Doubts on Market Risk- Tuckman Chapter 2- Maturity and bond price

[sdoshi004]

David

I am not able to understand the calculation of spot rate in the edit grid "tuckman ch2 maturity and return", Could you please shed some light on that. Also I would like to know the relation of future rate and coupon rate. In the e.g. when the forward rate 4.734% falls below coupon rate - 4.875%, the bond price increases to 100+. Would appreciate your response.

Thanks
Sumit

 

[David Harper CFA FRM]

Hi Sumit,

The spot rate calc is an FRM AIM (Tuckman Ch 2). Specifically, 2.9:
http://learn.bionicturtle.com/images/forum/spot_rate_from_dis1.png
That's a semiannual compound frequency. It may help to start with

V0*(1 + r/2)^(2T)=Vf
where V0 = initial value, Vf = final value, and (r) is the spot rate on a semi-annual compound frequency. Hopefully, that is a naturally compounding from v0 to vf.

so that:
Vf/V0 = (1 + r/2)^(2T) = 1/discount_factor
and we can solve for the spot rate (r) to get the formula above.

The second is subtle (Tuckam 2.3). It is only about the bond price change as we extend maturity: how does the forward rate compare to the coupon over the extended maturity? If forward > coupon over the extended period, then the bond coupon is insufficent to give enough return so the bond price comes down. On the other hand, in your example, the six-month forward (4.734%) < coupon, so the coupon is paying too much and the bond price must be lower than before. So this is about the trend in the bond price from: 6 months to 1 year to 1.5 years etc...with each extension, the bond price goes up/down to adjust for whether the coupon (4.875%) is paying too little or too much.

David

 

[sdoshi004]

Thanks David

I appreciate

Sumit