Fixed Income【Reading 50】Sample relevant, relative, following, 2012

spartan1

The following are the yields on various bonds. The relevant benchmark is that of Treasury securities.

Treasury Bond Yield	4.00%
Bond Sector Yield	4.50%
Comparable Bond Yield	6.00%
ABC Bond Yield	6.50%

Is the ABC bond undervalued or overvalued and why? Using relative value analysis, the ABC bond is:

A) undervalued because its yield is greater than that of Treasuries.

B) undervalued because its spread is greater than that of comparable bonds.

C) overvalued because its spread is greater than that of comparable bonds.

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The purpose of relative value analysis is to determine whether a bond is fairly valued. The bond’s spread over some benchmark is compared to that of a required spread to determine whether the bond is fairly valued. The required spread will be that available on comparable securities. In this example, the relevant benchmark was Treasury securities. The spread for ABC bonds over Treasuries was 2.5%. The spread for comparable bonds over Treasuries was 2.0%. The higher spread for ABC bonds means that they are relatively undervalued (their price is low because their yield is higher).

spartan1

The following are the yields on various bonds. The relevant benchmark is that of the bond sector.

Treasury Bond Yield	3.00%
Bond Sector Yield	3.25%
Comparable Bond Yield	5.75%
ABC Bond Yield	5.50%

Is the ABC bond undervalued or overvalued and why? Using relative value analysis, the ABC bond is:

A) overvalued because its spread is less than that of comparable bonds.

B) undervalued because its yield is less than that of Treasuries.

C) undervalued because its spread is less than that of comparable bonds.

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The purpose of relative value analysis is to determine whether a bond is fairly valued. The bond’s spread over some benchmark is compared to that of a required spread to determine whether the bond is fairly valued. The required spread will be that available on comparable securities. In this example, the relevant benchmark was the bond sector. The spread for ABC bonds over the bond sector was 2.25%. The spread for comparable bonds over the bond sector was 2.50%. The lower spread for ABC bonds means that they are relatively overvalued (their price is high because their yield is lower).

spartan1

The purpose of relative value analysis is to determine:

A) the return differential from riding the yield curve.

B) whether a bond is fairly valued using a benchmark yield.

C) whether a stock is fairly valued using present value calculations.

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The purpose of relative value analysis is to determine whether a bond is fairly valued. The bond’s spread over some benchmark is compared to that of a required spread to determine whether the bond is fairly valued. The required spread will be that available on comparable securities.

spartan1

Which of the following benchmarks would generate the greatest spread when used to examine a bond yield?

A) A U.S. Treasury security.

B) Bond sector benchmark.

C) The issuer of a specific company.

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The U.S. Treasury security would generate the highest spread because the yield on Treasury securities will be the lowest as they have the lowest credit and liquidity risk. The yields on a bond sector benchmark and for a specific company will be higher.

spartan1

Which of the following spreads will reflect the option risk in a callable bond?

A) The Z-spread only.

B) Both the nominal spread and the Z-spread.

C) The OAS only.

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The OAS is the option-adjusted spread. It is determined using a binomial tree where a spread (the OAS) is added to the benchmark yield to find the arbitrage-free value for the callable or putable bond. The arbitrage-free value is the imputed value equal to the current bond price. The OAS is referred to as an option-adjusted spread because the cash flows in the tree are adjusted to reflect the option of the bond (e.g. a callable bond’s price is capped at the call price when interest rates drop). The nominal spread is simply the bond’s yield minus the benchmark yield. The Z-spread is the spread that, when added to the spot rates from a yield curve, results in an imputed value equal to the bond’s current price. The nominal spread and the Z-spread do not adjust the cash flows for the bond’s option. Thus the calculated yield spread using both these measures will reflect the option risk in the bond, as well as the bond’s credit and liquidity risk. Because the OAS calculation adjusts the cash flows for the bond’s option-like characteristics, the calculated OAS is just a reflection of the bond’s credit and liquidity risk, relative to the benchmark spot rates.

spartan1

The use of which of the following benchmarks to generate a spread would not reflect credit risk?

A) A U.S. Treasury benchmark.

B) A global industry-yield benchmark.

C) An issuer-specific benchmark.

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An issuer-specific benchmark (another bond of the same company) would not reflect credit risk because the benchmark would incorporate the credit risk of the firm. Using a U.S. Treasury benchmark would reflect credit risk because the bond to be evaluated would have higher credit risk than either benchmark. The yield in a global industry is not typically used as a benchmark.

spartan1

Using the following interest rate tree of semiannual interest rates what is the value of an option free bond that has one year remaining to maturity and has a 5% semiannual coupon rate?

        7.30%
6.20%
        5.90%

A) 98.67.

B) 98.98.

C) 97.53.

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The option-free bond price tree is as follows:

		100.00
A → 98.89
98.67		100.00
	99.56
		100.00

As an example, the price at node A is obtained as follows:
PriceA = (prob × (Pup + (coupon / 2)) + prob × (Pdown + (coupon / 2)) / (1 + (rate / 2)) = (0.5 × (100 + 2.5) + 0.5 × (100 + 2.5) / (1 + (0.0730 / 2)) = 98.89. The bond values at the other nodes are obtained in the same way.
The calculation for node 0 or time 0 is
0.5[(98.89 + 2.5) / (1+ 0.062 / 2) + (99.56 + 2.5) / (1 + 0.062 / 2)] =
0.5(98.3414 + 98.9913) = 98.6663

spartan1

Using the following interest rate tree of semiannual interest rates what is the value of an option free semiannual bond that has one year remaining to maturity and has a 6% coupon rate?

         6.53%
6.30%
         5.67%

A) 98.52.

B) 97.53.

C) 99.81.

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The option-free bond price tree is as follows:

		100.00
A ==> 99.74
99.81		100.00
	100.16
		100.00

As an example, the price at node A is obtained as follows:
PriceA = (prob × (Pup + coupon/2) + prob × (Pdown + coupon/2))/(1 + rate/2) = (0.5 × (100 + 3) + 0.5 × (100 + 3))/(1 + 0.0653/2) = 99.74. The bond values at the other nodes are obtained in the same way.
The calculation for node 0 or time 0 is
0.5[(99.74 + 3)/(1+ 0.063/2) + (100.16 + 3)/(1 + 0.063/2)] =
0.5 (99.60252 + 100.00969) = 99.80611

spartan1

For a putable bond, callable bond, or putable/callable bond, the nodal-decision process within the backward induction methodology of the interest rate tree framework requires that at each node the possible values will:

A) not be higher than the call price or lower than the put price.

B) include the face value of the bond.

C) be, in number, two plus the number of embedded options.

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At each node, there will only be two values. At each node, the analyst must determine if the initially calculated values will be below the put price or above the call price. If a calculated value falls below the put price: Vi,U = the put price. Likewise, if a calculated value falls above the call price, then Vi,L = the call price. Thus the put and call price are lower and upper limits, respectively, of the bond’s value at a node.

spartan1

A bond with a 10% annual coupon will mature in two years at par value. The current one-year spot rate is 8.5%. For the second year, the yield volatility model forecasts that the one-year rate will be either 8% or 9%. Using a binomial interest rate tree, what is the current price?

A) 102.659.

B) 101.837.

C) 103.572.

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The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:
V1,U=[(100+10)/1.09+(100+10)/1.09]/2= 100.917
V1,L=[(100+10)/1.08+(100+10)/1.08]/2= 101.852
Thus
V0=[(100.917+10)/1.085+(101.852+10)/1.085]/2= 102.659