, I got confused in my previous post with the sign of DV01. Since DV01 is negative it's not clear if a + in the matrix means increase in amount or in the signed value.
The + for coupon and the - for yield are correct, if the amount of DV01 is meant.
Than IMHO time to maturity should have a + too.