The main drawback of the tradition approach of valuation is that it discounts every cash flow using the same discount rate. For example, let us take 5-year (7.00 per cent) Treasury security (maturing in 2010). The cash flow per Rs.100 of par value would be a payment of Rs.3.50 every six months and Rs.103.50 tenth 6-month period from now. However, the best way to see the 5-year 7% security is as a package of zero-coupon bonds whose maturity value and date is the amount and date of cash flow respectively. Thus, 5-year, 7% security should be viewed as 10 zero-coupon bond. The main reason is that it does not allow a market participant to realize an arbitrage profit by taking apart or "stripping" a security and selling off the stripped securities at a higher aggregate value it would cost to purchase the security in the market. This approach is known as an arbitrage-free valuation approach.
The difference between the traditional and arbitrage-free valuation approach is explained in the table 5.
Table 1: Comparison of Traditional Approach and
Arbitrage-Free Valuation Approach in 7% Treasury Security
|
Period
(6 month each)
|
Discount (Base Interest) Rate
|
Cash Flows per Rs. 100 of par value
|
|
Traditional Approach
|
Arbitrage-Free Valuation Approach
|
|
1
|
5-year Treasury rate
|
1-period Treasury spot rate
|
3.5
|
|
2
|
5-year Treasury rate
|
2-period Treasury spot rate
|
3.5
|
|
3
|
5-year Treasury rate
|
3-period Treasury spot rate
|
3.5
|
|
4
|
5-year Treasury rate
|
4-period Treasury spot rate
|
3.5
|
|
5
|
5-year Treasury rate
|
5-period Treasury spot rate
|
3.5
|
|
6
|
5-year Treasury rate
|
6-period Treasury spot rate
|
3.5
|
|
7
|
5-year Treasury rate
|
7-period Treasury spot rate
|
3.5
|
|
8
|
5-year Treasury rate
|
8-period Treasury spot rate
|
3.5
|
|
9
|
5-year Treasury rate
|
9-period Treasury spot rate
|
3.5
|
|
10
|
5-year Treasury rate
|
10-period Treasury spot rate
|
103.5
|
Under traditional approach interest rate on the bond is the yield of 5-year treasury security. In arbitrage-free approach the interest rate for a cash flow is the theoretical rate that the treasury security has to pay if it issued as a zero-coupon bond with maturity date equal to the maturity date of the cash flow. So, it is necessary to decide the theoretical rate that the treasury security has to pay on a zero coupon for each maturity. Zero-coupon treasury rate is also known as 'Treasury Spot Rate'. In the next chapter, we will understand how to calculate the treasury spot rate. When the value of a bond is calculated based on spot rate, the resulting value is known as arbitrage-free value.