Using semi-annual compounding with a zero-coupon bond is totally brain dead. There is nothing semi-annual about it. What they mean in the question is some weird thing like “An investor requires a 12% return (calculated on a semi-annually compounded basis)…”. Say what?
Mcleod Isn’t continuous compounding applicable when it is compounded for ever, in other words when the period of compounding is infinitely small? Would it be applicable for a 10 year horizon, I am not too sure… So our choice should be either the semi-annual convention or the annual convention, and I believe the book mentions very clearly – if US, and they do not mention time period – use semi-annual. CP
Continuous compounding means you are splitting the 10 year maturity into a number of periods approaching infinity. As you continue to split the number of periods more and more you will get a greater discount on the bond (approaching P*e^-rt). ie splitting into 12 monthly sub-periods: 1000 / (1.01)^120 = 302.99 1000 / 1.005^240 = 302.07 1000 / 1.0025^480 = 301.65 … 1000 * e^(-.12*10) = 301.19 I do remember the book saying to assume semi-annual compounding but that is more of an approximation for a zero coupon bond. In practice, however, I’d buy that bond at 301.19 and sell it at 311 all day long if I could.
cpk123 Wrote: ------------------------------------------------------- > Mcleod > > Isn’t continuous compounding applicable when it is > compounded for ever, in other words when the > period of compounding is infinitely small? Would > it be applicable for a 10 year horizon, I am not > too sure… > > So our choice should be either the semi-annual > convention or the annual convention, and I believe > the book mentions very clearly – if US, and they > do not mention time period – use semi-annual. > > > CP It’s not about the bond - a zero-coupon bond is continuously compounded by it’s very nature. It’s the ambiguity in the “Investor needs a 12% return over 10 years”. The problem says that you are supposed to interpret that as a meaning the investor wants a semi-annually compounded return of 12%. Applying the “semi-annual” convention that you use for bonds to an investor buying zeros is odd.
To compare apples to apples, you have to use semi-annual compounding, that is the only reason.
Except the bond is a pear (or something).
I think of it this way, JDV: You look at two bonds with identical maturities, risk, etc., but one offers semi-annual coupons, and the other doesn’t. They both will return $150 in 5 years (assuming the usual reinvestment rate assumption for the coupon-paying bond), and they both cost $100 today. Which one is better? How would you compare?
The coupon bond is obviously better because if they both return $150 for $100 the coupon bond is just a zero with all bunch of coupons for free.
The $150 is total return of each bond, i.e., cash in: $100 for each bond, cash out: $150 on each bond. Assume they plow back the coupons for you till the end, if that helps.
A coupon bond that “plows” coupons back in and returns a known amount is called a zero not a coupon bond. Now the question that is interesting is if you have a coupon bond and a zero with the same ytm (and all else equal and forget about tax effects) which do you like better?
If you expect interest rates to go down, go with the zero. If interest rates are expected to go up, go with the coupons ones. Otherwise, you should be indifferent, but take the zero for convenience, if anything.
Nope.
We don’t talk about taxes over here, you know?
That would depend if you prefer reinvestment risk to price volatility risk.
Nope
If the two bonds are identical in every respect, other than one offering coupons while the other doesn’t, and aside from taxes, and ignoring interest rates prospects, you should be indifferent about the two, except for convenience, you may want to choose the zeros. Lets hear your answer.
I would take the discount bond because: 1. There is no reinvestment risk. 2. Price volatility doesn’t matter if you hold the bond until maturity. 3. The assumption that you can invest the coupon payments at the YTM is usually unrealistic.
I agree with McLeod, although I would add that reason (2) is fairly difficult to use as reasoning if you have shareholders to answer to. A fairly strong incentive to choose the coupon bond (from a PM’s perspective) is its use to manage portfolio duration. If you (as a PM) have to explain the extra sensitivity in NAV from longer duration, there inlays a value in the coupon bond. Although, I’d still be interest to hear what the JDV spin will be.
Also, the convexity will be greater for the zero coupon bond (assuming equal maturity and yield).
Yes, but we excluded interest rate changes, so assume that interest rate is constant, then which bond you prefer?