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CFA Level II Alts & Fixed Income > Reading 47 - Valuing Bonds with Embedded Options > Flashcards

Reading 47 - Valuing Bonds with Embedded Options Flashcards

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CFA flashcards
1
Q

What is Relative value analysis in regards to bonds?

A

involves comparing the spread on the bond (over some benchmark) to the required spread and determining whether the bond is over or undervalued relative to a benchmark.

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2
Q

What is a binomial model?

A

Binomial means one of two ways. So it is a single factor model that, given an assumed level of volatility, suggests that interest rates have an equal probability of taking on one of two possible values in the next period.

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3
Q

What is an interest rate tree?

A

The set of possible interest rate paths.

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4
Q

What is the one underlying rule for constructing an interest rate tree?

A

The interest rate tree should generate arbitrage-free values for on-the-run issues of the benchmark security.

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5
Q

What are the 3 spread measures relating to relative value analysis in fixed income?

A
  1. Nominal spread
  2. Z-spread (zero volatility)
  3. OAS
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6
Q

Describe the nominal spread…..

A

Is the bond’s yield to maturity minus the yield on a comparable-maturity treasury benchmark security.

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7
Q

What is the problem with using a nominal spread?

A

It uses a single interest rate to discount each cash flow that makes up the bond; if the yield curve is not flat, each cash flow should instead be discounted at the appropriate spot rate for the maturity.

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8
Q

Describe the Z-spread?

A

Is the spread that when added to each spot rate on the yield curve, makes the PV of the bond’s cash flows equal to the bond’s market price.

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9
Q

When is it not appropriate to use the Z-spread?

A

if interest rates are volatile, it is not appropriate to use it to value bonds with embedded options because the Z-spread includes the cost of the embedded option.

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10
Q

Describe the OAS ?

A

Is the spread on a bond with an embedded option after the embedded option cost has been removed.

It’s equal to the Z-spread minus the option cost.

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11
Q

What are the 3 different types of bonds that can used as benchmark rates to calculate spreads??

A
  1. Treasury securities
  2. A specific sector of the bond market with a credit rating higher than the issue being valued
  3. A specific issuer.
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12
Q

Describe the backward induction valuation methodology?

A

Refers to the process of valuing a bond using a binomial interest rate tree.

** “backward” comes from the fact that to determine the value of a bond at Node 0, you need to know the values that the bond can take on a Node 1.

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13
Q

How is the value of the call of a callable bond calculated?

A

Value of call = Value of noncallable bond - value of callable bond

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14
Q

How is the value of put of a putable bond calculated?

A

Value of put = Value of putable bond - value of nonputable bond

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15
Q

What happens to the value of a callable bond as volatility rises?

A

Its value falls

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16
Q

How is the value of a given node in a binomial tree calculated?

A

It is the average of the % values of the two possbile values from the next period.

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17
Q

Describe the option-adjusted spread (OAS)….

A

In order to produce arbitrage-free values for a callable bond, interest rates must be adjusted for the option characteristics of the bond.

The OAS is the spread that forces the theoretical price to be arbitrage free.

18
Q

Which of the following does OAS measure, hint, it can be more than one of these.

Credit Risk

Liquidity Risk

Option Risk

A

Credit Risk & Liquidity Risk

19
Q

What does modified duration measure?

A

It measures a bond’s price sensitivity to interest rate changes, assuming that the bond’s cash flows do not change

20
Q

Why are modified duration and convexity not useful for bonds with embedded options?

A

b/c the cash flows form these bonds may change if the option is excercise.

21
Q

How do you calculate effective duration ?

A
22
Q

How do you calculate effective convexity?

A
23
Q

What is the Conversion Ratio in regards to Convertible Bonds?

A

Is the number of common shares for which a convertible bond can be exchanged.

24
Q

What is the conversion price in regards to convertible bonds?

A

= $ amount of par value divided by new shares of common stocks

25
Q

What is a hard put?

A

if there is a embedded put feature that requires the issuer to redeem the bond with cash.

26
Q

What is a soft put?

A

if there is an embedded put feature and the issuer has the choice of payment (cash, common stock , and/or subordinated notes)

27
Q

What is the conversion value in regards to a convertible bond?

A

Is the value of the common stock into which the bond can be converted

Conversion value = market price of stock * conversion ratio

28
Q

What is the straight value of a convertible bond?

A

is the value of the bond if it were not convertible.

29
Q

Why must the mimimum value of a convertible bond must be the greater of its conversion value or straight value?

A

Otherwise arbitrage opportunities would exist.

30
Q

What is the market conversion price?

A

The price that the convertible bondholder would effectively pay for the stock if she bought the bond and immediately converted it.

31
Q

What is the market conversion premium per share?

A

is the difference between the market conversion price and the stock’s market price

32
Q

How do you calculate the market conversion premium ratio?

A
33
Q

What is the premium payback period and how is it calculated?

A

Typically the coupon income from a convertible bond exceeds the dividend income that would have been realized if the stock were directly owned.The time is takes to recoup the per share premium is the premium payback period.

34
Q

How do you calculate the favorable income difference per share, which is used in the premium payback period ratio?

A
35
Q

The downside risk to a convertible bond is limited by the bond’s underlying straight value which it will not fall below.

A ratio to measure downside risk is the premium over straight value, how is it calculated?

A
36
Q

Sometimes the price of the common stock associated with a convertible issue is so low that it has little or no effect on the convertible’s market price, and it trades as though it is a straight bond.

What is this referred as?

A

A fixed income equivalet or busted convertible.

37
Q

Given the below data, how do you calculate the premium payback period for this convertible bond?

  • Market price of the bond : $925.00
  • Annual Coupon: 7.5%
  • Conversion Ratio : 30
  • Market price of stock : $28.50
  • Annual Stock dividend L $2.15 per share
A
38
Q

A convertible bond has a conversion ratio of 12 and a straight value of $1,010. The market value of the bond is $1,055, and the market value of the stock is $75. What is the market conversion price and premium over straight value of the bond?

A

The market conversion price is:

(market price of the bond) / (conversion ratio) = $1,055 / 12 = $87.92.

The premium over straight price is:

(market price of bond) / (straight value) − 1 = ($1,055 / $1,010) − 1 = 0.0446.

39
Q

A CFA charter holder observes a 12-year 7 ¾ percent semiannual coupon bond trading at 102.9525. If interest rates rise immediately by 50 basis points the bond will sell for 99.0409. If interest rates fallimmediately by 50 basis points the bond will sell for 107.0719. What are the bond’s effective duration (ED) and effective convexity (EC).

A

ED = (V- − V+) / (2V0(∆y))

= (107.0719 − 99.0409) / (2 × 102.9525 × 0.005) = 7.801

EC = (V- + V+ − 2V0) / (2V0(∆y)2)

= (107.0719 + 99.0409 − (2 × 102.9525)) / [(2 × 102.9525 × (0.005)2)] = 40.368

40
Q

A putable bond with a 6.4% annual coupon will mature in two years at par value. The current one-year spot rate is 7.6%. For the second year, the yield volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. The bond is putable in one year at 99. Using a binomial interest rate tree, what is the current price?

A

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 at all nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:

Vi,U = [(100 + 6.4) / 1.076 + (100+6.4) / 1.076] / 2 = 98.885

Vi,L = [(100 + 6.4) / 1.068 + (100 + 6.4) / 1.068] / 2 = 99.625.

Since 98.885 is less than the put price, Vi,U = 99

V0 = [(99 + 6.4) / 1.076) + (99.625 + 6.4) / 1.076)] / 2 = 98.246

CFA Level II Alts & Fixed Income (7 decks)

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