Wednesday, 28 September 2011

Valuing Fixed Income Securities

To value fixed income securities the Treasury spot rate curves are used. They are theoretical spot rate which can be derived either by observing, bootstrapping or interpolation. Through observation the spot rates can only be derived from Treasury Strips but there are several advantages and disadvantages associated with that. Treasury Strips have the basic advantage of being available for every maturity. On the other hand the liquidity problem exists as a major disadvantage. They have tax disadvantages because of the accumulated interest on strips and there are certain regions where the Non U.S. investor is provided tax advantage. In this way unanimous tax adjustments cannot be done. It is important to understand that zero coupon bonds have no intermediate cash flows and for this reason their discounting factor is the spot rate. Yield is only involved in coupon paying bonds. For this reason the rate on Treasury Strips is considered to be the spot rate because each coupon payment is stripped and can trade as a zero coupon bond.
With On the run issues spot rates can also be derived using the bootstrapping method. In this method the 1 year zero coupon bond is taken and its yield is the spot rate for one year. Then a two year coupon paying bond is taken at par so that its yield to maturity is its coupon rate. The first years coupon payment is discounted at the rate of 1 year zero coupon bond, the spot rate, and the 2nd year's coupon plus principle is discounted with 2nd years spot rate. Since the equation is equal to the par value, the spot rate for 2nd year is calculated. Similarly it is applied for all the maturities to get the theoretical spot rates. This method is known as bootstrapping and the rates gathered through it if drawn graphically are known as Treasury Spot Rate Curve which in fact is used to value Fixed income securities. The issue with on the run securities is that they are not available for all the maturities and relatively liquid than off the run issues. Their price might disrupt the yield calculated from their prevailing prices. In this method the bootstrapping along with interpolation is used.
To counter this problem, a blend of on the run and off the run securities is used and the method of bootstrapping and interpolation is used to get the spot rate curve. Again which securities to use as for similar maturities sometimes multiple off the run issues are available. Some analysts are of the view to use all the issues of Treasury in order to get spot rates which is a complex task and requires diligence.
Can only the Treasury spot rates be used to value fixed income securities? The answer is no! Alternatively to Treasury spot rates curve, the Swap rate curve could also be used to value fixed income securities. It is a noticeable thing that Swap rate curve is an alternative to Treasury Yield curve, not Treasury spot rate curve. To determine spot rates through Swap rate curve the method of bootstrapping is used. Swap rates can be gathered by knowing the inter-bank lending rates. LIBOR is a renowned rate used by banks for lending, the swap rates curve against LIBOR is called the LIBOR rates curve. Bootstrapping the LIBOR rates curve results in LIBOR spot rates curve which is used to value fixed income securities. Due to their advantages, the swap rates are becoming famous and used instead of treasury yield curve. They are above the government regulations, available for more maturities, does not account the technicalities associated with bonds as the principal is 'assumed' not actual and supply of swaps depend upon the number of counterparts.
One must not forget that Swap rates are a proxy to Treasury Yield rates not to Treasury Spot rates where as the method of deriving spot rates is similar. Once spot rates are measured, the future rates can be derived against the spot rates. In this way the circle runs and we can value the fixed income securities. 

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