A bond selection problem

Yesterday, l find a question posted by robbie2308

The question is like this:
Tom Holland, chief investment officer Zavier Investment Advisors during his meeting with the analysts discusses the impact of weakening economic activity. The equity market values are predicted to decline in the coming year and the negative GDP growth rate of the previous quarters is not expected to improve. Holland wants the investors to consider adding more fixed- income securities to their portfolios and limiting their equity exposure.

Holland observes, “Because of low government yields we should consider investment- grade corporate bonds over government securities. According to the consensus forecast among economists, the central bank is expected to lower interest rates in their upcoming meeting.”

After the meeting, Zandya Coleman, a fixed-income analyst selects the following four fixed- rate investment- grade bonds issued by Bliss Paper Company for investment (Exhibit 1).

Exhibit 1: Bliss Paper Company’s Fixed-Rate Bonds


Annual Coupon


*Bond X


Straight bond

Bond Y


Callable at par without a lockout period

Bond Z


Putable at par one and two years from now

Bond S


Convertible bond: currently out of money

* Note: All bonds have a remaining maturity of three years.

Coleman finds that demand for consumer credit is relatively strong, despite other poor macroeconomic indicators. As a result, she believes that volatility in interest rates will increase. Coleman also reads a report from Thomson Crew, a reliable financial and economic information provider, forecasting that the yield curve may invert in the coming months.

Assuming the interest rates forecast is proven accurate, the bond with the smallest price increase is most likely :​

X, Y , Z or S ?

Please explain

I have an answer but don’t know whether it is true or not.

My answer is to choose bond Y
My reason:
For callable bond,for the investor, it is like a straight bond- call option, since the volatility will increase and the interest rate might be decline, thus may make the value of the call option to increase (volatility and the underlying all move to the issuer’s favor)
Call option I think can be roughly seen like this:
(For a call option, value of option increase with volatility and underlying asset
For a put option, the value of option increase with volatility while decrease with underlying asset
So a short call option has negative delta and negative Vega
While a long put option has negative delta and positive Vega

Δcall option= Delta+ Vega

we have already known:
Δcallable bond= Δstraight bond( >0)- Δcall option(>0),
so callable bond increase less than straight bond

For putable bond ,for the investor, it is like a straight bond+ put option
The value of put option I think can be roughly seen like (in this question)

Δput option=Vega- Delta

volatility increase, and underlying will increase because the interest rate decline, in this situation, the value of put option will also increase,
so the putable bond will increase more than the straight bond.

Since the question asks us the most likely: (i think it is not likely that for the call option is deep out of the money while the put option is deep in the money, vice versa,I think the most possible situation is that they all out of money, and we can suppose the two Options’ delta are the same, this suppose only are used to simplify the problem)

Also, we can use the equation like:
callable bond= straight bond-Delta1- Vega
putable bond= straight bond+ Vega- Delta2
Δcallable bond- Δputable bond= -Delta1+ Delta2- 2Vega

Δcallable bond< Δstraight bond< Δputable bond

For convertible bond, for the investor, it can be an option to convert bonds into stocks, from the question, we know that, the economic activity is weaken, which l think will make stocks lose some value, also, it is out of money, so l think maybe
Δconvertible bond ≈ Δstraight bond

So, based on these conditions and equations, l think that bondY, which is the callable bondmay with the smallest price increase.

Could someone tell me if my answer is right or not?
If l make some mistake, please point it out.
Thank you very much

Lol. Didn’t read through your whole explanation but I think you may be overthinking it.

If the yield curve is expected to invert, this implies that forward yields are expected to decline, so the issuer’s call option will be in the money, hence the callable bond value will increase at a decreasing rate (i.e. smaller price increase compared to an option-free bond and putable bond).


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I totally agree with your idea, but I still have a question:
If l use the equation like l have just mentioned: (l correct a little mistake here)
Δcallable bond= Δstraight bond-delta1-vega1
Δputable bond= Δstraight bond+vega2+(-delta2)

We know that the interest rate will decline, so it may make the callable bond in the money, so delta1 >delta2 , also, Vega is always positive,
So, Δcallable bond< Δputable bond
Can l understand like this?

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Yes, you can.

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Thanks for your help!
By the way, i have no idea if this statement is true or not:
Δconvertible bond ≈ Δstraight bond
Because i think the stock will perform poorer in some years later because of the economic activity is weaken, and the interest rate is decline which will make the value of the bond increase, so for the investor, the probablity of him to convert the bond into stocks is lower and lower, thus to my conclusion.

I will re-write as:

Δconvertible bond = Δstraight bond + Δcall option

So the change in the convertible bond price would depend on whether the call option is:

  • in the money (share price > conversion price): then likely Δconvertible bond > Δstraight bond

  • out of the money (share price < conversion price): then likely Δconvertible bond ≈ Δstraight bond

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That’s all l want to know, thank you!
It’s a pleasure to communicate with you.

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