I’m having trouble understanding what spot rates are for fixed income securities.
So the book says that what I understand to be a basic way of valuing a bond, you would simply use one discount rate. However I’m guessing because of the fact that interest rates rise the further you go into the future (at least under normal economic conditions), then you need to be compensated more for the added uncertainty associated with the longer tenure. Therefore, a more appropriate way to value a cashflow from a bond is to use these adjusted interest rates i.e. these so called spot rates? Am I on the right track so far?
Moving on… the book says
“Spot rates are yields-to-maturity on zero-coupon bonds maturing at the date of each cash flow.”
(Institute 407)
Institute, CFA. 2016 CFA Level I Volume 5 Equity and Fixed Income. CFA Institute, 07/2015. VitalBook file.
The citation provided is a guideline. Please check each citation for accuracy before use.
This statement I don’t understand at all. The way I interpret it is…
Take a cashflow from any year, this becomes a 1 year zero coupon bond with a face value of that cashflow, discount it by this so called spot rate and you will get the discounted value of that cashflow for any given year.
So effectively, the way I’m reading it, you break down a bond into constituents and then simply add them together, whereby the constituents are these zero coupon 1 year bonds.
And the spot rates are called spot rates because the discount rates that are used to discount each cashflow is effectively derived from the spot market???
Sorry, it’s all very blurry at the moment.
It isn’t so much that using spot rates is more appropriate than using YTM; it’s simply a different approach.
A spot rate is a discount rate for a spot payment: one cash flow at a given time in the future.
Suppose that you have a 5-year, annual pay, 6% coupon, $1,000 par bond. You can determine the price (today) of the bond by:
- Discounting the $60 payment 1 year from today at the 1-year spot rate,
- Discounting the $60 payment 2 years from today at the 2-year spot rate,
- Discounting the $60 payment 3 years from today at the 3-year spot rate,
- Discounting the $60 payment 4 years from today at the 4-year spot rate,
- Discounting the $1,060 payment 5 years from today at the 5-year spot rate, and
- Adding all of those present values,
or,
- Discounting the $60 payment 1 year from today at the bond’s YTM,
- Discounting the $60 payment 2 years from today at the bond’s YTM,
- Discounting the $60 payment 3 years from today at the bond’s YTM,
- Discounting the $60 payment 4 years from today at the bond’s YTM,
- Discounting the $1,060 payment 5 years from today at the bond’s YTM, and
- Adding all of those present values.
The point you need to understand is that you have to arrive at the same (present) value under the first method as you do under the second, lest there be an arbitrage opportunity.
I wrote an article on par rates, spot rates, and forward rates that goes into all of the details: http://www.financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/
Full disclosure: as of 4/25/16 there is a charge for all of the articles on my website.
I see, I think I follow now.
In principle, you always value a bond at spot rates for each maturity the bond pays a coupon (and principal at maturity). Simply choose the appropriate yield curve and discount each payment at the respective spot rate. Spot rates are discount rates for maturity X to ‘today’. Forward rates are discount rates for maturity X to maturity Y, so to say.
The yield to maturity is the internal rate of return (IRR) of a bond when held until maturity. By discounting all cash flows with the YTM the bond’s price is calculated. It literally tells you: what return am I getting if I buy this bond and hold it until I receive the face value? (Given all cash flows are reinvested at the YTM). Each bond has its own YTM depending on number/size of cash flows and at what interval they occur.