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
Callable at par without a lockout period
Putable at par one and two years from now
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 ?
I have an answer but don’t know whether it is true or not.
My answer is to choose bond Y
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