It is not easy to determine the theoretical value of non-treasury securities. However, we can use the treasury spot rate for the valuation of non-treasury security. To find the value of non-treasury securities, there is a need to add some premium (yield spread) to reflect the additional risk in the treasury spot rate. The rate comes after such addition is used to discount the cash flows of non-treasury security. The addition of all discounted cash flows is the value of non-treasury security. For example, assume that 5-year treasury spot rate is 7% and the appropriate yield spread for non treasury security is 175 basis points. In such a case, all cash flows will be discounted at treasury spot rate plus 175 basis points i.e. 8.75% (7% + 175 basis points).
As we studied in the previous chapter that credit spread increases with maturity. So taking fixed spread for valuing non-Treasury securities is not appropriate. This is the one main disadvantage of this approach. To overcome this drawback, dealer firms typically use term structure of credit spreads. These firms estimate a term structure for credit spread for each credit rating and market sector. The typical term structure of credit spread increases with maturity. The term structure is not same for all credit rating. Generally, lower credit rating leads to steeper term structure of credit spreads.
When the credit spreads for a given credit ration and market sector are added to treasury spot rates, the resulting term structure is used to value the bonds of issuers with that credit rating in that market sector. This term structure is known as a benchmark spot rate curve or benchmark zero-coupon rate curve.
Table 1 represents the calculation for valuing non-treasury security using benchmark spot rate curve.
Table 1: Calculation of Arbitrage-Free Value of Hypothetical 7% 5-year
Non-Treasury Security Using Benchmark Spot Rate Curve
|
(a)
|
(b)
|
(c)
|
(d)
|
(e)
|
(f = d + e)
|
(g)
|
|
Period
|
Years
|
Cash Flow
in Rs.
|
Spot Rate in %
|
Credit Spread
in %
|
Benchmark
Spot
Rate in %
|
PV in Rs.
|
|
1
|
0.5
|
3.5
|
2.7589
|
0.15
|
2.91
|
3.4498
|
|
2
|
1.0
|
3.5
|
3.0356
|
0.15
|
3.19
|
3.3911
|
|
3
|
1.5
|
3.5
|
3.2856
|
0.25
|
3.54
|
3.3208
|
|
4
|
2.0
|
3.5
|
3.5563
|
0.25
|
3.81
|
3.2458
|
|
5
|
2.5
|
3.5
|
3.8659
|
0.35
|
4.22
|
3.1533
|
|
6
|
3.0
|
3.5
|
4.1068
|
0.40
|
4.51
|
3.0620
|
|
7
|
3.5
|
3.5
|
4.3574
|
0.45
|
4.81
|
2.9639
|
|
8
|
4.0
|
3.5
|
4.6012
|
0.45
|
5.05
|
2.8669
|
|
9
|
4.5
|
3.5
|
4.9812
|
0.55
|
5.53
|
2.7380
|
|
10
|
5.0
|
103.5
|
5.1225
|
0.60
|
5.72
|
78.0589
|
|
Arbitrage-Free Value of a 7% 5-Year Non-Treasury Security is
|
106.2504
|
The column (e) represents the term structured credit spread. The addition of spot rate and credit spread gives the Benchmark spot rate given in column (f). The last column shows the present value of the cash flow. The last row of this column shows the Arbitrage-Free Value of a 7% 5-Year Non-Treasury Security.