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, âBecause 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.â

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 Companyâs Fixed-Rate Bonds**

**Bond**

**Annual Coupon**

**Type**

*Bond X

2.0%

Straight bond

Bond Y

2.0%

Callable at par without a lockout period

Bond Z

2.0%

Putable at par one and two years from now

Bond S

2.0%

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* :â

X, Y , Z or S ?

Please explain

*I have an answer but donât 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 issuerâs 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*)

*Îcall option= Delta+ Vega*

we have already known:

Îcallable bond= Îstraight bond( >0)- Îcall 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)

*Îput 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 Optionsâ 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*

*Îcallable bond- Îputable bond= -Delta1+ Delta2- 2Vega*

**Conclusion**

**Îcallable bond< Îstraight bond< Îputable 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

**Îconvertible bond â Îstraight bond**

So, based on these conditions and equations, l think that **bondY, which is the callable bond**may 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**