Yield Curve Analysis

What is a yield curve?

The simplest approach to observe the interest rates in the market is to draw the yield curve from the YTM of traded bonds. Let say you are valuing a bond which has not traded today, how will you do that? Answer is to use the YTM of traded bond and add required premium to it to value the non-traded bond.

When we obtain a plot relationships between YTMs and term to maturity of a set of traded bonds, we can identify the functional relationship between time and yield, this is known as yield curve.

Limitations of Yield Curve

The YTM of a bond assumes a single rate, at which all the cash flows of a bond are discounted. This actually translates into a valuation proposition where, cash flows accruing at varying points in time are all discounted at the same rate, i.e. the YTM of the bond, this translates a yield curve to a flat yield curve which is may not be practically possible for longer period of time.

We know that rates for varying tenors are not uniform, but different. If this were true, we can not use the same YTM for valuing all the cash flows of a bond and spot rates for respective maturities are required to value the bonds. I don’t discuss more on this concept as this is beyond the scope of CFP curriculum. To read more you can download book of FIMMDA or any reputed Fixed Income book.

We begin with types of yield curve:

Broadly the yield curve can be zero coupon yield curve and YTM curve.

Zero Coupon Yield Curve (source: www.nseindia.com)

YTM Curve (source: NDS OM)

Lets now observe the shapes of the yield curve and interpretation of the same: 

Upward Rising

This is a normal yield curve. This yield curve indicates economic growth. In this shape of yield curve yield increases with increase in the maturity.

Downward Slopping

This yield curve indicates that yield declines with increase in maturity. This shape indicates economic recession or slowdown in economy.

Flat Yield Curve

This shape of yield curve indicates the transition in the economy because yield is same irrespective of maturity.

Another shape can be Humped. Humped yield curve represents initial rise in yield but overall shape of the curve in downward as maturity increases.

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Yield to Call and Yield to Put

Yield to Call:

When a bond is callable (when repurchased by the issuer before the maturity), Yield to Call is to be calculated for the bonds, which is the same calculation of the YTM, but assumes that the bond will be called, so the cash flow is shortened.

Illustration:

Assume Rs.100 (FV) 7%, 5 year bond is selling at 104.69 and the first call date is 4 years from now. The call price is Rs.101.50. if the bond pays semi-annual interest, calculate yield to call.

Answer:

PV = -104.69

PMT = 3.5

N = 8

i/y = ?

FV = 101.50

Yield to Put

Calculation is same as Yield to Call, but when the bond holder has the option to redeem the bond back to the issuer at a fixed price (normally face value) on specified date. So the yield to investor is calculated by the shortening the cash inflow.

When bonds are having call or put options their price behaviour is not same as with a normal bond.

You can see the price path of the callable bond, when yield is more than coupon, bond price behave like a normal bond but when yield is less than coupon, price of a callable bond doesn’t increase like a normal bond because when yield is less than coupon there are more chances of the bond to get called.

Now lets observe impact of put option on price:

A puttable bond behaves like a normal bond when yield is less than coupon of the bond. But when yield increases price of the puttable bond doesn’t fall like a normal bond because of the right available with holder of the bond to place it back to the issuer at a fixed price which is normally face value.