NZDX - How are quoted yields calculated?

Hi All,

If I look at securities quoted on the NZDX (I'll use BNZ080 as an example), they quote the unit price and the yield:

http://www.nzx.com/markets/NZDX/bnz080

Can anyone explain exactly how the yield is calculated?

Using the numbers on that page at the time of posting they show:

Date = 6 Nov 2009
Sell per $100 = $107.691
Nominal Interest = 8.42%
Interest Paid = 6 times a year
Next Interest = 15 Dec 2009
Maturity = 15 Jun 2017

Yield on Sell = 6.600% (presumably the Yield to Maturity?)


Can anyone explain how to get the 6.600% from the above data?


A worked example using the above data would be most helpful if possible. In an attached excel workbook would be sublime!


Thanks,

Alan.

Alan, it's a straight forward bond pricing calculation, but you have a couple of things that are incorrect in your posted data.

the coupon is semi annual, and the maturity date is 2012, for current purposes (I haven't looked, but maybe there is a right to extend?)

I find the bond calculator at www.directbroking.co.nz very handy for pocket or purse, otherwise I use my trusty 40 year old HP 12C

plug in the details, use T+3 as settlement date, 6.6% as yield to maturity, and per $1000, you will see the cum-int price is exactly as you have stated $107.691 for $100

HTH

p.s. I haven't found anything to assist with pricing perpetuals that have an annual rate reset........ but perpetuals with a fixed coupon in perpetuity is easy Price = Coupon/Yield

Hi Xerof,

Quote:

---

Originally Posted by Xerof

Alan, it's a straight forward bond pricing calculation, but you have a couple of things that are incorrect in your posted data.

the coupon is semi annual, and the maturity date is 2012, for current purposes (I haven't looked, but maybe there is a right to extend?)

---

That explains why I couldn't even get close!

I mistook the '6' to mean 6 times a year, rather than every six months.

To be fair, that is very misleading (on the NZX website), since it explicitly says 'Int Frequency'. A frequency is expressed in 'events per unit of time' (often 'Hz' being 'per second or 'per annum'). Hence '6' implies '6 per annum'.

Ah well. Live and learn :-)


It does however explicity state that maturity is 15 Jun 2012 (despite the title of the bond at the top of the page) so my bad on that one for sure!

Quote:

---

Originally Posted by Xerof

I find the bond calculator at www.directbroking.co.nz very handy for pocket or purse, otherwise I use my trusty 40 year old HP 12C

plug in the details, use T+3 as settlement date, 6.6% as yield to maturity, and per $1000, you will see the cum-int price is exactly as you have stated $107.691 for $100

---

I tried that calculator:

http://www.directbroking.co.nz/direc.../bondcalc.aspx

If I put in:

Security = BNZ080

and let it populate for me, then enter:

Cum Interest Price = $107.691
Settlement Date = 11 Nov 2009 (three working days hence)

it calculates the yield as being 6.60% (in agreement with the NZX website) so they are consistent with each other.


I would love to know what your 'trusty 40 year old HP 12C' comes up with ;-)

Any chance you would be able to run the calcs and post the answer with the detailed sub-calcs?

I realise this is being a bit 'cheeky' but it is not too bad I think (acquisition, five interest payments, and redemption, so only seven 'events') and I am keen to see how they get the 6.60% as the websites are black-boxes that just give the final answer.

I understand that to get the 6.60% you would actually have to iteratively adjust the (unknown) yield to find the rate that gives a zero NPV, but if you could show the calcs using the (known) answer of 6.60% I would be extremely grateful.

Quote:

---

Originally Posted by Xerof

p.s. I haven't found anything to assist with pricing perpetuals that have an annual rate reset........ but perpetuals with a fixed coupon in perpetuity is easy Price = Coupon/Yield

---

Yeah - much harder with periodic interest adjustments to a variable rate.

I would imagine, off the top of my head, that one should assume the interest rate resets correspond to the current 1, 2, 3, .... n year benchmark rates to calculate it?

So, if the rate is reset on 1 Apr 2010 to the one-year swap rate plus 2%, then perhaps we would assume that the one-year swap rate on 1 Apr 2010 will be the current average rate, and similarly for future resets on 1 Apr 2011 and onwards?


Thanks,

Alan.

Quote:

---

Originally Posted by Alan3285

I would love to know what your 'trusty 40 year old HP 12C' comes up with ;-)

Any chance you would be able to run the calcs and post the answer with the detailed sub-calcs?

I understand that to get the 6.60% you would actually have to iteratively adjust the (unknown) yield to find the rate that gives a zero NPV, but if you could show the calcs using the (known) answer of 6.60% I would be extremely grateful.

---

Okay - I got it.

This explains how to do the detailed calculation:

http://www.nzdmo.govt.nz/securities/...mo-19sep09.pdf

Specifically, section 5.1 on page 9 sets out the formula.

I tried it with the BNZ080 data and it works perfectly.


Thanks,

Alan.